IMPERIAL INSTITUTE OF HIGHER EDUCATION
Table of Content
Table of Content .................................................................................................................... 1 1.0 Introduction .................................................................................................................... 2 1.1 Assignment Objectives .............................................................................................. 2 1.2 Organization Background .......................................................................................... 2 2.0 Problem Background ..................................................................................................... 4 2.1 Issue Definition .......................................................................................................... 4 3.0 Project Description......................................................................................................... 5 3.1 Contract of Leather Line ............................................................................................ 5 3.2 Limitations ................................................................................................................. 6 3.3 Project Goal ............................................................................................................... 6 3.4 Summery of the Scenario ........................................................................................... 6 4.0 Theory of Analysis ......................................................................................................... 7 5.0 Analysis and Calculations .............................................................................................. 9 Cost Calculation ............................................................................................................... 10 6.0 Findings and Recommendations .................................................................................. 13 7.0 Reference ..................................................................................................................... 14
Quantitative Methods
(Masters of Business Administration)
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IMPERIAL INSTITUTE OF HIGHER EDUCATION
1.0 Introduction 1.1 Assignment Objectives
Understand what is Linear Programming and other methods are. Identify the best method for the given Scenario. Explain the outcomes of the Calculations. Understand the Problem scenario in an organization Present an inclusive justification with use of figures and illustrations to support all the decisions made in calculations.
1.2 Organization Background The main objective of this report is to analyze the given scenario and make the best choice for more profit and less cost for the Organization.
DSI Footwear
This company started as a small family business by Mr. D. Samson Rajapaksha in 1962. And after 1970 sons of Mr. D. Samson Rajapaksha took over the business. Since then the company was company was controlled by board of directors and later on the company divided in to multiple companies and formed DSI group of companies. Today DSI footwear is the largest footwear manufacturing company in Sri Lanka and DSI has over 2000 employees with modern equipments, machinery and high technology.
Quantitative Methods
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IMPERIAL INSTITUTE OF HIGHER EDUCATION
The DSI produce vast types of shoes for the local market and sales of shoes are done in DSI Showrooms Island wide. Below shows some of the shoe products in the market Eva/Rubber flip flops Children’s Sandals Ladies/Gents Sandals Leather Shoes Canvas Shoes Rubber Boots Indoor Slippers Sport Shoes International Market of DSI is very large and shoes are distributed all over the world especially in countries like Asian Countries, America, Africa, Europe and the market is still expanding.
Figure 1: Distributing Countries of DSI footwear [Source: DSI footwear]
Quantitative Methods
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IMPERIAL INSTITUTE OF HIGHER EDUCATION
2.0 Problem Background
DSI Company is fully equipped with all the machinery and very experienced team of employees who are able to manufacture shoes that is necessary for day today sales. But in some seasons like January, December (when school start/festival seasons) the production capacity of all the manufacturing plants are not enough for the very high demand. Therefore in above special occasions DSI Company outsources the production of shoes to some extent. This analysis and the calculations take place in the outsourcing segment of the organization
2.1 Issue Definition The outsourced company is “Leather Line� which is a small company and they produce different types of shoes. However before accepting the stocks DSI does a quality check on each and every shoe they out sourced. In this scenario the contract was as below.
Special request of shoes are Walkline 1 and Walkline 2 which is a very famous and two of most salable shoes in festive seasons. DSI requested altogether 2,000 sets of shoes from both types. Materials and other necessities like man force and machinery are self supplied by the Walkline and have to produce shoes for next year festive season. As in the contract at least fourty percent (40%) of the produced shoes are to be made from Walkline 1. And different sizes of the shoes are given to produce different numbers.
Quantitative Methods
(Masters of Business Administration)
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IMPERIAL INSTITUTE OF HIGHER EDUCATION
3.0 Project Description
3.1 Contract of Leather Line After the agreements are signed as above resources are allocated for the production of the shoes. ď ś Even though a shoe is not done by a single worker, overall process time for Walkline 1 shoe is 5 Labor hours due to complex implementation of the shoe and the increased comfortability factor. And for this shoe, manufacturing cost is Rs 500 per shoe.
ď ś For the manufacturing of the Walkline 2 shoe takes less time because it is cheaper shoe than the Walkline 1 and the comfort ability is lower than the Walkline 1 shoe. Therefore the total labor hours to produce 1 shoe are 3 Labor hours. The manufacturing cost for this shoe is Rs 450
Figure 2:
Walk Line 1
Walk Line 2 (yellow & Gray) [Source: DSI Footwear]
The foot Manufacturer has decided to use 25000 of total Labor hours and may use additional labor hours if necessary.
Quantitative Methods
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IMPERIAL INSTITUTE OF HIGHER EDUCATION
3.2 Limitations Other companies who has outsourced by DSI is neglected Shoe sizes are neglected Shoe Quantities by the sizes are neglected Only totally quantity is considered.
3.3 Project Goal The goal is to minimize the cost of production and produce the shoes keeping the conditions.
3.4 Summery of the Scenario
Units to be Produced
6,000
Number of Brands
2 (Walkline 1, Walkline 2)
Percentage of production
Walkline 1 minimum 40%
Walkline 1 Labor hours per unit
5
Walkline 2 Labor hours per unit
3
Total labor hours
25000
Cost of Walkline 1 per unit
500
Cost of Walkline 2 per unit
450
And the ultimate goal is to minimize the cost of production to get the maximum profits
Quantitative Methods
(Masters of Business Administration)
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IMPERIAL INSTITUTE OF HIGHER EDUCATION
4.0 Theory of Analysis
To carry out the analysis of the prices of the Dialog Telekom car TV set, the technique of “Descriptive Statistics” is used. Linear Programming – “Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and non-negativity constraints. Simplistically, linear programming is the optimization of an outcome based on some set of constraints using a linear mathematical model.” (Bellman R, 2006)
Linear Programming “Linear programming can be viewed as part of a great revolutionary development which has given mankind the ability to state general goals and to lay out a path of detailed decisions to take in order to “best” achieve its goals when faced with practical situations of great complexity.” (GEORGE B. DANTZIG, 2002)
Linear Programming – “Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions. A typical example would be taking the limitations of materials and labor, and then determining the "best" production levels for maximal profits under those conditions.” (Stapel, Elizabeth, 2010) There are 2 types in linear programming. They are Quantitative Methods
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Graphical method Simplex method
Graphical Method When there are only two variables it can be demonstrated using “x” and “y” in a graph. Therefore graphical representation is possible.
Simplex Method When there are more than two variables graphical representation is impossible because we cannot produce more than two dimensional graph in a book. Therefore simplex method is used where they introduce slack variable to solve the mathematical problem
Conclusion In this specific scenario there are only two variables. They are Walkline 1 and Walkline 2 which are two types of shoes. Therefore Graphical method is used.
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5.0 Analysis and Calculations
The calculations of the scenario is done as below
Object: Minimize C = 500a + 250b where “a”, “b” are the units of Walkline 1 and Walkline 2
Subject to: Total Units: Product 'Walkline 1' percentage:
a + b ≥ 6,000 a/(a+b) ≥ 0.4
Labor Hours: Non Negativity:
5a + 3b ≥ 25000 a+b≥0
=> 6a - 4b = 0
Find A: a+b= 6a - 4b = 4a + 4b = 10a = a= b=
6,000 0 24,000 24,000 2,400 3,600
1st Eq. 2nd Eq. 1st Eq. * 3 3rd Eq + 2nd Eq.
Coordinates are (2400, 3600)
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IMPERIAL INSTITUTE OF HIGHER EDUCATION
Find B: 5a + 3b = a+b= 3a + 3b = 2a = a= b=
25,000 6,000 18,000 7,000 3500 2500
1st Eq. 2nd Eq. 2nd Eq. * 3 1st Eq. - 3rd Eq
Coordinates are (3500, 2500)
Find C: Using the Equation a + b = 6000 When b = 0; a = 6000 Therefore point C = (6000,0)
Cost Calculation Point A: 500a + 250b = C a = 2400, b = 3600 therefore; 1,200,000 + 900,000 = 2,100,000
Point B: 500a + 250b = C a = 3500, b = 2500 therefore; 1,750,000 + 625,000 = 2,375,000
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Point C: 500a + 250b = C a = 6000, b = 0 therefore; 3,000,000
Graphical Representation of the Equations
6a – 4b = 0 a + b = 6,000 5a + 3b = 25,000
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Summarized Graph Points
Coordinates
Costs
O
∞
∞
A
(2400,3600)
2,100,000
B
(3500,2500)
2,375,000
C
(6000,0)
3,000,000
The Chosen Point = A Walkline 1 production = 2400 Walkline 2 Production = 3600 Cost = Rs. 2,100,000
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6.0 Findings and Recommendations
This scenario is about outsourcing contract of DSI. Two types of shoes are outsourced which named Walkline 1 and Walkline 2. And some conditions are given to the contractor. The main target of this analysis is to find the best number of shoes to be made with the minimum cost. With the cost of the unit price equation is made and using that equation and other conditional equations problem is calculated and solved as below. Since there are only two variables, Walkline 1 and Walkline 2 graphical representation method is used. And the necessary area of the graph is highlighted using four points in the graph which are A, B, C and O. After the calculations A, B, C, O Base points values and cost is calculated and compared in a table. After all the calculations and analysis it is unveiled the amount of Walkline 1 and Walkline 2 to be produced. Walkline 1 Walkline 2
2400 3600
One main condition is that Walkline 1 production should be above 40 percent. In this case after calculations it is shown as 66.6%. Therefore the condition is satisfied. And among that costs that is calculated this ratio is the best to save the money and to reduce cost. Therefore the recommendation for the manufacturing of the shoes is to produce 2400 of Walkline 1 shoes and to produce 3600 of Walkline 2 shoes.
Quantitative Methods
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7.0 Reference
DSI Footwear. Available at: http://www.dsifootwear.com/ [Accessed July 15, 201] DSI Footwear. Available at: http://www.dsifootwear.com/internationalMarkets.php [Accessed July 15, 2010]. DSI Samson Group. Available at: http://www.dsi.lk/catalogue.php?&limit=0&coid=SSL&docname=1.jpg&coname= &logo=DSI.bmp [Accessed July 15, 2010]. Linear Programming -- from Wolfram MathWorld. Available at: http://mathworld.wolfram.com/LinearProgramming.html [Accessed July 15, 2010]. Linear Programming: Introduction. Available at: http://www.purplemath.com/modules/linprog.htm [Accessed July 15, 2010]. LinearProgramming_article.pdf. Available at: http://www2.informs.org/History/dantzig/LinearProgramming_article.pdf [Accessed July 15, 2010]. M. Walk Black2.jpg (JPEG Image, 580x447 pixels). Available at: http://www.mbtshow.com/images/M.%20Walk%20Black2.jpg [Accessed July 15, 2010]. NEOS. Available at: http://wiki.mcs.anl.gov/NEOS/index.php/NEOS_Wiki [Accessed July 15, 2010].
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