Impact Magazine Autumn 2020 by Impact Magazine from The Operational Research Society

D R I V I N G I M P R O V E M E N T W I T H O P E R AT I O N A L R E S E A R C H A N D D E C I S I O N A N A LY T I C S

AUTUMN 2020

SIMULATION HELPS NHS LANARKSHIRE

Pro Bono OR: analysis, modelling and facilitation to improve decisions and impact in the third sector

Predicting critical care resources required for the worst-case scenario

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WE HAVE HELPED OVER 100 CHARITIES

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ANALYSTS RESPOND TO COVID-19 Modelling disease transmission and aiding resource management

O.R SUPPORTS HEALTH SERVICES IN WALES © theskaman306/Shutterstock

Pro Bono OR projects provide a wide range of support: • Strategic planning/review • Data analysis and insight • Options appraisal • Decision-making • Process improvement • Impact measurement

A unique partnership delivers improvement to NHS services and patient outcomes

21-10-2020 14:02:04

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E D I TO R I A L Since the Spring issue was published, we have lived in interesting times. As I have been working from home since my retirement, in some respects the pandemic has not affected me, though many family celebrations had to be cancelled. For many, however, the last few months have been devastating. Many people have risen to the challenge that society faces, most obviously, in the UK, the National Health Service. Analysts have sought to play their part, and I’m pleased to be able to include some accounts of what they have been doing in this issue of Impact. The lead article tells us about a three-way collaboration, between NHS Lanarkshire, data scientists from the University of Strathclyde Business School and simulation modelling experts of Simul8, to create a data model to predict critical care needs at the start of the COVID-19 pandemic. Christine Currie reports what academic researchers have been doing to give analytical support in the areas of disease transmission and resource management. Our new columnist, Nicola Morrill, whom we welcome, looks at how O.R. can support decision-makers, with examples from the battle against the virus. Our other columnist, Geoff Royston, reflects on the Rules of Contagion. An article focussing on the work of an analytical group, The Health Modelling Centre Cymru, reports how it is making an impact through dialogue between modellers, clinicians and NHS managers. The group has been instrumental in the planning for the Grange University Hospital just outside Newport, a new 560 bed specialist and critical care centre which is due to open next year. A massive effort enabled the hospital to be partially opened almost a year early to provide vital extra beds through the coronavirus outbreak. I hope you enjoy reading these and the other articles, which show how O.R. and analytics have made an impact in the UK, Germany, Japan, Portugal and Slovakia. Electronic copies of all issues are available at https://issuu.com/orsimpact. For future issues of this free magazine, please subscribe at http://www.getimpactmagazine.co.uk/.

The OR Society is the trading name of the Operational Research Society, which is a registered charity and a company limited by guarantee.

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Graham Rand

OPERATIONAL RESEARCH AND DECISION ANALYTICS Operational Research (O.R.) is the discipline of applying appropriate analytical methods to help those who run organisations make better decisions. It’s a ‘real world’ discipline with a focus on improving the complex systems and processes that underpin everyone’s daily life – O.R. is an improvement science. For over 70 years, O.R. has focussed on supporting decision making in a wide range of organisations. It is a major contributor to the development of decision analytics, which has come to prominence because of the availability of big data. Work under the O.R. label continues, though some prefer names such as business analysis, decision analysis, analytics or management science. Whatever the name, O.R. analysts seek to work in partnership with managers and decision makers to achieve desirable outcomes that are informed and evidence-based. As the world has become more complex, problems tougher to solve using gut-feel alone, and computers become increasingly powerful, O.R. continues to develop new techniques to guide decision-making. The methods used are typically quantitative, tempered with problem structuring methods to resolve problems that have multiple stakeholders and conflicting objectives. Impact aims to encourage further use of O.R. by demonstrating the value of these techniques in every kind of organisation – large and small, private and public, for-profit and not-for-profit. To find out more about how decision analytics could help your organisation make more informed decisions see https://www.theorsociety.com/about-or/or-in-business/. O.R. is the home to the science + art of problem solving.

CO N T E N T S 7

PREDICTING CRITICAL CARE NEEDS DURING A PANDEMIC

4 Seen Elsewhere

Analytics making an impact

Gillian Anderson and Frances Sneddon report how simulation was used to predict critical care needs for NHS Lanarkshire

IMPROVING RESOURCE UTILISATION IN PROTOTYPE VEHICLE PRODUCTION Christian Weckenborg, Karsten Kieckhäfer, Thomas S. Spengler, Patricia Bernstein and Marko Hahn show how O.R. methods helped improve capacity scheduling at Volkswagen’s Pre-Production Centre

COMMUNITY-BASED O.R. AND THE CO-CREATION OF KNOWLEDGE IN TIMES OF CRISIS Neil Robinson shows how Community-based Operational Research helped one town after the largest earthquake ever to hit Japan

HEALTHY O.R. IN WALES Paul Harper tells us how the Health Modelling Centre Cymru is making an impact on health services and training NHS staff in O.R. methods

PACKING SHOES EFFICIENTLY Manuel V.C. Vieira and Flora Ferreira describe how the implementation of mathematical programming models offers considerable time and cost savings to a Portuguese shoe manufacturer

TACTICAL RECONSTRUCTION AND FAST O.R. AT THE MARITIME WARFARE CENTRE Stephanie Monks and Hayley Bird report on the delivery of tactical and operational advice to the front line of the Royal Navy by the Maritime Warfare Centre Operational Analysis Team

11 Operational Research in a time

of crisis Nicola Morrill demonstrates that O.R. is making an impact at this time of crisis

25 A Lay Person’s Guide to the

Analytical Responses to Covid-19 Christine Currie reports how analytics researchers are supporting decisions in the battle against the virus

39 Universities making an impact

Brief report of two postgraduate student projects

47 OutbReak

Geoff Royston considers the Rules of Contagion, concluding that a deeper understanding of them should be of wide benefit

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Reusing Articles in this Magazine

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SEEN ELSEWHERE MEASURING SOCIAL DISTANCE

The need for social distancing, (or should it be unsocial distancing?), is something that most, but not all, of the population have taken on board since March. But is it effective? How to assess how far the requirements are being followed? Researchers at Newcastle University’s Urban Observatory developed a dashboard to help understand the impact of social distancing measures on people and vehicle movement within a metropolitan city in real time. Their analysis of over 1.8 billion individual pieces of observational data, as well as other data sources, with deep learning algorithms, informs and updates the dashboard in real time. They have produced models which can measure the distance between pedestrians in public places. Using a traffic light indicator system, the algorithm anonymously identifies and labels people who maintain safe distances, while flagging certain instances in red where social distancing measures are violated. This enables bottlenecks where social distancing cannot be maintained to be identified. For further details see http://bit.ly/MeasuringSocialDistance.

SHOULD THE MIDDLE SEAT STAY EMPTY?

In July Arnold Barnett, professor of management science and statistics at MIT and world-renowned expert on aviation safety, calculated that the risk of contracting COVID-19 from a nearby passenger is about 1 in 4300. Under the ‘middle seat empty’ policy,

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that risk falls to about 1 in 7700. Middle-seat passengers are at higher risk than others, though not that much higher, according to Barnett’s calculations. He notes that ‘when the plane is full, risk is also higher for passengers in the window and aisle seats’. The risk of actually dying from COVID-19 as a direct resulting of flying is ‘probably less than one in 500,000’, Barnett estimates, which, while small, is considerably higher than the probability of dying as a result of a commercial plane crash. See https://bit. ly/middleseatrisk.

on the short term (4-6 weeks), and against forecast scenarios looking several months ahead. The WSP team have been embedded in the local modelling team working closely with local analysts and planners from the Clinical Commissioning Group and the Local Authority. The model outputs are also informing local NHS ‘restart’ programmes for hospital and community services. The importance of modelling at a local system level has been demonstrated in this work. Local demographics, the timing of the first wave and the nature of local services have all been shown to have an impact on local planning decisions. For further information please contact peter.lacey@ thewholesystem.co.uk.

WORST CASE WINTER SCENARIOS

The Whole Systems Partnership (WSP) have been working with a number of local health and care systems using a COVID-19 simulation model developed using System Dynamics. The core SEIR (Susceptible, Exposed, Infectious, Recovered) model is complemented by estimates of impact on key services across hospital and community settings. The model is currently being calibrated to each local hospital system making it possible to explore the potential ‘reasonable worst case’ scenario over the winter. In the host system WSP have worked since early April to refine the model assumptions using local actuals. This has given local planners greater confidence in planning services against nowcasting outputs, focussing

COVID-19 STRESSES SUPPLY CHAINS

Anna Nagurney’s book, ‘Networks Against Time: Supply Chain Analytics for Perishable Products’, co-authored with M. Yu, A.H. Masoumi, and L.S. Nagurney, and published by Springer in 2013, analyses the impacts of a variety of supply chain disruptions. In March, the day after the World Health Organization declared the COVID-19 pandemic, her article, ‘How coronavirus is upsetting the blood supply chain’, was published in The Conversation (see http://bit.ly/Nagurney). It was subsequently updated and published as ‘The COVID-19 pandemic and the stressed supply chain’, in Coronavirus Chronicles in Analytics magazine (see http://bit.ly/Nagurney2).

Supply chains have been especially stressed during the COVID-19 pandemic. The USA blood supply chain is stressed for numerous reasons, including fewer collection sites for donations due to closures of universities, and fear of coronavirus striking donors and those who labour in blood services. Food supply chains have also been negatively impacted by the pandemic, from meat and dairy to fresh produce supply chains. Many meat processing plants have had workers contract COVID-19, resulting in closures, subsequent sanitisation of facilities and redesign for physical/ social distancing. Some dairy farmers have resorted to throwing out milk, and potato farmers their potatoes, because the supply chains are broken. Even freight service providers and warehouse employees have taken ill, further disrupting the supply chain networks. The cost is great to farmers and society as prices rise and children go hungry with increasing food insecurity. Many in the O.R./analytics community are making intense efforts to combat stresses in supply chains.

GOING UP?

In another article in The Conversation, published mid-August, Christian Yates, Senior Lecturer in Mathematical

Biology, University of Bath, asked whether the Coronavirus cases in the UK are rising (see http:// bit.ly/ChristianYates). He argued that, with the reopening of schools in the UK rapidly approaching, it was critical to know if cases of coronavirus were going up, because further loosening restrictions could significantly exacerbate the problem. His conclusion? Are cases rising? Well, maybe. But maybe not. Local hotspots, there was concern about areas in the North-West of England at the time, invite more intensive testing. If those tests pick up a higher proportion of people who test positive, then this could also lead to a rise in the proportion of positive tests across the country without the disease necessarily increasing everywhere. By the time this is read, we will know whether an increase in cases led to several local lockdowns, or even the reimposition of a national one.

The programme is led by Professor Christopher Edwards, Education Theme Lead at Lancaster University’s Data Science Institute, and Dr Deborah Costain, Associate Dean for Postgraduate Studies at Lancaster University’s Faculty of Science and Technology. Professor Edwards said: ‘Our aim is to promote excellence and innovation in the training of current and future health data scientists at all career stages in both public and private sectors. This work will build on the success of our existing masters offering, underpinned by the interdisciplinary approach to data-driven research and education provided by the Data Science Institute’.

ROLLS-ROYCE RESPONDS DELIVERING HEALTHFOCUSED DATA SCIENTISTS

As part of an Institute of Coding consortium, led by Coventry University, Lancaster University is launching a new programme to produce data scientists equipped to provide insights that will improve health outcomes. The 12-month conversion course will give graduates from a range of different academic areas expertise and insights into health-related data science working towards an MSc qualification. The primary goal is to respond to the shortage of data science and AI specialists in the UK. The first cohort will be recruited onto the existing Data Science MSc programme in October 2020. The second and third cohorts will be recruited onto a new Health Data Science programme.

Rolls-Royce’s R2 Data Labs lead a data analytics alliance to aid COVID-19 economic recovery. In April, RollsRoyce said its R2 Data Labs had ‘assembled an alliance of leading companies across commerce, banking, travel, technology and research to use data analytics to find new and practical ways to support the global response to the virus’. Caroline Gorski, director of R2 Data Labs, said the aim is to ‘bring together datasets from all across industry that have not usually been accessible to the public domain’. ‘We believe that if we can contribute datasets that wouldn't otherwise be released outside a company or industry’s domain, then we can open up the realm of possibility’, she added. One goal is to look at a broad set of economic, behavioural and

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sentiment data in the hope of offering insights and practical applications to the global COVID-19 response. A second objective is to find and nurture economic green shoots in the wake of the devastation virus lockdowns are causing to businesses worldwide. Gorski asked: ‘Can we use [data] models to identify lead indicators signalling economic recovery cycles that global businesses can use to build operating confidence in investment and activities that shorten or limit recessionary impacts?’ See http://bit.ly/RRResponse for more details.

COVID-19 MATHS

Richard C. Larson, Mitsui Professor, Post-Tenure, in MIT’s Institute for Data, Systems and Society, published an article, http://bit.ly/TheRvalue, which sought to shed light on two mathematical quantities that have governed our lives in the battle against COVID-19. These are R0 (‘R naught’), the basic reproductive number, and H, herd immunity. We all need to know about them and – most importantly – about our roles in determining their values. As we have been frequently told, R0 needs to be below 1, otherwise the number of infections will grow at an alarming rate. In the article, Larson demonstrates that herd immunity, a political hot potato in the UK at the start of the pandemic, is dependent on R0, so there is only one statistic we need to keep an eye on. Larson argues that the key is this: Past values of R0 are provided by historical data – depicting human behaviour and disease characteristics; future values of

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R0 are determined by you (and me and all of us).

DIY SIMULATION

Simul8 provided a free simulation model to help hospitals assess how many ICU beds and surge capacity will be needed to meet demand as case numbers rise. This simulation can tell how many ICU beds will be utilised as well as how many temporary surge beds will be needed to meet demand. There’s also a facility to change the mortality rates in both these areas so the impact of having the appropriate type of beds on survival rates can be estimated. The simulation is populated with placeholder data but it’s simple to update the parameters with any dataset. See http://bit.ly/ Simul8simulator.

ISEE Systems have made available a simulator that looks at the spread of COVID-19 through a city. The simulator allows you to implement policies, change assumptions about disease and see the impacts in real time. See http://bit.ly/ iseesimulator.

PROMISE THE MOON?

An article in the Huffington Post, http:// bit.ly/HuffPostMoonshot, Operation Moonshot: Four Astronomical Hurdles The Government Must Overcome, responded to the UK Government’s plans for a mass Covid-19 testing programme, with results available within minutes, to allow people to behave in a more normal way without ear of making others ill. One of the hurdles discussed is the potential for false positives. According to Professor Sir David Spiegelhalter, Winton Professor of the Public Understanding of Risk in the Statistical Laboratory at the University of Cambridge, there is a “huge danger” with the project, because of the potential for a “very large number of false positives” that could leave thousands of people self-isolating unnecessarily. He told BBC Radio 4’s Today programme that experts in his field were “banging their heads on the wall” at the proposal. “Mass screening always seems like a good idea in any disease – ‘Oh yes, let’s test everybody’. But the huge danger is false positives – no tests are perfect, it is not a simple yes/no thing.” He said the threshold would have to be set to a level that would “pick up anything that hints at being infectious”, meaning that the tests would “always generate a very large number of false positives”. “If you only have 1% false positives and you’re testing the whole country, that’s 600,000.” The other three hurdles? The technology doesn’t actually exist, the manufacture and distribution of the tests, and the support network required.

PREDICTING CRITICAL CARE NEEDS DURING A PA N D E M I C © Cryptographer/Shutterstock

GILLIAN ANDERSON AND FRANCES SNEDDON

NHS LANARKSHIRE IS THE THIRD LARGEST HEALTH BOARD IN SCOTLAND, serving a population of 655,000 across rural and urban communities in Lanarkshire. Its 12,000-strong team of staff work in communities, health centres, clinics and offices in the

region and at three district general hospitals. When COVID-19 emerged, it posed huge questions for healthcare organisations globally. How much capacity would be needed to care for those who became infected? Would there be enough ventilators and

G. ANDERSON AND F. SNEDDON

other equipment to care for patients appropriately? And so much more. At NHS Lanarkshire, advice from both UK and Scottish governments had suggested that the major NHS Trusts (in England and Wales) and Health Boards (in Scotland) prepare for the worst-case scenario of a fivefold increase in demand for critical care in the Spring 2020 peak of the COVID-19 pandemic. This left NHS Lanarkshire with the challenge of trying to predict, at very short notice, the critical care resources they would actually require over the coming weeks and months.

SIMULATION TO PREDICT CRITICAL CARE NEEDS

Time was of the essence for decisionmaking and preparations required for the potential demand surges. Working in close collaboration with NHS Lanarkshire, the University of Strathclyde Business School health systems experts used Simul8 modelling software to predict critical care needs at the start of the COVID-19 pandemic. NHS Lanarkshire was able to reshape centrally produced forecasts and make informed and accurate decisions based on local circumstances. This was done by creating a digital simulation that accurately replicated the expected flow of COVID-19 patients through the critical care department, using sophisticated modelling software from Simul8. Contrary to earlier government advice, the model highlighted that the Health Board had already made sufficient additions to its capacity to be able to manage the projected surge in critical care needs brought on by the pandemic. This meant the costly adaptations to resourcing needs that

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would have otherwise been wasteful were avoided, as well as providing front line staff and capacity planners with peace of mind.

that we were able to give them the answer within two weeks, and roughly seven to ten days before the COVID-19 peak started, was vital in helping them manage this pandemic

Dr Nicola Irvine, consultant physician, doctoral researcher and one of the team leads in this successful collaboration: ‘Once the executive team at Lanarkshire had set their key question – which was what will be your critical care need and do we currently have the resource and the capability to meet that? – the fact that we were able to give them the answer within two weeks, and roughly seven to ten days before the COVID-19 peak started, was vital in helping them manage this pandemic’.

CREATING THE SIMULATION

Simul8 digital simulation software was used to create the model for this advanced new planning approach. ‘As its name suggests’, said Chandrava Sinha from the Department of Management Science at the University of Strathclyde, who worked with Nicola Irvine and Gillian Anderson in building the simulation model, ‘digital models are approximate representations of any real-life system. They are basically mathematical or statistical models created using a computer which tries to best mimic and present a real life scenario or a

proposed scenario, and to then answer various “what if ” questions to help decision-makers make a very well informed decision’. A crucial element of the modelling process for NHS Lanarkshire was the use of data that the team were able to build into the simulation. To cut through any conflicting evidence and to make the model as accurate to local needs as possible the team drew on a range of data sets. This included very localised community data, such as population profiling, as well as national trends that were being received from central government. It also included wider international data from countries such as Italy and Spain where the pandemic wave was a few weeks ahead. This approach allowed the team to create a model that was as accurate as possible to local needs. Chandrava added: ‘This data all fed into the model and then gave us the maximum utilisation of beds across all different categories on a week-by-week basis for the whole first wave of the pandemic’.

COLLABORATING FOR SUCCESS

Dr Irvine emphasises the need for a ‘triumvirate of executive expertise, clinical expertise and modelling expertise’ in building and implementing a successful model such as this one. The clinician understands the behaviours of the organisation at floor level; the modeller is able to interpret that nuanced dynamic environment and to simplify and abstract data into a model that can be usefully predictive; and an executive team will have the overview needed to ask the

the turnaround time for testing the number of people who were presenting with suspected COVID – two days – was causing bottlenecks in the emergency department

Dr Irvine: ‘Simul8 modelling meant that we could say “here is the likely impact from COVID-19, but your other inpatient resources are predicted to be impacted too and you need to have a plan in place for this”’.

WIDER ADOPTION OF SIMULATION

most pertinent questions, and then the authority to act on the predictions of the model.

the European Centre for Disease Control’.

We were able to constantly update our simulation using data from the local hospitals and authorities, as well as from wider resources such as the intensive care audit and information from the European Centre for Disease Control

IDENTIFYING THE WIDER IMPACT

‘Validation is also a key part of any modelling process’, says Dr Irvine. ‘You want to make sure that you’ve captured the process that you are modelling, the environment, the disease, the activity etc. Crucial to this was the daily information that we were receiving from the hospital’s management team. We were able to constantly update our simulation using data from the local hospitals and authorities, as well as from wider resources such as the intensive care audit and information from

In modelling for COVID-related planning, the research team realised that it was not just critical care that would be affected by the pandemic, but other areas of healthcare services would see knock-on effects too. ‘We were aware that other patients with emergency medical problems were presenting in smaller volumes’, said Dr Irvine, ‘but the turnaround time for testing the number of people who were presenting with suspected COVID – two days – was causing bottlenecks in the emergency department. This had potential to disrupt emergency care and other areas of urgent care, such in acute medical units’. Further insights were also generated via the model in predicting that even while cases in the community were reducing, there were also some potential issues about infection being transmitted within the hospital that would need mitigating as well.

The University of Strathclyde research team is led by Professor Robert Van Der Meer and includes Dr Nicola Irvine, Gillian Anderson, Chandrava Sinha and Holly McCabe as healthcare modelling specialists. The success of the Simul8 model in assisting NHS Lanarkshire at the beginning of the pandemic means that Holly and Gillian are now developing the model to support the development of an Early Warning System for the next stage in the COVID-19 pandemic. Professor Van Der Meer said: ‘The Strathclyde model really demonstrates the value of simulation for critical decision-making. The approach provides evidence for those factors that are unknown and does so by generating an extremely localised picture of the situation. It is from here that you can make confident decisions where the risk has been mitigated significantly’. ‘We are grateful for the fantastic working relationship that our team has developed with NHS Lanarkshire, which really has been pivotal in the success of this initial project. Together

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we are now looking ahead at further applications of our simulation tool to support the Health Board. This includes the next possible peak and how to manage resources under the added pressures during the winter months’.

to deliver the trial in a virtual environment and get a very clear picture of the outcomes without the associated risk or costs makes it a lot easier to achieve buy-in, and this makes digital simulation truly invaluable

As for wider applications, Dr Irvine is now a strong advocate for the use of

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digital simulation not just in critical care but throughout health services. ‘To be honest, I struggle to think of any applications in healthcare where simulation modelling wouldn’t be useful’, she said.As a clinician, these models allow you to create a virtual, experimental laboratory where you can see the patient, staffing and efficiency outcomes when testing different systems. To deliver this as a real-life trial would be cumbersome and it would take a long time, which would receive a lot of opposition. To instead be able to deliver the trial in a virtual environment and get a very clear picture of the outcomes without the associated risk or costs makes it a lot easier to achieve buy-in, and this makes digital simulation truly invaluable.

Gillian Anderson is a Research Associate at Strathclyde University who has been supporting health related modelling with the Scottish Government Modernising Patient Pathways Programme since 2014. She has led several projects and was responsible for driving the use of DES in the NHS in Scotland as part of a Whole Systems Patient Flow approach to care. Frances Sneddon is the CTO of Simul8 Corporation. With over 20 years ORMS experience, her mission is to create simulation software that is so intuitive, fast and effective that anyone can use it to make critical decisions and deliver serious impact across their organisation. Born and raised in North Lanarkshire, Frances took particular interest in this project and was delighted Simul8 could help her local area.

OPERATIONAL RESEARCH IN A TIME OF CRISIS Nicola Morrill

TO WRITE ABOUT THE IMPACT that Operational Research (O.R.) can have, does have and could have…… where to start? Perhaps at the beginning. O.R. as a term was originally used in Britain during World War II to refer to scientific research done to integrate new radar technologies into Royal Air Force tactics. The term expanded to include the provision of support to military officers in developing and planning combat operations. It is a discipline that has grown out of providing support in times of crisis and is well versed in supporting emergency response. It also has a key role to play in supporting medium- and long-term planning.

SO, WHAT EXACTLY IS O.R.?

The million-dollar question! Formally, it is defined as a scientific approach to the solution of problems in the management of complex systems, which enables decisionmakers to make better decisions. It is about real-world applications, supporting improved decision-making. A lifelong learning discipline, if that is possible. The O.R. toolset and its links with other disciplines have evolved over time and continue to do so. This is primarily in response to the changing nature of challenges; more complex, dynamic and interconnected. The current COVID-19 situation and climate change are prime examples of this. So, what is O.R. again? The definition has proved difficult to pin down. I like to focus on what it can achieve, how it can help, rather than the specific tools it uses. A mix of science and art used to help ‘clients’ see the wood from the trees. If you have a knotty issue, chances are O.R. can help you in some way.

QUESTIONS O.R. CAN HELP ANSWER, ILLUSTRATED THROUGH ITS SUPPORT TO COVID-19 CHALLENGES

To give you a flavour of the nature of some of the questions O.R. can help with, it feels apt, given the origins of O.R. and the current global situation, to share some examples of how O.R. is helping with challenges presented by COVID-19. This is by no means exhaustive and was identified via an Internet search. Here are some of the areas, in the open domain, where O.R. has and is providing support: • What is the best way to reorganise dialysis companies and reduce disruption to 650 sufferers receiving treatment at The Wessex Kidney Centre? (see https://bit. ly/DialysisServices) • How many ICU beds and surge capacity will be needed to meet demand as case numbers rise? (see https://bit. ly/ICUSimul8) • What areas of the UK are most vulnerable to the effects of COVID-19? (see https://bit.ly/vulnerabilityindex) • What potential resourcing requirements may be needed to meet incoming demand and continue to provide high-quality end-of-life care? (see https://bit.ly/endoflifecaremodelling) • What is the demand for an independent food bank likely to be? How do we best meet that demand? (see https://bit.ly/Foodbanksbays) • How can the local authority maximise the involvement of their new volunteer workforce? (see https://bit. ly/Covidvolunteers) • What is the impact on patient experience of a combination of specific nursing innovations? (‘COVID-NURSE’) (see https://bit.ly/Covidnursingcare) • What might the mental health effects of COVID-19 be? (see https://bit.ly/ORSupportingNHS) • Should Yale limit the number of people gathering for events and, if so, what would constitute a safe size? (see https://bit.ly/EDKaplan) • What are the public behaviours and attitudes related to COVID-19? (see https://www.scrubcovid19.org/) • What is my supply chain exposure? What shortages should I anticipate? What are my resource requirements? (see https://bit.ly/AMMSSupplyChain) This is just a snapshot of the support being provided by O.R. experts covering operational to strategic; across business, government, charity, international development; and immediate and near term in outlook.

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WHO USES O.R.?

Admittedly I am slightly biased here, but all organisations, no matter their size, will have a question that O.R. can help with. If you’re not using it, you should be! So, what challenge do you have that O.R. could help with? If you are a decision-maker within an organisation, what questions about your medium and long term might you need support with? Do you need help defining the question you need help with? WANT TO LEARN MORE?

O.R. also has a role to play with strategic decisionmaking and, in particular, exploring and de-risking the longer-term future. Over time, when it is appropriate to do so, there will be much more, I am sure, that O.R. will be able to say about how it contributed to the current situation and a richer set of questions O.R. helped with will emerge. There are special issues of the Journal of the Operational Research Society and the European Journal of Operational Research aimed at doing just this.

WHO DOES O.R.?

I believe what binds those engaged in doing O.R. is a collective enjoyment of ‘solving’ puzzles, tricks and messes. Noting that not all challenges can actually be solved! Coupled with the positive impact that O.R. can make; the practical, real-world help. We are found in large companies, Small-Medium Enterprises, one-person companies, universities, central government, local government, charities. Slightly unhelpfully, often not with the title ‘O.R.’! Typically, we have a quantitative background, though some ‘specialise’ into more qualitative areas of O.R., such as problem structuring.

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Nicola Morrill is a Systems Thinking Consultant at Dstl, a certified coach and the current Diversity Champion of the O.R. Society. She writes in a private capacity - all views expressed are her own and all examples are available in the open domain. You can contact her on Nicola.impact@gmail.com.

MAP OF UK TO SHOW POSTULATED VULNERABILITY AREAS (https://github.com/britishredcrosssociety/covid19-vulnerability)

This is the first ‘column’ from me in Impact. My background is O.R. and while undertaking general management roles I was struck by how this really helped me. I am keen to broaden awareness of the use of O.R. within such roles – it is such a powerful discipline – and I’d like to use this ‘column’ to do just that. If you have a particular challenge and you wonder how O.R. has or could help let me know. If you are an academic or practitioner and think there is a bit of O.R. that would benefit from having a light shone on it, let me know. I’ll use your thoughts for inspiration for the next ‘column’. In the meantime, I’ll leave you with a quote I like from Russ Ackoff: ‘Managers are not confronted with problems that are independent of each other, but with dynamic situations that consist of complex systems of changing problems that interact with each other. I call such situations messes. Problems are extracted from messes by analysis. Managers do not solve problems, they manage messes’. Thanks for reading and see you in the next issue!

I M P R OV I N G R E S O U R C E U T I L I S AT I O N I N P R OTOT Y P E V E H I C L E PRODUCTION CHRISTIAN WECKENBORG, KARSTEN KIECKHÄFER, THOMAS S. SPENGLER, PATRICIA BERNSTEIN AND MARKO HAHN

IN THE AUTOMOTIVE INDUSTRY, prototype vehicle production is an essential step within the product development process. Before production ramp-up and launch of any new car model, many prototype vehicles are required, mostly for testing but also for internal and external presentations. For the Volkswagen brand (VW), approximately 3000 of those prototype vehicles are manufactured annually by 1200 employees of the Volkswagen Pre-Production

Center (VPC). Due to shortages in manufacturing capacity, a large portion of production orders of VW prototype vehicles is outsourced to external manufacturing service providers every year. The shortages are mainly driven by an increasing product variety along with more extensive tests of functionality and an increase in electric vehicle components. Since outsourcing of orders is very costly, increasing the internal manufacturing volume is a reasonable

In close cooperation between academia and industry, we evaluated Operational Research solutions for the Volkswagen Pre-Production Center’s capacity scheduling problem In close cooperation between academia and industry, we evaluated Operational Research solutions for the VPC’s capacity scheduling problem, which had previously been solved manually. Firstly, we developed and implemented a prototype for capacity scheduling based on binary integer programming. The prototype revealed a substantial potential to increase manufacturing volume by generating optimised plans. For that reason, we subsequently developed a spreadsheet-based decision support system for everyday planning. The tool was validated in a pilot test, revealing the cost savings of improved utilisation of internal resources to lie in the six-digit euro range per annum. In the following, we detail the characteristics of the capacity scheduling problem at the VPC and specify the critical factors to the success of our collaboration. The organisational structure of the VPC’s manufacturing department is subdivided into organisational units (OUs). One master craftsperson

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leads each OU, and the associated personnel are responsible for the timely completion of the orders centrally assigned to the OU. The centralised function of capacity scheduling decides on the executing OU and the assembly period of each order. Decisions on internal and external manufacturing and scheduling have to follow the aim of maximising the internal manufacturing volume to reduce the costs spent on external manufacturing of orders. Within the planning period, compliance with the internal and external capacity restrictions has to be ensured for each OU. Two capacity constraints restrict the production volume. First, sufficient capacity of power-driven hoisting platforms is required. These are stationary devices to lift vehicles by their frames, and each prototype vehicle requires one hoisting platform throughout its assembly.

Second, each OU has a prespecified number of skilled workers, providing a predetermined personnel capacity which must not be exceeded. The planning process is further restricted by release and due dates of each order, the availability of parts and components, and the clarification of the vehicles’ technical specification. Approximately 500 orders have to be allocated among 30 OUs within a planning period of 60 days. Therefore, the VPC faces a tremendous number of possible order allocations in their capacity scheduling and requires decision support on this problem. A general illustration of the planning problem is given in Figure 1. As a first step, we developed a binary integer programming (BIP) model to compare the results of the current (manual) planning procedure with the results from mathematical programming. The BIP maximises the internal manufacturing volume. © Informs. Figure Reprinted with Permission

option to cut manufacturing costs substantially. Therefore, the planning task of capacity scheduling – the allocation of vehicle orders to manufacturing capacity – can be considered an important lever to improve resource utilisation, given the limited internal manufacturing capacity.

FIGURE 1 THE PLANNING PROBLEM OF THE VOLKSWAGEN PRE-PRODUCTION CENTRE.

Constraints are introduced to ensure that each order is assigned to one OU and during a feasible assembly period. Moreover, it is guaranteed that the capacity of personnel and hoisting platforms is not exceeded in any OU and period. Orders already started are not allowed to be reallocated. We assume each period to comprise one day in a real-world setting.

We compared the plans obtained by the BIP with the manually generated plans. On average, we found the total manufacturing volume to increase by 38.7% using our plans rather than the manually generated ones We compared the plans obtained by the BIP with the manually generated plans. On average, we found the total manufacturing volume to increase by 38.7% using our plans rather than the manually generated ones. This is mainly due to better utilisation of the personnel capacity with an increase of about 36%. The average hoisting platform utilisation, though, remained on its former level. In the majority of cases, the hoisting platforms are operated at their capacity limits. Regarding the orders’ characteristics, on average, more orders (+10%) with a longer duration of the assembly activity (+12%) as well as more hours of assembly per order (+32%) are selected by the BIP for internal assembly compared with the manual planning. Therefore, we came up with the idea of introducing a general planning rule to decide on the allocation and schedule of orders. Choosing orders

with an unusually long duration yields no consistently beneficial solution – the rule aims at utilising hoisting platforms over time but neglects the personnel capacity. Choosing orders with many hours of assembly per order aims to utilise the personnel – this rule neglects the hoisting platform capacity over time. Therefore, we considered the tradeoff between the two resource types as essential and suggested selecting those orders that have a high ratio of hours of assembly to its duration. Utilising this planning rule, orders generating as much manufacturing volume (hours) as possible per unit of hoisting platform capacity and time unit should be chosen. Using the BIP, we were able to generate sound insights into the potential of increasing the manufacturing volume. The implementation, however, raised some drawbacks, particularly since additional commercial software was required and it did not comprise a comfortable user interface. The VPC maintains preference toward spreadsheetbased solutions because planners are familiar with their functionality, and the spreadsheet software package is available in the corporation. To exploit some of the potentials we decided to develop a tool for everyday planning and implemented a decision support system (DSS) in Microsoft Excel and utilised Visual Basic for the algorithm.

To exploit some of the potentials we decided to develop a tool for everyday planning and implemented a decision support system We faced two major challenges: determining the structure and interface of the spreadsheet model

and developing a suitable planning algorithm. First, we introduced the main sheet comprising all relevant information on orders, mainly information imported from a data warehouse (Figure 2). Input data are automatically read and illustrated in white-shaded cells. This information, extracted from Enterprise Resource Planning (ERP), serves as parameters for the capacity scheduling problem. All planning functionality is based on Visual Basic and called using the blue buttons at the top of the spreadsheet. Data illustrated are generated arbitrarily for confidentiality reasons. The sheet additionally serves to control the automated functions such as data synchronisation and launch of the planning algorithm. We paid particular attention to developing a user-friendly interface that allows for hands-on interaction and improves the system’s acceptance among the users. We opted to use colours to indicate different events in the planning tool consistently throughout the DSS. For example, we indicate whether data can be manipulated manually, such as planning results given in blue-shaded cells, or may not be manipulated manually, such as external information shown in white-shaded cells. Furthermore, we highlight updated information visually after the data synchronisation using orange-shaded cells. Additionally, a feasibility check of data from the data warehouse is implemented to indicate inconsistent data sets using red-shaded cells. Differences between the ERP data and the results of the planning algorithm are highlighted in yellowshaded cells. The resulting quality of the plan generated by the algorithm is reported visually, subdivided by OU. Here, personnel and hoisting platform utilisation is of particular importance.

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The utilisation of personnel and hoisting platforms is reported using utilisation diagrams individually for the different organisational units in the DSS (Figure 3). Colours are used to differentiate between the resource types. Available and utilised hoisting platform capacity is illustrated on the right-side scale in orange. Personnel utilisation is illustrated on the leftside scale differentiated by completed orders (grey), started orders (green), and planned orders (blue). Diagrams are generated using Visual Basic functionality. Data illustrated are generated arbitrarily for confidentiality reasons. Regarding the planning algorithm, we decided to follow a heuristic approach that integrates three components: initialisation, constructive method, and improvement method. While during initialisation ERP data on the manufacturing orders is fed into the DSS, the constructive method

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ensures that orders are assigned to the OUs and assembly periods according to the planning rule derived from the BIP results. The generated plans may, however, violate capacity restrictions. Overcoming these violations by outsourcing orders is the aim of the improvement method. The performance of the DSS in comparison with the manual planning approach and the BIP in terms of internal manufacturing volume as well as the utilisation of available capacity (personnel and hoisting platforms) is reported in Figure 4 in terms of obtained mean values for internal manufacturing volume, personnel utilisation, and hoisting platform utilisation. Levels are scaled arbitrarily for confidentiality reasons. On average, the algorithm increases the internal manufacturing volume and personnel utilisation by around 25% when compared with manual planning results, whereas the hoisting

platform utilisation remained almost the same. For the DSS, we had to introduce additional constraints from the real-world problem which are unconsidered in the BIP. Therefore, the BIP results overestimate the real potential. During a two-month pilot test, we held regular meetings to validate the generated schedules and give tutorials on how to use the DSS. As most of the logic of the DSS is implemented in Visual Basic and works invisibly in the background, we invested much time in explaining the theory behind the model, the underlying assumptions, and the implemented planning rules. This helped to build trust in the tool for the members of the VPC. At the end of the pilot test, our tool was implemented for capacity scheduling in everyday planning. As expected, the generated plans exhibited excellent quality and significantly increased the utilisation of personnel and the

FIGURE 3 UTILISATION DIAGRAMS REPORTING THE UTILISATION OF PERSONNEL AND HOISTING PLATFORMS. USED WITH PERMISSION FROM MICROSOFT.

FIGURE 4 COMPARISON OF THE RESULTS OF OUR DSS WITH MANUAL PLANNING AND THE RESULTS OF OUR PROTOTYPE BASED ON BIP.

internal manufacturing volume. The VPC estimated the cost savings to lie in the six-digit euro range per annum, attributed to the reduced amount of outsourcing activities. A further substantial benefit resulted from a decreased internal planning

effort, which gives the VPC more time to concentrate on the continuous improvement of their planning processes. This resulted in considerably improved data management and data transparency, making the application of the DSS even more valuable. Since

we based the planning on ERP data, higher data transparency and improved data control mechanisms were established. Using the tool, planners perceive what their data are used for and how bad data negatively influence the planning quality.

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Using the tool, planners perceive what their data are used for and how bad data negatively influence the planning quality

well known from software development projects. Intensive communication was supported among all team members about the project status, the need for modifications, and the next steps.

Several critical factors made our collaboration successful. Firstly, the relationship between academic and industrial partners is of mutual trust, which was built during a series of workshops before the actual collaboration. Secondly, we gained the valuable support of the management of the VPC, facilitating a successful composition of the project team and the deployment of effective project management. The fruitful cooperation between the planning department, the IT department, and academia were of utmost importance for the project’s success. It would not have been possible without the full support of the management. Further, we decided to utilise an agile procedure following the Scrum framework

Christian Weckenborg leads the research field on Digitization at the Institute of Automotive Management and Industrial Production at Technische Universität Braunschweig, Germany.

Patricia Bernstein is the former Head of the manufacturing department of the PreProduction Center of Volkswagen in Wolfsburg, Germany.

Karsten Kieckhäfer is Professor of Production and Logistics Management at FernUniversität in Hagen, Germany.

Marko Hahn took her place and is currently the Head of the manufacturing department.

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Thomas S. Spengler is Professor of Production and Logistics Management and Head of the Institute of Automotive Management and Industrial Production at Technische Universität Braunschweig, Germany.

FOR FURTHER READING Weckenborg, C., K. Kieckhäfer, T.S. Spengler and P. Bernstein (2020). The Volkswagen Pre-Production Center Applies Operations Research to Optimize Capacity Scheduling. INFORMS Journal on Applied Analytics 50: 119–136.

CO M M U N I T Y- B A S E D O. R . A N D T H E CO - C R E AT I O N O F K N OW L E D G E I N T I M E S OF CRISIS NEIL ROBINSON

IMPACT © THE OR SOCIETY

COMMUNITY-BASED OPERATIONAL RESEARCH may be one of Operational Research’s least appreciated sub-disciplines. Today, with the world reeling from the COVID-19 pandemic, it might become one of the most important. Could the spectacular bottom-up revitalisation of a disaster-hit Japanese town offer lessons for the way ahead?

The largest earthquake ever to hit Japan struck on a March afternoon nine years ago. Its epicentre was 43 miles off the Tōhuku region’s Oshika Peninsula, and its hypocentre – its sub-surface point of origin – was at an underwater depth of approximately 18 miles. With a magnitude of 9.0, it qualified as a “great” quake – that is, one capable of inflicting total destruction.

So powerful that it shifted the entire island of Honshu 8ft to the east, the shock triggered a tsunami whose waves topped a dozen storeys in height. They travelled towards shore at up to 400mph before sweeping over the Japanese mainland, killing in excess of 15,000 people and leaving hundreds of thousands homeless. Among the worst-affected areas was Minamisanriku, a small coastal town in the Miyagi prefecture. More than 800 residents died or were lost, and around 3,000 buildings were destroyed. The devastation encompassed roads, schools, hospitals and other infrastructure. The beach, for so long the heart of a 17,000-strong community heavily reliant on its fishing industry, was buried beneath a giant slew of debris. Confronted with the prospect of post-disaster recovery on a massive scale, the Japanese government set aside US$263 billion for intensive reconstruction and revitalisation across 20 prefectures. Yet, redevelopment efforts quickly proved uneven, with some projects inevitably taking precedence over others. Minamisanriku was not high on the list of priorities. Incidents such as the meltdown at the nearby Fukushima nuclear plant dominated the political and economic agendas, rendering official action sluggish and fragmented. In tandem, the town increasingly feared the advent of “dark tourism” – a phenomenon rooted in visitors’ fascination with the lingering effects of death and desolation. As the crisis dragged on, locals decided to take matters into their own hands. The remarkable story that followed would redefine long-held conceptions of bottom-up regeneration. It would

show how “active leadership” can turn tragedy and despair into renewal and hope. It would demonstrate the significance of networks, cultural practices and collective interventions in shaping project management. It would even give rise to what is now being hailed as a revolutionary and resolutely positive form of tourism – one rooted in resilience, sustainability, place-based practices and natural beauty. And it would shed fresh light on one of O.R.’s less appreciated sub-disciplines.

CBOR should entail “meaningful community engagement” COMMUNITY-BASED O.R.: PUTTING THEORY INTO PRACTICE

Community-based O.R. – also known as CBOR or simply community O.R. – is thought to have its origins in the USA, where O.R. practitioners began working with communities in the late 1960s. There were similar collaborations in the UK by the mid-1970s, and the designation “community O.R.” was coined around a decade later as the OR Society sought to apply its members’ expertise to “real-life” problems beyond the public and private sectors. Although a formal definition remains elusive, several recent additions to the literature have argued that CBOR should entail “meaningful community engagement”. This, it has been suggested, ensures that communities themselves have a substantial say in framing issues and actions alike. Of particular interest in the case of Minamisanriku is CBOR’s role in

disaster management. Historically, much of the focus in this field has been on mitigation, preparedness and response – the first three stages of the disaster operations cycle that has been widely used for more than 30 years – with the notion of recovery relatively overlooked. “It’s now generally recognised that community participation is an important element of disaster management,” says Professor Mihaela Kelemen, a member of the research team that analysed Minamisanriku’s renaissance. “This might involve risk perception, vulnerability assessments or building resilience, all of which are obviously useful. Yet even today the emphasis is largely on observable characteristics that can be modelled and measured, as a result of which most approaches to disaster management – even those that do encourage community participation – still tend to be primarily top-down and driven by policy.” In Minamisanriku, by stark contrast, the approach was conspicuously bottom-up and driven by locals. “The principal motivation came from fishermen,” says Kelemen. “They reasoned that reconstruction would be a long and slow process if left to the government and that there was an urgent need to move things forward themselves.” A fundamental corollary of this realisation was that community leaders had to become project leaders. In other words, the people of Minamisanriku would take the lead in determining their own collective future. As one fisherman remarked when interviewed by researchers: “Someone had to make a start to pull things together and get life back on track.”

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LESSONS IN PROJECT MANAGEMENT

outreach, the clean-up campaign and related fundraising activities eventually

attracted more than 3,000 volunteers – not just from elsewhere in Japan but

Community-based interventions for postdisaster recovery Pre-Disaster

• Integrate cultural context and community features into any planning decisions űű Be culturally aware of the socio-historical environment of potentially disaster-prone communities űű Put in place training for voluntary and official services at the local level for emergency disaster procedures űű Ensure all potentially vulnerable areas are supplied with the necessary equipment űű Provide education programmes for volunteers and residents űű Put in place safe physical spaces űű Promote the value and necessity of sharing

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This “active leadership” first manifested itself in the identification of objectives and relevant stakeholders. The beach rapidly assumed centre stage, with the community embarking on a huge clean-up operation after local youngsters complained that they missed playing on Minamisanriku’s golden sands. “We did it to fulfil the dreams of our children,” one community leader told researchers, “because if such dreams come true then our community becomes more united and resilient in its attempts to build back.” Thus, the overarching goal of “building back better” was born. As this idea gathered momentum via word of mouth and increasing media Immediately Post-Disaster

• Be aware of cultural traditions concerning the loss of loved ones, property and livelihood űű Provide communal grieving spaces and places of communal congregation űű Consider the cultural role of emotional, social and psychological counselling and deploy the most appropriate support mechanisms űű Use “cultural animation”, a form of intervention that can be developed and employed by local agencies in the aftermath of disaster* űű Promote a more cooperative model of rebuilding and new business generation Planning for the Future

• Put people at the centre of participatory reconstruction and work with communities at risk

űű Wherever possible, decentralise actions and decisions űű Consider the interactions and mutual strengths of multi-agency networks űű Assess the tools and resources needed for mutual cooperation űű Establish emergency committees than can work together to put in place interventions if needed (rather than wait to react) űű Adopt a more holistic approach that integrates the rebuilding of the general infrastructure with that of livelihoods and local markets űű Ensure community remobilisation in the planning process and allow affected households and businesses to take collective action by developing their own plans for recovery Source: Goulding, C, M. Kelemen and T. Kiyomiya (2018) European Journal of Operational Research 268: 899. *More information about this approach can be found in the paper.

from other countries, including the USA and the UK. Subsequently, as the project expanded, stakeholder management emerged as an essential task. The tension between the community and the government, each of which had a distinct vision of Minamisanriku’s journey back to normality, was among the conflicts that demanded constant and careful attention. Communication and interpersonal skills were crucial. “Without well-meaning collaborative efforts,” said one community leader, “it’s hard to make any progress.” Few residents had been spared some sort of human or material loss, so empathy was imperative. So, too, was the need to share in success – even if many of the “victories” were often small. Here, the “softer” skills of disaster management were very much to the fore. As one local observed: “Participation gives me a sense of

achievement. It changes my mood. If I don’t do anything then I’ll worry too much about my future, my family, my children… The leaders give us hope.” Finally, project leaders had to grasp the sociocultural context of their endeavours. Japanese culture is overwhelmingly hierarchical, authoritarian and respectful of seniority, yet Minamisanriku’s bottomup and self-led recovery flew in the face of these traditions. “The project’s leaders had to show considerable skills to navigate such a complex social and cultural map,” says Kelemen, a Professor of Business and Society at Nottingham University Business School. “Ultimately, these softer skills were probably even more important than the technical skills that are predominantly associated with more conventional projects. Enormous sensitivity was required, and this could actually be the key lesson from

Minamisanriku in terms of the broader application of CBOR.”

A FRAMEWORK FOR THE CO-CREATION OF KNOWLEDGE

Drawing on Minamisanriku’s experience, Kelemen and her fellow researchers propose a novel framework for “building back better” in the wake of disaster. As can be seen in Figure 1, this takes as its starting points the concepts of culture and community. “In the sphere of O.R.,” says Kelemen, “these are understandably seen as factors that are difficult to explain and even harder to quantify or measure. As Minamisanriku’s renaissance has shown, though, the fact that they’re inherently ‘fuzzy’ doesn’t mean that they don’t matter. The reality is that everything flows from them, and failure to account for

FIGURE 1 THE SOCIOCULTURAL DYNAMICS OF POST-DISASTER RECOVERY Source: Goulding, C, M. Kelemen and T. Kiyomiya (2018). European Journal of Operational Research 268: 892.

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them can diminish the effectiveness of any intervention – or, worse still, lead to the wrong kind of intervention altogether.” As shown in the panel on an earlier page, such a framing need not be confined only to the recovery phase: it can also be applied in preparing for and safeguarding against disaster. None of this means that disaster can be prevented, but it should at least mean that the effects can be more easily dealt with – and that the impact of a similar disaster, should tragedy strike again, will be lessened. Today, of course, such thinking has arguably unprecedented resonance. The far-reaching consequences of the COVID-19 pandemic and lockdown have brought crisis to communities all around the globe, and the challenges of responding at a more localised level are likely to persist for many years. With this in mind, believes Kelemen, what the story of Minamisanriku truly reveals is the enduring value of the cocreation of knowledge.

workers, the people who tend to go undeservedly unnoticed when times are comparatively calm – these individuals and groups have a wealth of highly significant insights to offer, which is why their voices need to be heard. As ‘insiders’, they bring experience, on-theground know-how and common sense when there are decisions to be made or solutions to be devised. I think it’s fair to say that many interventions haven’t taken sufficient account of this in the past.” According to the research team’s analysis, one of the beauties of Minamisanriku’s resurgence was that nobody claimed to have all the answers. In the parlance of academia, it was a pluralist and participatory undertaking. Today, as the world moves from shock to adaptation to whatever might pass for “new normals”, this ethos may mark the way forward. “No-one in Minamisanriku took the view that they had plenty to convey and precious little to

The far-reaching consequences of the COVID-19 pandemic and lockdown have brought crisis to communities all around the globe, and the challenges of responding at a more localised level are likely to persist for many years

FOR FURTHER READING

“Minamisanriku proved that anyone can be a difference-maker, and we’re seeing that again now,” she says. “Community members, frontline

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absorb,” says Kelemen. “Everybody contributed something to the process, and everybody derived something from it as well. As O.R. practitioners, we should be very excited by such a dynamic.”

softer skills were probably even more important than the technical skills that are predominantly associated with more conventional projects. Enormous sensitivity was required, and this could actually be the key lesson from Minamisanriku in terms of the broader application of CBOR Neil Robinson is the managing editor of Bulletin Academic, a communications consultancy that specialises in helping academic research has the greatest economic, cultural or social impact.

Goulding, C., M. Kelemen and T. Kiyomiya (2018). Community-based response to the Japanese tsunami: A bottom-up approach. European Journal of Operational Research 268: 887–903. Lin, Y., M. Kelemen and T. Kiyomiya (2017). The role of community leadership in disaster recovery projects: Tsunami lessons from Japan. International Journal of Project Management 35b: 913–924. Lin, Y, M. Kelemen and R. Tresidder (2017). Post-disaster tourism: Building resilience through community-led approaches in the aftermath of the 2011 disasters in Japan. Journal of Sustainable Tourism 26b: 1766–1783. Midgley, G., M. P. Johnson and G. Chichirau (2018). What is community operational research? European Journal of Operational Research 268: 771–783. Ufua, D.E., T. Papadopoulos and G. Midgley (2018). Systemic lean intervention: Enhancing lean with community operational research. European Journal of Operational Research 268: 1134–1148.

A L AY P E R S O N ’ S G U I D E TO T H E A N A LY T I C A L R E S P O N S E S TO COV I D -1 9 CHRISTINE CURRIE

COVID-19 WAS FIRST REPORTED TO THE WORLD HEALTH ORGANISATION in December 2019 and over the course of 2020 has transformed the way that the whole world works and interacts with each other. I will not repeat the history of the pandemic, which is well-known, but instead I aim to provide a short guide to the analytical work that has been reported in the academic literature over the past six months. There has been an explosion in work in the area and this article is in no way a comprehensive report but instead a guide to key projects in the area and the value that O.R. can bring to supporting efforts responding to Covid-19. I’ve structured this article around two key themes identified in a paper published in the OR Society’s Journal of Simulation (Currie et al. 2020), which was written both to show the potential of modelling to solve key decisions in a pandemic situation and also to act as a call to arms for academics and practitioners working in the area. Written early in the pandemic (March 2020), the focus of the original paper was very much on how to get through the huge peaks in hospitalisation seen around the world in spring 2020 rather than how to manage ‘the new normal’ and this article extends that work to include some thoughts on how O.R. may be useful as we move forward.

DISEASE TRANSMISSION

Within the UK, modelling of disease transmission has been dominated by large groups such as the Imperial College Covid-19 response team, led by Neil Ferguson, whose much publicised and detailed, UK-specific, individual-based simulation model was instrumental in informing government policy on when to introduce the national lockdown. There are interesting counterpoints to this within the O.R. literature, most notably the scratch models introduced by Ed Kaplan who worked with Yale University and the state of Connecticut on a set of modelling studies around reducing transmission of Covid-19 (Kaplan, 2020). He describes the work as policy

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modelling, being very focussed around a key set of questions. In contrast to the models developed by Ferguson and his colleagues, the models Kaplan describes are small and were coded quickly to produce fast results. The questions being considered involve the timing and size of university events such as graduation to avoid large-scale transmission and how social-distancing measures could be used to manage demand for intensive care beds in the State of Connecticut. Also relevant for disease transmission is how to manage a return to in-person working while minimising the risk of transmission between staff in a workplace and between staff and the customers they serve. Agent based modelling is a standard tool for assessing impact but scheduling can also be used to minimise the overlap of separate groups (or bubbles) within communal spaces. There is a need for decision analysis tools that will help with weighing up the risks of opening up and relieving economic/social pressures versus remaining isolated and reducing disease transmission.

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There is a need for decision analysis tools that will help with weighing up the risks of opening up and relieving economic/social pressures versus remaining isolated and reducing disease transmission In March 2020, Dr Tedros Adhanom Ghebreyesus, Director General of the World Health Organisation, encouraged a strategy of ‘Test, test, test’ to combat the virus and working out an efficient way of doing this has been a priority internationally. Discrete event simulation is a great tool for making processes more efficient and Simul8 have a free-to-download model of a drive through testing centre (see http://bit.ly/Drivethroughtesting) that is designed to help with the logistics of the testing process. Recent reports in the media suggest that there is currently an urgent need for analytical work on demand estimation and management of tests alongside streamlining of processes within the testing laboratories.

RESOURCE MANAGEMENT

In a health emergency, medical resources, notably standard and intensive care unit (ICU) hospital beds and healthcare staff, are of paramount importance. Simulation modelling that allows the testing of different what-if scenarios has been vital for understanding how healthcare systems would cope as the pandemic progressed. Discrete event simulation models, in particular, incorporate the randomness and uncertainty inherent in the arrival and service processes rather than working with expected numbers. Given the time pressures involved, having generic models that are ready to go and simply need data inputs, makes development much smoother and quicker. It also ensures that much of the model validation process can be carried out prior to the emergency, reducing the chances of silly mistakes. Repositories such as Mike Allen’s ‘Python for healthcare modelling and data science’ (see http://bit.ly/pythonsnippets) are invaluable here. Within the resource management space are other much more difficult decisions such as how to ration care. In a rather sobering blog post from early March, Christina Pagel discusses how triaging should be carried out in a pandemic (see http://bit.ly/Pagelblog). The majority of triage protocols exclude those who are too well and those who are too sick but forget to take account of how long patients stay in the unit. For an ICU, as Christina Pagel argues, the scarce resource is the number of bed-days, not the number of beds. As we (hopefully) move beyond the peak of the pandemic and hospitals restart their non-urgent services, considerable work will need to be done to return the system to the state it was

O.R. methods will help to develop an efficient and effective ‘new normal’ as the world recovers from the annus horribilis of 2020

It is very clear that O.R. methods will help to develop an efficient and effective ‘new normal’ as the world recovers from the annus horribilis of 2020. The analytical community also needs to be prepared for future pandemics that will surely come and the possibility of a second wave of Covid-19 as the northern hemisphere winter approaches. in at the beginning of 2020. Recent work, available online, in the Journal of Simulation by Richard Wood models the impact of Covid-19 on elective waiting times (Wood, 2020) and headline figures show that restoring performance could take two years, assuming additional capacity injections of 12.5%, costing an estimated £14.7bn. While this is a worst-case scenario it shows the scale of the issues that the NHS will face as we move forward.

HOW CAN O.R. BEST SUPPORT DECISIONS DURING A PANDEMIC?

A key point that has come out in much of the work published during the pandemic is the need to develop models and algorithms very quickly with a large number of unknowns. There is a need for more work on the rapid development of conceptual models and also how best to use the scratch models that act as a first answer to a key

question. Rapid development should not mean careless development without any checking of the model or algorithm output as the UK exam results fiasco has perhaps underlined a little too well. The fact that so little was known about Covid-19 at the start of the pandemic has also made it imperative to communicate the uncertainty in model input data and how that uncertainty affects the results. Communicating model uncertainty to non-modellers is difficult but decisionmakers need to understand where models and algorithms might not be robust and might include errors.

ACKNOWLEDGEMENTS

The author acknowledges the help given by John Fowler, Duncan Robertson, Kathy Kotiadis, Tom Monks, Stephan Onggo and Antuela Tako. Christine Currie is Associate Professor of Operational Research at the University of Southampton and Editor of the Journal of Simulation, one of the OR Society’s academic journals. Her expertise lies in decision making under uncertainty, applying mathematical optimisation and simulation to address real world challenges.

FOR FURTHER READING Currie, C. S. M., J. W. Fowler, K. Kotiadis, T. Monks, B. S. Onggo, D. A. Robertson and A. A. Tako (2020). How simulation modelling can help reduce the impact of COVID-19. Journal of Simulation 14: 83–97. Kaplan, E. H. (2020). COVID-19 scratch models to support local decisions. Manufacturing & Service Operations Management 22: 645–655. Wood, R. M. (2020). Modelling the impact of COVID-19 on elective waiting times. Journal of Simulation DOI: 10.1080/17477778.2020.1764876.

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H E A LT H Y O. R . I N WA L E S PAUL HARPER

THE DEMAND FOR HEALTHCARE SERVICES in the UK continues to increase and the deficit between supply and demand proves to be economically costly and typically has a detrimental impact on factors such as waiting times, quality of care, NHS staff morale and patient satisfaction. From an O.R. perspective, healthcare systems are stochastic in nature; that is, they typically operate in an environment of uncertainty and variability, both at scale and within highly complex and connected networks. For example, imagine planning and managing the services in a large hospital, both operationally (on a day to day basis) and more strategically to plan ahead. Hundreds of patients may expect to pass through

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different care pathways each day, each with varying resource needs required in an efficient and effective manner. Help is needed to forecast demand, schedule clinics, calculate the workforce size and skill-mix needed, and to roster staff. Furthermore decisions must be made on how best to schedule operating theatres and assign them to surgeons, how to reduce waiting times and cancellations within budgetary constraints, improve health outcomes, and make decisions on where to locate services geographically to ensure equitable coverage or the ability to reach patients within a critical time limit. But the hospital is just one part a much larger connected healthcare system. What happens here is

influenced by, and influences, policy decisions within primary care and GPs, community care, social care, preventive care services and public health for example. Whilst the NHS is in many places working hard to improve services, one might reflect that it is typically carried out in silos that don’t consider the wider system view, so changes in one part might actually have an unintended and undesired impact elsewhere. Seemingly, given such immense pressures on services and current levels of funding, the NHS and indeed healthcare systems globally, therefore can’t simply do more of the same if it is to be sustainable. Staff are already working incredibly hard and the system is mostly at full capacity, but perhaps the NHS can try and work smarter with the help of O.R. With O.R. methods we can build mathematical and simulation-based models of current processes and use them to explore “what if?” scenarios to evaluate the likely consequence of different ways of working whilst incorporating the stochasticity and complexity, and move towards optimally configured services. This is much safer than experimenting with changes to the system for real and seeing what happens.

Staff are already working incredibly hard and the system is mostly at full capacity, but perhaps the NHS can try and work smarter with the help of O.R.

THE HEALTHCARE MODELLING CENTRE CYMRU

The Health Modelling Centre Cymru (hmc2) is helping to create impact through an on-going dialogue between

modellers, clinicians and NHS managers, encouraging them to engage, innovate and test alternatives using O.R. methods, and to train NHS employees themselves in O.R. tools. One novel initiative of hmc2 was the creation of a researchers in residence programme in partnership with the Aneurin Bevan University Health Board (ABUHB). The modelling unit sits within ABCi (Aneurin Bevan Continuous Improvement) and currently consists of four O.R. modellers who are the first of a new generation of modellers to be embedded within the NHS Wales. Joint funding between the University and ABCi allowed the permanent appointment of Dr Gartner as the ‘Aneurin Bevan Senior Lecturer in O.R.’, helping to cement the relationship and strategic partnership between the two organisations. Joint working agreements allow the team to operate from office space at both the University and in the Health Board. ABCi also has matchfunded several PhD studentships and has hosted to-date 30 MSc student summer research projects. ABCi exists to help and support clinical teams to improve the safety, quality and efficiency of care they deliver with a strong focus on patient experience. The unique opportunity to be embedded within this team brings numerous benefits to the O.R. analysts: not only are they directly linked with improvement coaches, financial planners, senior managers and clinicians, but they are regarded by NHS staff as ‘colleagues’, giving them access to a wide range of opportunities to pioneer novel modelling techniques within the NHS. The team also works closely alongside the Information Department. The ability to speedily provide the necessary data has been key in allowing the modellers to

progress their analyses and deliver results at pace. The modelling unit is making a significant contribution impacting on the efficiency, effectiveness and quality of healthcare provided by ABUHB to a population of nearly 650,000.

the O.R. analysts are regarded by NHS staff as ‘colleagues’, giving them access to a wide range of opportunities to pioneer novel modelling techniques within the NHS

A WIDE VARIETY OF APPLICATION

Over the past six years since its launch, the appetite for modelling across the Health Board has by far exceeded expectations and the team receives enquiries from across the full range of functions and specialities in the health board: clinical and support services; primary, community, and hospital based. A range of O.R. techniques have been used to approach the problems such as forecasting, demand and capacity planning, simulation, optimisation, and scheduling. Some of the projects commissioned from the team in which modelling tools have been applied include: • Supporting the design of a new £350M hospital build; • Modelling the dynamics of day surgery flow and clinic flow at Royal Gwent Hospital; • Analysing the effect of individuals presenting in A&E under the influence of alcohol; • Designing an innovative tool to support caseload management for Mental Health Teams;

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• Evaluating the impact of Frailty Teams on emergency presentations and admissions; • Investing the effects of changing the shift patterns of staff in a Pathology Laboratory; • Modelling workforce requirements for digitisation of health records; • Modelling patient flow in Fracture and Orthopaedic clinics. The successful results of these projects have enabled senior managers and clinicians to recognise the value of the O.R. approach at ABUHB such that modelling techniques have now truly become an integral part of design and delivery of their services.

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A range of O.R. techniques have been used to approach the problems such as forecasting, demand and capacity planning, simulation, optimisation, and scheduling

and applying Operational Research methods for improving our NHS services and patient outcomes.” Alongside research in collaboration with neighbouring Cardiff and Vale University Health Board, and for other NHS partners across the UK, the wider impact of the work has included:

Judith Paget, ABUHB Chief Executive noted: “The modelling unit’s success has led to better planning for the organisation and better analysis: far better decisions are made as a result of the input of the modellers.” Trish Chalk, Clinical Futures Lead at ABUHB added “This unique and innovative partnership has delivered considerable impact in developing

• Realising net efficiency gains of £1.6M per year in the emergency department at University Hospital of Wales through improved staff rostering and better use of A&E resources; • Redesign and optimisation of mental health caseloads resulting in improved health outcomes for severely mentally ill adults across South Wales (measured by a reduction in the Adult Camberwell Assessment of Need

•

(CANSAS) per patient by an average of 51%, reduced time off work due to severe mental health episodes by 65% and a reduction in the number of crisis admissions by 66%) and avoiding ineffective and unnecessary acute hospital admissions by 79% with associated annual cost savings of £7.3 million. Demand and capacity modelling to inform the introduction of the NHS Wales national 111 telephone helpline for people needing urgent healthcare advice out-of-hours, resulting in improved patient experiences and a reduction of 26% in ambulance journeys; Reducing the mortality of trauma patients across South London by 54% and stroke patients by 60%, through the creation of a new facilities and urgent care processes designed using mathematical models; Optimising master surgical schedules for operating theatres across several NHS hospitals resulting in annual cost savings of £0.9 million that have been re-invested into other vital patient care services. Providing modelling support for Welsh Government’s decision to implement a Single Cancer Pathway for all patients in Wales, thus becoming the first UK nation to introduce a single waiting time target. Our research quantified the necessary resourcing levels and additional funding required for implementation that was subsequently announced by the Cabinet Secretary for Health and Social Services. Provision of hospital capacity planning tools in use across the UK.

This unique and innovative partnership has delivered considerable impact in developing and applying Operational Research methods for improving our NHS services and patient outcomes This work has been disseminated nationally and internationally, in the media and at a range of events designed to engage the public with O.R. The Cardiff University team have received several awards in recognition of their innovative approach and real-world impact, including a Times Higher Education (THE) award for ‘Outstanding Contribution to Innovation and Technology’.

RESPONDING TO COVID-19

The value of O.R. and benefits of our close partnership with NHS Wales were again evident as the COVID-19 crisis hit the U.K. Members of the modelling team were immediately deployed to help with initial demand and capacity planning and logistics for vital local resources, as the virus threatened to overwhelm the healthcare services. In fact, early on in the crisis, the Gwent region (served by the ABUHB) had one of the highest rates of infection anywhere in the UK. O.R. has been instrumental in the planning for the Grange University Hospital just outside Newport, a new 560 bed specialist and critical care centre due to open in 2021. Thanks to a herculean effort, the hospital was partially opened (some 350 beds) almost a year early to provide vital extra beds through the coronavirus outbreak. Other responses made by the modelling team included exploration of

mass testing logistics, and discussions with the Chief Scientific Office for Wales on the economic impact of the mitigation phase and probabilistic modelling with non-homogeneity considerations to estimate the predicted number of cases and assessment of intervention strategies.

TRAINING IN HEALTHCARE MODELLING

The team has developed a set of training courses in healthcare modelling in conjunction with the PenCHORD Group at Exeter University. These are aimed at NHS staff who wish to learn more about how O.R. modelling can help with their improvement projects, but also for those keen to develop their own skills. A number of successful training programmes have run over several years, including one-day workshops on Data Analysis in Excel, Presenting and Displaying Data, Systems Thinking in Healthcare, and Essential Statistics in Healthcare. To-date, in collaboration with the NHS Delivery Unit, more than 350 NHS Wales staff have attended these training courses. More recently the modelling unit have introduced a Modelling Fellows programme. During the first cohort of six members of health board staff who had chosen to undertake an ABCi Modelling Fellowship, we taught a number of O.R. skills and techniques to develop their own projects. These included the potential impact of additional pharmacy and therapies staff in the emergency department, modelling optimal nursing ratios for pressure ulcer prevention, forecasting scheduled care demand and the development of a decision support

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improvement and future service design.” She also outlined how her new skills are benefiting her in the workplace: “I am currently applying the learning to current practice, looking at forecasting seasonality for front door therapies and modelling follow up variation.”

tool to assist with elective orthopaedic scheduling. These training courses lead onto the possibility of a part-time MSc study in O.R. and Applied Statistics at Cardiff University. “The ABCi mathematical modelling team delivered interactive teaching across the course and were

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extremely engaging and supportive,” said one of the first cohort of modelling fellows, Emma-Jayne. “I have a greater understanding and appreciation of mathematical and O.R. modelling and the vital resource it can be to support therapy services in everyday planning, quality

Paul Harper, Professor of O.R. in the School of Mathematics, Cardiff University, is the director of the Health Modelling Centre Cymru and of the Cardiff University Data Innovation Research Institute. He is a Fellow of the Learned Society of Wales (FLSW), a Companion of the O.R. Society and has been appointed as member of sub-panel 10 Mathematical Sciences for the Research Excellence Framework (REF) 2021.

PAC K I N G S H O E S E F F I C I E N T LY ANUEL V.C. VIEIRA AND M FLORA FERREIRA

SAVANA SPECIALIZES IN THE PRODUCTION OF CHILDREN’S FOOTWEAR, using top quality materials, such as leather, latex, wool, etc. Savana is always searching to improve its processes as they were aware of some of the inefficiencies in their packaging process. With this concern, they asked us to improve the packaging process during a European Study Group with Industry that took place Oporto, Portugal. These are week-long workshops, where in the first day the industry partners present their problems. The academic partners form several groups, one for

each problem, and they work all week in these problems. On the last day, the academic partners present their conclusions and suggestions. Later, a report is written and sent to the respective industry partner.

THE PACKAGING PROCESS

Savana produces children’s shoes in EU sizes ranging from 18 to 40. When a new line of footwear is introduced, the appropriate box size is selected manually from a limited choice. Boxes of the same size are used for footwear of various types and sizes. The

footwear ordered by each customer is then packed into one or several large cardboard boxes, and these cardboard boxes are size customized for each set of shoe boxes to pack. The cardboard boxes will henceforth be referred to as containers. Different shoe sizes and models can be packed into each container to be delivered to a single customer. The shoe boxes are packed with the label facing up for easy inspection (See Figure 1). The goal of the company is to pack the full order while minimizing the number of containers and, as the containers are not fixed size, also minimizing their volume. Due to the frequent introduction of new models in the production environment, the manual selection of the box sizes is frequently a timeconsuming task. Furthermore, empty space in the containers, mainly in those with different shoe box sizes, was common to find. For example, Figure 1 shows a container containing nine shoe boxes. However, some visible empty spaces could possibly be eliminated. In this context, Savana wished to improve the packing process by eliminating manual box selection; reducing the choice of boxes and minimizing the empty space in a cardboard box; and automating the container design and subsequent packing of the individual boxes in each client’s order. Therefore, Savana was facing two difficulties: 1. Assigning pairs of shoes to the appropriate shoe box; 2. Assigning shoe boxes to the appropriate container. In this sense, the entire problem was split into two main packing stages. In the first stage, there is a box

FIGURE 1 A CARDBOARD CONTAINER CONTAINING THE SHOE BOXES

selection process in which the most suitable box is selected for each pair of shoes (size) with the constraints that shoe boxes cannot be too tight or too loose. As a goal, the number of selected box types should be kept to a minimum, since similar boxes are easier to pack. This resembles an assignment problem, where we minimize the number of different boxes used. This is a 0–1 linear programming model applied to every new type of shoe entering production. The second stage deals with the packing process of the shoe boxes into one or more containers. The novelty of this problem lies in the fact that the shoe boxes are packed into several containers and each container has three open dimensions, which increases the difficulties. In this stage, we proposed a step-by-step procedure to reduce the inherent difficulties of dealing with the problem as a whole.

and the boots are arranged as shown in Figure 3. Figures 2 and 3 show how a pair of shoes or boots should be placed in a shoe box. The red numbers are the size of the box and the shoe size.

FIGURE 2 SHOE BOX WITH A PAIR OF SHOES

ASSIGNING SHOES TO BOXES

Pairs of shoes are appropriately arranged in the boxes as in Figure 2,

FIGURE 3 SHOE BOX WITH A PAIR OF BOOTS

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simplifies the packing of shoe boxes into containers.

PACKAGING SHOE BOXES INTO SEVERAL CONTAINERS

FIGURE 4 TOO LOOSE SHOE BOX

FIGURE 5 TOO TIGHT SHOE BOX

The box size should be chosen so that there is not too much empty space inside the box (see Figure 4) and, at the same time, there is no deformation of the footwear due to lack of space, as illustrated in Figure 5. Every time Savana had a new model to produce, they would produce one pair of every size for this model, stop the production, and choose the appropriate shoe boxes manually for each size. We proposed a mathematical program to decide which shoe boxes should pack each model/size of footwear before production starts. This can be done in advance, because for each new model, Savana must produce a test model/size. With this test model, the measures of other sizes can be estimated and the appropriate shoe box chosen. In addition, the mathematical program minimizes the variety of different shoe boxes, which

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Shoe boxes are packaged into several customized containers made of cardboard, as seen in Figure 1. Due to customer’s restrictions on container sizes, the manufacturer usually packs no more than 20 boxes (or 10 boxes, in the case of larger boxes used for boots) in each container. The packing process of an even number of equal shoe boxes was already carried out efficiently by the company. But often the shoe boxes are not equal. For example, to pack 14 shoe boxes, they would make a container large enough to fit 14 shoe boxes, as if all boxes were equal and occupying the space needed for the largest one. Thus, they could pack orders as in Figure 6, with shoe boxes spread all over, which does not please their customers. For some reason, they also utilised tight cardboard containers

that would deform the shoe boxes, see Figure 7. Despite the problem being easy to understand, and we can make use of a mathematical program, this is too large to be solved as a whole. Thus, we proposed a three-step technique. The three steps are: 1. determine the number of containers to be used; 2. distribute the boxes within the containers; 3. calculate the sizes of the containers.

Step 1: Determine the number of containers

The determination of the number of containers was straightforward at Savana. They assumed that each container packages 20 boxes (for shoes) or 10 boxes (for boots), and then given an order, they decide the number of containers. Our first approach, during the meeting, followed these ideas.

FIGURE 6 TOO LARGE CARDBOARD CONTAINER

FIGURE 7 TOO TIGHT CARDBOARD CONTAINER

However, later, we argued that the threshold of 20 should be dropped and the number of shoe boxes could vary from container to container. Depending on the size of shoe boxes, the container may carry between a minimum of 10 and a maximum of 50 boxes.

Step 2: Distribute the boxes amongst the containers

The distribution of the boxes among the containers for a given order to a single customer was determined by ordering the shoe boxes by size. As boxes are easier to pack when they are similar, this is a good strategy. We proposed a mathematical program to deal with the first two steps at the same time, which improved the process. We allowed the number of shoe boxes per container to not be fixed, but decided depending on a specific customer’s order. In the operational research literature this is called a bin-packing problem and can be solved using a mathematical program. This decides the number of containers and distributes the shoe boxes amongst the containers, where the goal is to minimize the

number of containers. With this approach, the total number of containers used in a single order can be reduced.

Step 3: Calculate the sizes of the containers

In this step, the size of the containers and the exact position of each shoe box is determined. This process was done manually by the company, but their idea was to start to do it automatically. In this sense, it is important to precisely determine the size of each container and the exact position and orientation of each shoe box in it.

it is important to precisely determine the size of each container and the exact position and orientation of each shoe box in it. In this step, we assumed that we know the number of containers and which shoe boxes are to be placed in each container. For this, we proposed another mathematical program whose goal is to minimize the volume of each container. This must be solved for each container.

The placement of shoe boxes into a container and the size of the containers must obey some constraints imposed by customers. They require that shoe boxes must be facing up for label inspection and can rotate. They are also preferably packed in one level for easy inspection. As a result of customer requirements, the size of the containers must satisfy the following constraints: (1) the longest edge cannot exceed 80cm; (2) the other two edges cannot exceed 60cm and (3) twice the width plus height added to the length cannot exceed 300cm. These impositions ensure that the container cannot be too large, and will not be too heavy.

CONCLUSIONS

Our work indicated how the overall packing process can be automatized and sped up. The process of assigning shoes to boxes is simple and can be implemented in a computer system. It gives a realistic estimate of the shoe box to be used for each size of a new model. This process only uses the measurements obtained from a test model/size. The proposed process automatically determines the containers’ sizes and a near optimal arrangement of the individual shoe boxes inside containers and reduces the empty space inside containers. When the number of boxes was larger than 13, the shoe manufacturer was packing shoe boxes on two levels. The manufacturer believed that it would be the only way to pack such a number of boxes without surpassing the container dimensions imposed by its clients. However, our work showed that using one level is often the best packing solution.

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The implementation of the mathematical programming model proposed offers considerable time and cost savings. The implementation of the mathematical programming model proposed offers considerable time and cost savings. Savana collaborator: ‘The implementation as a computer-program of the algorithm proposed to deal with decisions – how many containers are required to pack a customer's order and how to distribute the shoe boxes among the containers – has led to a significant reduction in time consumption of my work. I am very satisfied and I

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believe that the implementation of the proposed model will help the company save both time and money.’ Manuel V.C. Vieira is Assistant Professor at NOVA University of Lisbon and member of the research centers CMA-UNL (Portugal) and GERAD (Canada). He obtained his PhD on Optimization from TUDelft. His scientific interests are optimization problems with applications in industry, with publica-

tions on facility layout and container loading problems. Flora Ferreira is a researcher at the Centre of Mathematics at the University of Minho, Portugal. She received her Ph.D. in Mathematics from the University of Minho in 2014. Her research focus is on mathematical modeling, data analysis, and machine learning which is strongly driven by practical questions and multidisciplinary collaborations.

FOR FURTHER READING Vieira, M.V.C., F. Ferreira, J. Duque and R. Almeida (2019). On the packing process in a shoe manufacturer. Journal of the Operational Research Society. https://doi.org/10.1080/01605682.2019.1700765

U N I V E R S I T I E S M A K I N G A N I M PAC T EACH YEAR, STUDENTS ON MSC PROGRAMMES in analytical subjects at several UK universities spend their last few months undertaking a project, often for an organisation. These projects can make a significant impact. This issue features a report of a project recently carried out at two of our universities: Warwick and Southampton If you are interested in availing yourself of such an opportunity, please contact the Operational Research Society at email@theorsociety.com IMPROVING MARKETING STRATEGY OF AN E-COMMERCE COMPANY (Jan Kreuter, University of Warwick, MSc Business Analytics)

Competition among e-commerce companies is increasing because of a greater number of companies and the ease with which prices and products on different websites can be compared. Therefore, the effectiveness of the marketing strategy plays a crucial role as to whether a company is successful or not. Analytics can help these companies to have a competitive advantage, systematically capitalise on opportunities and hold their own in the market. In cooperation with Exponea, a Slovak marketing analytics company, Jan’s project helped an electronics e-commerce company, one of Exponea’s clients, with annual revenues of more than £300m, to improve their marketing strategy. Jan worked in Exponea’s Artificial Intelligence department under the supervision of Daniar Rusnak. The project’s aim was to identify the characteristics of customer clusters for the e-shop in both B2B and B2C segments. All in all, there was over a year’s worth of behavioural

data of all visitors to the website including which products they viewed or bought or from which marketing channel they came from. Through clustering analysis, Jan was able to segment their customers into groups and provide a deep understanding of their behaviour on the website. The clusters were created using attributes related to the web engagement and purchases (price, category), and also considered time-related aspects, such as time between touchpoints. The results enabled the client to tailor their marketing campaigns to the preferences of each cluster. Furthermore, a recommendation system helped to offer those products to customers which they are most likely to buy, based on the products they prefer on the website. Jan was able to show through the results of the clustering analysis that the optimal number of clusters is four for both B2B and B2C customers. The clusters differed in the time the customers made their decision, the price-ranges of products they purchased

and likelihood to re-order. For both customer segments, one cluster of customers were highly engaged with the website and spent the most on average. The products which should be recommended to the customers in the future are different for B2C and B2B customers, due to their different intentions to visit the website. Jan’s project allows the e-commerce company’s marketing strategy to focus on tailoring campaigns to customer preferences and create a unique customer experience on the website through web and e-mail personalization. Daniar Rusnak (Senior Analytics Consultant) commented that “Jan Kreuter’s efforts in analysing the behaviour of the different clusters have proven that applying additional analytical techniques can help our clients to understand their customers better and help them to improve their marketing strategy. We are planning to use these results for other clients in the future.”

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TRAINING OPTIMISATION AND LEARNER ASSESSMENT THROUGH DATA EXPLOITATION (Joseph Bampton, University of Southampton, MSc Operational Research)

Babcock is a leading provider of critical, complex engineering services which support national defence, save lives and protect communities. Babcock manages all aspects of the land training cycle, delivering over 758,000 training days to over 5,000 students annually for the British Army and producing personnel that are knowledgeable, skilled and competent to operate in the most challenging circumstances. Babcock have formed a strong link with CORMSIS at the University of Southampton, one of the largest groups of its type in the UK, spanning Mathematical Sciences and Southampton Business School. CORMSIS has an established breadth and depth in Operational Research with strong long-standing links to industry. Joseph’s project gave a range of benefits to Babcock, including insight into the current training, potential social improvements and the capacity to make a more efficient training system. On a social level the models are able to identify potentially struggling students, thus indicating where additional support is needed. Along with benefiting Babcock, the students may also see benefits. Struggling students may only be weak due to their placement. By identifying the student’s strengths as well as their weaknesses they are more likely to be helped to

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reach their full potential through informed allocation. The project not only succeeded in providing a foundation for the analysis of struggling students, but it highlighted the importance of data and what can be achieved through analysis. The findings of the project allowed Babcock to establish a solid starting point with their future predictive analysis projects, providing valuable evidence in support of developing Machine Learning models. In weekly meetings with Babcock and the university supervisor, discussion of the analysis provided insight into previously unseen trends within the data. These insights gave further direction to the project which proved essential for the implementation of the predictive algorithms. Within the predictive stage Joseph employed a set of machine learning algorithms to identify each student’s risk of failure based upon several data points. Although data exploration techniques had been taught during the course, machine learning was not something he had studied. A desire to expand his knowledge combined with the collaboration with the academic supervisor from the University of Southampton and project sponsors proved essential to master and apply this new area of expertise. Christopher Clift, Director of Training Capability, Defence Training:

“The project undertaken was a discrete project that enabled a number of follow-on activities in Babcock’s training optimisation programme. It forms the first stage of the end-toend Adaptive Learning Enterprise framework that assesses the initial learner entry point and trajectory through all stages including immersive, individual, and collective training. “The outputs from this project, the follow-on projects, and our ongoing academic research will allow us to significantly reduce outflow linked to training and reduce the customer’s operational costs. The outputs will also ensure learners who are likely to experience or are experiencing difficulties are identified early and the most appropriate support interventions are deployed. The project has had a significant positive impact on our approach to understanding and modelling learner data throughout the whole learner journey and their progression into the operational environment.” Following the successful project, Joseph was brought into the team full time at Babcock to further develop the work started during the MSc. The project received both the Boeing award for Mathematics and the OR Society’s May Hicks award, while helping to contribute to Joseph’s Distinction for his Master’s Degree.

TACTICAL RECONSTRUCTION AND FAST O.R. AT THE MARITIME WARFARE CENTRE STEPHANIE MONKS AND HAYLEY BIRD

THE MARITIME WARFARE CENTRE (MWC) is a unique military and scientific establishment that provides direct support to the front line. With a staff of around 100 service and civilian personnel, including representatives from the Defence Science and Technology Laboratory (Dstl), Ministry of Defence (MOD) and industry, there is a wide range of expertise to help solve problems and provide warfare advice wherever and whenever it is needed. The MWC Operational Analysis Team is

responsible for supporting the delivery of tactical and operational advice by military staff to the front line of the Royal Navy.

WHAT IS TACTICAL RECONSTRUCTION?

One of the team’s most important activities is tactical reconstruction. The tactical reconstruction method is a defined process which involves the detailed post event understanding and analysis of a range of data. It is used to

with considerable fidelity is a core element in our delivery of battle-winning tactics.”

AN EXAMPLE OF ITS APPLICATION: EXERCISE JOINT WARRIOR 19-1 AND OPERATION PENSEIVE

ROYAL NAVY TYPE 23 FRIGATE HMS KENT, AT SPEED OFF THE SOUTH WEST COAST OF SCOTLAND DURING EXERCISE JOINT WARRIOR 19-1

assess the performance or effectiveness of maritime units during an event, operation or exercise. The team collate large quantities of quantitative and qualitative geospatial and signal data from maritime units, and re-create maps of actual activity which can be critically analysed to understand the situation and decisions made by key players; and identify areas of improvement for current and future Royal Navy tactics.

WHY DO WE DO TACTICAL RECONSTRUCTION?

We have identified three reasons for using tactical reconstruction. Firstly, the approach creates a basis for analysis of

big data. Tactical Reconstruction is able to ‘make sense’ of large quantities of geospatial and signal data and display it in an easy to understand format that can be communicated to maritime units. Secondly, it helps the MWC understand the performance and effectiveness of maritime units. The ‘quick-time’ nature of tactical reconstruction enables MWC to pass back invaluable performance assessments during training and exercise. Thirdly, it supports the MWC in identifying improvements to Royal Navy tactics. Through reconstruction the MWC are able to provide quantitative analysis of tactics, techniques and procedures which can then be communicated to the frontline. Captain Chris O’Flaherty, Captain of the Maritime Warfare Centre, observed that “Tactical Reconstruction and the ability to replay operational and training events is at the core of tactical development. My team’s ability to conduct such reconstruction rapidly and

Exercise Joint Warrior is the largest military exercise in Europe, bringing together the Royal Navy, the Royal Air Force and the British Army, as well as forces from other nations. The exercise runs through a range of crisis and conflict scenarios that could be realistically encountered in operations, such as territory disputes, terrorist activity and piracy. Exercise Joint Warrior 19-1 (JW19-1), which took place in April 2019 was an opportunity for MWC to develop and test operational analysis techniques used for supporting UK and NATO worldwide operations, exercises and trials. The opening image shows an Astute class nuclear submarine in company with the Type 23 frigate HMS Kent being over flown by a German navy P3 maritime patrol aircraft during JW19-1.

Exercise Joint Warrior is the largest military exercise in Europe, bringing together the Royal Navy, the Royal Air Force and the British Army, as well as forces from other nations

Operation PENSEIVE The MWC analysis team conducted post-event analysis of Exercise JW 19-1, known internally as Operation PENSEIVE. The team used the opportunity to apply a number

IMPACT | AUTUMN 2020

of operational analysis techniques, including tactical reconstruction, for supporting exercises and operations around the world.

There is therefore a tradeoff between delivering high quality evidence based analysis, and providing an assessment within the time it is required for making a decision

Aims and Objectives MWC’s primary interest is the tactics employed by assets, for example, ships of the fleet, building up a long-term view and assessing, for instance, whether the correct tactics are employed and whether new tactics are required. The aims of the PENSEIVE Team were therefore: • To provide analysis and an account of success of Exercise Joint Warrior serials (a defined practice from a single domain or multi-threat domain with a clear start and end point) with regards to the Tactics and Procedures followed by the UK Royal Navy and Royal Marines. • To enable the MWC assess its own capability to deliver rapid operational research support to operations, exercises and trials.

FIGURE 1 EXAMPLE OF TRACK RECONSTRUCTION TO SUPPORT OP PENSEIVE ANALYSIS AT MWC

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‘Fast O.R.’ vs ‘Full O.R. Faster’ What’s better:

that in the fast-time turn around environment, fast-OA is the best method.

• Conducting Full Operational Research studies (detailed modelling and simulation) to determine why events happened and enhance the Royal Navy’s understanding? Or

The Operation PENSEIVE Approach

• Conducting Fast Operational Research which emphasises a question and targeted data collection for establishing what is happening now? This is a debate over which the MWC analysis team agonise frequently. Of course, it would be ideal to complete a full modelling study, and delve into the data to fully understand the situation which would provide a rich base of evidence to the Navy. However, this takes time and there is often a requirement for an answer within hours, or a few days. Nevertheless, doing a fast analysis of a sample of the data available often raises more questions than it answers. There is therefore a trade-off between delivering high quality evidence based analysis, and providing an assessment within the time it is required for making a decision. During Operation PENSEIVE, the MWC analysis team completed track reconstruction (plotting geo-physical data obtained onto mapping software – see Figure 1) and Fast O.R. or, rather, Fast OA, as Operational Analysis is the terminology used in Defence to describe Operational Research. Table 1 highlights the features and benefits of a Fast OA approach when compared to full OA studies. When looking at the ‘Methodology’ and ‘Measure of Effectiveness’ comparators in particular, it is clear

The team completed Fast OA of selected serials each day during the two-week exercise within a four-hour period; delivering daily ground truth reconstructions of fast OA findings of selected serials to the Joint Exercise Planning Team and Captain MWC. The daily approach can be seen in the adjacent display. The daily routine 9.00 – 10.00: Data sorting: 0 Quantitative (geospatial) 0 Qualitative textual (signals from ships) 0 Satellite imagery 10.00 -10.30: Reconstructed GPS tracking 10.30 – 12.00: Made assessment on success of serial 13.00: Brief to Captain MWC 14.00 – 17.00: Preparations for following day

Analytical Challenges There are numerous challenges that the team face when doing Tactical Reconstruction and Fast OA during a major Navy Exercise: • Data: Either too much data, or a lack of data arriving into MWC. The team cannot predict in advance the amount of data we will receive. This can cause either gaps in the information, or an overwhelming amount of data to sort and analyse. Further, differing data formats can cause issues as we are relying on ships

OA APPROACH Very generalised

FAST OA Hard OA; addressing a well-defined

description of the likely question feeding into a structured OA approach

Application Scope

methodology and clear quantified result

also address problematic questions where a flexible methodology might lead to qualified results Green paper validation and developing

performance, assessment or green paper

concepts of operation/employment/use and

development

operation orders

Specific question(s) Rigid and procedural

Focus

Describe what events happen

effectiveness

Combination of hard and soft OA techniques;

Model validation, equipment

Methodology

Measure(s) of

FULL OA

Quantitative and/or binary pass/ fail outcomes that should be both measurable and achievable

Tendency to be broad Iterative process with room for curiosity driven digressions Identify why events happen Qualitative third-person perspective built on first-person narratives and system data

Tendency to rely on system recordings

Tendency to emphasise the operator

and discrete observations. Likely to

narrative that describes motivations. Possible

concentrate on the system(s) identified

that complementary data from a wider

in the data collection plan

number of systems is available

Trial instructions detailing the necessary

Standing orders and books of reference

activities

detailing system recordings and text

Trial seariders* and additional data

No seariders* or additional data collection

collection equipment

equipment

Tendency to draw on stakeholder views.

Peer review, and possible red teaming,

Caveated by ‘quick look’ label attached

explicitly included during staffing. More likely

to the output

to be revisited at a later stage.

Report Timescale

Within three weeks

In excess of three months

Contribution to

Rare that understanding based on a

An aspiration to develop understanding from

broader understanding

series of analyses is conducted

a series of analyses exists

Data Collection

Preparations Support

Scrutiny/Challenge

Customers Confidence in results

Technology development and equipment assessment Fair to Good

Tactical development and warfare assurance Good to Very Good

TABLE 1 FEATURES OF FAST OA VS FULL OA *A SEARIDER IS A MEMBER OF MOD CIVILIAN STAFF WHO IS ON BOARD A NAVY VESSEL FOR THE BENEFIT OF FAST-TIME ANALYTICAL OUTPUT.

companies completing forms in a robust manner. • Time pressures: Completing Fast OA within 4 hours to deliver useful insights to the Captain MWC is a challenge. • Analysis Bias: Working within a fast-paced environment can mean that analysts begin to see false trends and unintentionally focus on data supporting a working hy-

pothesis, instead of fully designing the analytical question at the start of the process. However, a fantastic team working ethic; skilled, experienced analysts, with a structure to the analytical approach; and support from a forward team based at sea all make the Fast OA experience a rewarding and impactful one.

DATA SCIENCE AND ARTIFICIAL INTELLIGENCE

Learning lessons from the past Where the team have completed Fast OA and reconstruction and received a larger amount of data to work with during previous Joint Warrior Exercises, it has been possible to begin to understand bottlenecks that form at data processing points.

IMPACT | AUTUMN 2020

FIGURE 2 REPRESENTATION OF THE DATA SORTING PROCESS IN SIMUL8 MODEL.

A larger Dstl team created a process view using Simul8 in order to review of the system itself. This enabled the analysis team to improve the data flow from ships to analysts. One improvement was the implementation of programmed scripts to automatically sort qualitative data into a more manageable format (see Figure 2).

Fast OA and reconstruction delivered a daily brief to the Joint Tactical Exercise Planning Staff in line with the dictated ‘battle rhythm’ of the command and control of the training exercise

IMPACT AND OUTCOMES

Fast OA and reconstruction  Delivered a daily brief to the Joint Tactical Exercise Planning Staff in line with the dictated ‘battle rhythm’ (schedule) of the command and control of the training exercise.

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 Completed daily analysis of 4-6 of the previous day’s exercise activities alongside presenting a view of their success from a MWC perspective. This analysis was presented in a quad-slide format allowing for various vignettes (for example a narrative, overview and recommendations) to be presented alongside imagery in a concise brief.  Identified areas for MWC Tactical development to take forward with regards to tactics, techniques and procedures that can be trialled and released to the frontline.  Identified areas for analytical improvement such as data collection methods and process to getting data back to MWC, improvement in the Artificial Intelligence for automating signal analysis and instigating debate around ‘Fast OA’ vs ‘OA Faster’. Stephanie Monks is the Defence Capability Change Manager at the Met Office. She was the Defence Science and Technology Laboratory (DSTL)

team leader of the staff working at the Maritime Warfare Centre. Hayley Bird is a lead analyst for the newly established Tactical Reconstruction team based at the Maritime Warfare Centre. Whilst in its infancy, the team plans to expand on and develop the skills demonstrated during Operation PENSEIVE and provide the Navy with a comprehensive resource of track reconstruction and analysis of simulation, trials and exercises and real time events. Content includes material subject to © Crown Copyright (2020), Dstl and MOD. This material is licensed under the terms of the Open Government Licence except where otherwise stated. To view this licence, visit http://www.nationalarchives.gov. uk/doc/open-government-licence/ version/3 or write to the Information Policy Team, The National Archives, Kew, London TW9 4DU, or email: psi@nationalarchives.gov.uk

Geoff Royston

You have almost certainly caught a virus sometime (hopefully not the latest coronavirus). Maybe your computer has had a viral infection too? And have you ever caught an idea? My column in this issue of Impact focuses on things that can spread quickly and widely, as in a classical epidemic, and what analysis can tell us about such outbreaks. They are not confined to the spread of biological or computer pathogens, or of tangible things such as wildfires, but extend to a variety of other often non-material outbreaks – such as financial crises, adoption of innovations, and indeed, ideas. It has been prompted (of course) by the current global COVID-19 epidemic and draws upon the recently published ‘The Rules of Contagion’ by Adam Kucharski, a mathematical epidemiologist at the London School of Hygiene and Tropical Medicine. MODELLING EPIDEMICS

Current news coverage of COVID-19 must have ensured that most people are now all too aware of the characteristic growth curve of an epidemic; the accelerating rise to a peak in cases, and then a (often rather less rapid) fall as the number of cases declines. Such curves are a portal into the realm of mathematical modelling of epidemics. Again, something that lately has been much publicised. As The Rules of Contagion describes, a seminal early use of mathematics in epidemiology was by the surgeon Ronald Ross (who in 1902 had won the Nobel Prize for his work on how mosquitoes transmit malaria). Ross was not only a medic but also a keen amateur mathematician and he put this to good use in his later work. His key analytical innovation, later developed by Anderson McKendrick and William Kermack, was to move beyond previous approaches to the mathematical analysis of epidemics, which were essentially no more than descriptive curve-fitting exercises, to an approach which ‘lifted the bonnet’ by considering the

processes driving epidemics and then modelling these with corresponding equations. The huge advantage was that it was then possible to do ‘what if?’ tests with the resulting model, varying key process parameters, particularly those that might be controllable, e.g. the probability of transmission from an infected person, and see what effect this had. Many people will now be familiar with the R value, the average number of new cases generated by transmission of an infectious agent from someone who is infected with it to someone who is not. Whenever R exceeds one, the number of cases will grow, and grow at an increasing rate – that acceleration is what characterises a classical epidemic. If R starts and stays below one however, the epidemic will fail to take off. When R has started above one and then falls below that, because of increasing immunity, or because it is driven down by control measures, the epidemic will begin to die out. Kucharski notes that R can be broken down into key multiplicative components: duration of infectivity, opportunity for spreading by interactions between hosts, probability of an interaction leading to transmission, and proportion of a population who are susceptible – DOTS for short. (A nice example of the application of the Fermi approach that I discussed in Guesstimate That! Impact Spring 2016). Such decomposition of R into DOTS can help in considering what measures might reduce the magnitude of one or more of its components and thus assist in controlling an epidemic. The Rules of Contagion provides a much fuller account of modelling infectious disease outbreaks, with some fascinating examples and coverage of other key aspects such as the important role that social and other networks play in associated phenomena such as localised hotspots and ‘superspreaders’ of disease. However, the book also shows how the concepts extend far beyond the biological sphere. BEYOND BIOLOGY

‘Epidemics’ can occur with a large range of non-biological outbreaks – for instance the uptake of a technological innovation. That suggests a common underlying mechanism. The underlying fundamentals are simple enough; you need an agent (e.g. a virus, an idea) capable of occupying – © https://coronavirus.data.gov.uk/cases

OutbReak

REPORTED DAILY CASES OF COVID-19 IN THE UK

‘infecting’ – a host (e.g. a body, a mind) that is susceptible to such ‘infection’ by that agent, and a way (e.g. coughing for a virus, texting for an idea) that copies of the agent can be transmitted from the host to multiple other hosts. Given those basic building blocks an accelerating outbreak amongst its potential hosts can occur for an agent – any agent. So for example, the uptake of innovations such as the colour television or the videorecorder typically follows an epidemic-type growth and decline pattern. A new product emerges and some people (‘early adopters’) buy it, this is observed by (‘transmitted to’) others, who like (are ‘infected’ by) and act on the idea of owning it; their ownership is then observed and copied in turn by others. Uptake can be slow and linear or fast and non-linear (epidemic-like), depending on the values of the components of R (the DOTS), and will decline as the market saturates (fewer ‘susceptibles’). Such processes were described in the Diffusion of Innovations, a seminal 1960s book (now in its fifth edition!) by the sociologist Everett Rogers. INFODEMICS

Perhaps the most pervasive example of contagion in the non-biological domain is the spread of information, ideas and ‘memes’, ranging from the adoption of scientific theories to the ability of great tits to peck through milk bottle tops to get the cream. Information spread can happen very rapidly and widely, especially online. Often this can be helpful, but sometimes the spread of information or ideas is harmful, and unfortunately it is false information that tends to spread furthest and fastest. (Because, for example, misinformation is often newsworthy by being outrageous, or because people are receptive to it because it chimes with their other beliefs.) The WHO have highlighted ‘infodemics’ as a major global health challenge. Kucharski discusses the problem of misinformation about health by considering the story of resistance to MMR vaccine, originating from a discredited paper by the (now struck-off) medic Andrew Wakefield, and spread by a vocal online anti-vaccination movement. 48

IMPACT | AUTUMN 2020

CONCLUSION

The Rules of Contagion goes on to discuss a variety of other phenomena – such as computer malware, financial bubbles, social and anti-social behaviour, that can be contagious. In some of these cases – financial bubbles, for example – contagion is high and epidemics are observed (R over 1) in others, shootings and suicides for example, there is evidence of contagion but, fortunately, there are generally only a few knock-on events (R below 1). The similarities between the dynamics of the spread of infectious disease and the dynamics of non-biological contagions are not only interesting, but have also been useful in devising possible measures, targeting one or more of the DOTS factors identified for the former, to influence the latter. For example, Kucharski points out that the adoption of measures analogous to public health interventions has proved quite promising as a way to reduce gun and knife crime, and that dissemination of fake news that often follows disasters can be successfully overtaken by quickly responding with corrective tweets. A deeper understanding of The Rules of Contagion should be of wide benefit. Dr Geoff Royston is a former president of the OR Society and a former chair of the UK Government Operational Research Service. He was head of strategic analysis and operational research in the Department of Health for England, where for almost two decades he was the professional lead for a large group of health analysts.

SIMPLE CONTAGIOUS SPREAD: R = 2

About 95% of a population needs to be vaccinated to prevent outbreaks of measles. (This is another use of R; the proportion of a population that needs to be immune to stop an epidemic breaking out is, roughly, 1 − 1/R0 where R0 is the average number of new cases generated by an infected person at the start of an outbreak, when susceptibility is high. For measles R0 is very big – about 15, so 1 − 1/R0 is 93%). In places where anti-vaccination beliefs have spread and taken root, outbreaks of measles, with the associated fatalities, are now occurring. An ‘infodemic’ can feed an epidemic – and indeed vice versa, as has been happening with fears of COVID-19 providing fertile soil for the spread of all sorts of dangerous myths about prevention or treatment, potentially opening up a truly vicious circle of mutual reinforcement.

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Articles inside

TACTICAL RECONSTRUCTION AND FAST O.R. AT THE MARITIME WARFARE CENTRE

PACKING SHOES EFFICIENTLY

HEALTHY O.R. IN WALES

COMMUNITY-BASED O.R. AND THE CO-CREATION OF KNOWLEDGE IN TIMES OF CRISIS

PREDICTING CRITICAL CARE NEEDS DURING A PANDEMIC

IMPROVING RESOURCE UTILISATION IN PROTOTYPE VEHICLE PRODUCTION