CAPITAL BUDGETING IN HOSPITALS – A GOAL PROGRAMMING APPROACH

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 4143-4154 © TJPRC Pvt. Ltd.

CAPITAL BUDGETING IN HOSPITALS – A GOAL PROGRAMMING APPROACH VEERESH MALAGI1, SANDEEP KUMAR K2 & HARISH BABU G A3 1 2

Department of Mathematics, Jain University, Bangalore, India

Department of Mathematics, Hyderabad Institute of Technology and Management), Medchal (Dist.), Telangana, India 3

Department of Mathematics, REVA University, Rukmini Knowledge Park, Yelahanka, Bengaluru, Karnataka, India

ABSTRACT In order to fully develop the rationale for prescribing the goal programming approach for hospital capital expenditure analysis, we first present the institutional characteristics that prevent the successful application of most efficiencyoriented models to the nonprofit hospital case. We then review several specific and generic economic models that others have considered appropriate for capital expenditure analysis in hospitals. The purpose of this discussion is to point out the weaknesses of these models and to establish a theoretical basis for employing the goal programming approach instead.

The goal programming model for capital analysis is then developed and applied to an actual hospital capital budgeting situation.

KEYWORDS: Hospital Goals, Data, Budget & Constraints

INTRODUCTION Managerial authority in nonprofit hospitals is shared— not necessarily equally—between two groups: doctors and administrators [11, 17]. Each of the two "managements" formulates their own individual policies and pursues

Original Article

Received: Jun 10, 2020; Accepted: Jun 30, 2020; Published: Jul 20, 2020; Paper Id.: IJMPERDJUN2020394

objectives that may not coincide or may even be in direct opposition to one another. This situation is certain to affect hospital resource allocation and thus must be considered in proposing any resource allocation model, whether descriptive or prescriptive. Specifically, the model must address itself to the question of who the decision maker actually is and who’s objective function (whether expressed in terms of profits, output, or utility) is to be maximized.

A proposed model must also deal with the fact that the industry’s primary concern is with delivery of high quality health care services as is evidenced by the nature and the large number of regulations imposed on both the institutions and the individuals who provide these services. Hospital, clinical and personnel licensure and certification requirements cover almost every facet of the health care delivery system. Obviously, the imposition of these and other self-imposed quality standards exercise a significant influence on hospital resource allocation in diverse and material ways [16].

Because most of the models advocated in the literature for hospital resource allocation are economic in nature, the peculiar cost-revenue relationship created by the industry’s third-party, cost-based reimbursement system becomes relevant. This unique system effectively removes incremental cash flows or more specifically, the excess of hospital revenues over costs—as an objective criterion for measuring allocation efficiency in capital spending. For example, in the extreme case, when a hospital’s patient revenues are completely based on the cost of providing patient services, efforts aimed at cost reduction through capital expenditures will also result in reduction of net revenues by an identical amount. Revenues will always equal costs, hence, the present value of net cash flows will be www.tjprc.org

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negative at any rate of discount above zero.

Even in non-extreme cases, the usefulness of this traditional economic measure of allocation efficiency is diminished to the extent that revenues are reimbursed costs, because the spending unit can never realize the full value of any cost-reduction program. And the problem is compounded by the fact that a physician’s own entrepreneurial efficiency is enhanced by any capital investment that enriches or expands the institution’s capacity in his particular area of medical specialty. Since he assumes a share of managerial authority in hospital resource allocation decisions for personal economic gain, but does not directly share in the responsibility for cost control, the outcome, in economic terms, is better described by models that differ materially from the “theory of the firm” approach.

Two groups of models have been presented in the literature as being more or less applicable to (or at least useful in) hospital capital investment analysis. The first group includes capital expenditure models designed especially for public utilities and planned economies. The second is comprised of two subcategories constructed for nonprofit hospitals that [11] has dubbed “organism” and “exchange” models, respectively.

A cost-based reimbursement system and nonprofit status are not unique to hospitals. Public utilities operate under a revenue limitation similar to that of the hospital's cost-based system, in which their rates of return on investment (profit divided by capital investment) are specified by regulatory agencies. Further, utilities are legally required to provide a certain level of service upon demand. Thus, output and capacity, expressed in common units of measure are parameters in both of these capital budgeting models [2, 10].

In simple terms, the decision criterion used by both models is the minimization of the present value of total costs of new capital investments, discounted at a rate of interest representing a cost of capital. Superficially at least, this criterion seems to hold promise for the hospital case; however, hospital output and capacity cannot readily be expressed in common units of measure. In fact, hospital output has never been satisfactorily defined [14] and treating output and capacity as parameters would force hospital decision makers to create intolerable rigidities in the allocation of beds and ancillary services among competing medical specialties (e.g., surgery, pediatrics and obstetrics). Even if this difficulty could be surmounted, the addition of a quality variable to the model would still be required and this would present an even more difficult problem. A model cannot simultaneously maximize one variable (quality) while minimizing another (cost).

Organism models treat the hospital as an entity with its own goals usually the maximization of profits, output, and/or quality of services. Exchange models, by contrast, suggest that the relevant goals are those of the doctors, administrators, and/or trustees associated with the hospital, and treat the hospital as an institution that enables these individuals to attain their own goals through exchange. In their attempts to fit models of the hospital into the usual mold of the theory of the firm, proponents of the organism models suggest, implicitly or explicitly, that the hospital capital expenditure decision process should be compatible with the institution's basic objective. Profit maximization models fail as a result of the cost-based reimbursement system under which hospitals operate, because they prevent capital investment projects from generating revenues in excess of costs [17]. Output and quality maximization models likewise fail because there exists no common unit of measure for either hospital output or the quality of health care services, as discussed earlier. In addition, since most available measures of hospital output are derived qualitatively and are expressed in terms of the numbers or types of services rendered per patient day or bed day [14], they do not add materially to the precision or reliability of the organism model, but merely emphasize and support the idea of a multiplicity of goals inherent in the institutional setting. Further, the exchange models deal with such goal sets in a superior manner.

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DATA OF THE PROBLEM The literature dealing with mathematical programming applications to capital budgeting problems are quite extensive [1, 3, 4, 8, 15, and 18] and span quite a number of years. Its applications to universities, media planning, and sales effort allocation, for example, are well known [5, 12, and 13]; however; its use in allocating resources in nonprofit hospitals has received little attention.

The model we use is based on the technique developed by Charnes and Cooper [5] in which the goals are specified as constraints in a linear programming format, along with additional variables which represent allowable deviations from the goals. The objective function specifies the priorities in achieving the goals.

As stated earlier, while members of a hospital's medical staff are not directly responsible for controlling the institution's cost structure; they often assume an inordinately large role in the allocation of resources to competing capital projects. But cost control is the responsibility of the administrators. It is imaginable, in the extreme case, that pitched battles would be the rule in capital budgeting sessions, as the two "managements" vie for larger shares of the total budget, with the physicians, on the one hand, seeking to extend the hospital's medical facilities, and the administrators, on the other hand, pressured by third-party sponsors, opting for cost-reduction (administrative) projects. (This scenario is descriptive of the approach taken in the university hospital that supplied the information for the application of the model described in the next section.) Even while operating under a common set of institutional goals, the two groups often disagree over capital allocations simply because each ranks the several institutional goals in a different order of priority. Given the need to resolve goal conflicts, the goal programming model appears to be particularly suited to the hospital application.

The first step in applying the model is that of establishing a set of institutional objectives. Once these broad operational goals are established, the administrative and the medical staffs must separately assign their own priority coefficients to each goal. The next step involves evaluating a number of capital investment proposals in terms of the institution's goals and its environmental constraints. A set of numerical weights are devised that "measure" the contributions of each investment proposal toward achievement of one or more goals. Additionally, the impact of each project on the hospital's licensure, financial, physical, and operating policies and regulations are assessed and, together with the measures of goal achievement, formulated into a set of goal programming constraints. The model is then solved twice under a budget constraint set—once using the medical staff's objective function and again using that of the administrative staff. The two solutions are compared in the final step for the purpose of establishing concurrence on mutually acceptable projects and exploring means for compromise on the rest.

The goal programming model described in this section was applied in a 450 bed, Govt. Hospital, Hyderabad. The department chairmen of the medical school were members of the hospital's Executive Committee, along with the hospital director and certain members of his staff. The chief of staff and chairman of the department of surgery was chairman of the Executive Committee. The relevant information is given in Table 1.

Project #: Description Goal www.tjprc.org

Table 6.1: Summary of Hospital Capital Budget Data 2 3 4 5 Hospital Expansion Expansion of Brain Hospital Industrial of Surgical Epidemiology Scanner Training Engineering Facility Department Dept.

Goal % Goal % Goal % Goal % Goal % 1

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7

Patient Screening Clinic

Office Leased Space

Goal %

Goal % editor@tjprc.org

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Achievement:

Staff Positions: Net Investment: Annual Operating Cost Annual Depreciation Expanse Average/Day Patients: Outpatients: Inpatients: Revenues:

1-45% 5-55%

1-10% 4-80% 2-10%

2-10% 5-20% 4-20% 6-50%

1-10% 3-45% 7-5% 2-15% 4-25%

1-5% 3-20% 5-30% 7-45%

2-35% 6-25% 7-40%

3-100%

17

3

4

4

8

5

-

Rs. 603,000

Rs. 425,000

Rs. 1,100,000

Rs.12,000

Rs.60,500

Rs.783,000

-

Rs. 408,420

Rs. 126,127

Rs. 265,000

Rs. 79,5000

Rs. 137,110

Rs. 476.6

Rs.9,750

Rs. 38,710

Rs. 53,125

Rs. 160,000

Rs. 1,500

Rs. 11,110

Rs. 156,600

-

0 1.25

-

-

-

20

-

Rs. 360,000

-

Rs. 1,875

-

Rs. 191,000

-

2 1 Rs. 191,625 Rs. 75,000

Expense Rs. 95,000 Rs. 70,470 reduction: Space 3,930 ft2 400 ft2 600 ft2 3,000 ft2 800 ft2 800 ft2 1,500 ft2 requirements: Net incremental Rs. Rs. Rs. Rs. 634,001 Rs.527,219 Rs. 97, 610 Rs. 698,130 cash 1,026,875 89,000 9,750 requirements * Calculated as follows: First Year Cash Outflow – (Revenues + 45% Annual Depreciation Charge – Cost Reduction); for project #1 these are: Rs. 1,011,420 – 360,000 – 17,419 – 0 = Rs. 634,001 Again, in order to keep the model’s dimensions within reasonable bounds, 7 capital investment projects were selected to be presented here from the many submitted for consideration to the Executive Committee. The basis for inclusion in our model was the individual projects’ interactive characteristics, both with one another and with the hospital’s environmental and operating constraints. The cost and operating data included in the hospital’s capital budget for the 7 projects chosen for analysis are presented in Table 1.

HOSPITAL GOALS The hospital's institutional goals, as formulated by this committee, are presented in Table 2.

Sl. No. 1.

2.

3.

4.

5.

6.

7.

Table 2: Institutional Goals with Assigned Priority Coefficients Priority Coefficients Institutional Goal Medical Administrative Staff Staff Facilitate teaching and research.

50 2 Create a center of excellence in health care.

30 4 Maintain a skilled and motivated force of health care workers.

7 17 Elevate the standards of health care in the United States.

6 5 Satisfy the demand for health care in the community.

3 34 Improve the social and economic climate in the community.

3 1 Provide effective management in order to achieve institutional efficiency 1 37

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and effectiveness.

Total

100

100

The numerical values listed in the columns headed “Medical Staff” and “Administrative Staff” are the priority coefficients independently assigned by the two staffs. While the goals were jointly determined, the two sub-groups assigned their respective sets of coefficients in isolation from each other. Since the sum of each priority coefficient set is 100, the individual coefficients represent a percentage that measures the relative weights of each of the goals.

Admittedly, the coefficients are a type of measurable utility function. However, the two basic objections to use of the measurable utility-the assumptions regarding interpersonal comparisons and stability of the function are overcome in this instance. Interpersonal comparisons are not made in the model since it provides a “correct” answer for each group only and since we discard the coefficients after each capital budgeting session and create new ones each year, we admit to the impermanence of the specific sets of weights used here. Hence, the use of measurable utility is legitimate in this case.

The goals were then divided into 3 sets by each subgroup and labeled primary, secondary, and tertiary goals, designating their descending order of importance. The division was arbitrary and made merely to reduce the dimensions of the formulated model. The goal sets are presented in Table 3.

Table 3: Goal Sets and Weights Medical Staff Administrative Staff Goal Set Goal No. Weight* Goal No Weight* Primary 1 50 5&7 71 Secondary 2 30 3 17 Tertiary 3, 4, 5, 6&7 20 1, 2, 4&6 12 Total 100 100 * Equals the sum of the priority coefficients from Table 2.

Constraint Set Formulation The central feature of the mathematical programming technique is the translation of the many relevant projects, environmental and institutional variables into a set of problem statements called constraints. The first 7 constraints specified in this application limited project acceptance to no more than one of each of the 7 projects submitted. Thus, constraints 1-7 take the form

X i 1

(i = 1, 2, 3… 7)

Where Xi represents the fractional acceptance for project i.

The next 3 constraints specified were institutional constraints. First, in the opinion of certain state legislators and members of the local Staff, the hospital employed too many people for the number of patients served. Consequently, the hospital found it imperative to keep the staff-patient ratio below 3.6 to 1. The hospital’s average full-time equivalent employee count at the time stood at 1,296, with an average daily patient census of 383. To remain within the externally imposed limits, the following staff-patient relationship was specified for the hospital: Current staff + new staff  3.6 (current census + new patients/day) Substituting the current employment and census figures and the incremental project staffing and patient data from Table 1, the relationship is restated as www.tjprc.org

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1,296 + (17X1 + 3 X2 + 4 X3+ 4 X4+ 8 X5+ 5 X6)  3.6(383+ 1.25 X1+ X3+ 20 X6) This inequality simplifies to constraint number 8: 12.5 X1+ 3 X2+ .4 X3+ 4 X4+ 8 X5 - 67 X6  82.8 Second, the hospital had a limited amount of space available in which to expand. This limitation was two dimensional. Total space was rationed and most space was special purpose (i.e. laboratory, patient rooms and administrative-examination space could not be mixed). Thirty-six unused patient rooms were available in the hospital, but since all 7 projects in total called for only 23 additional rooms, the constrained space was limited to the administrativeexamination space (1,500 square feet available) and the laboratory space (4,000 square feet available). These space limitations could be eased, however, if project number 7 were selected, since it would provide an additional 1,500 square feet of administrative – examination space.

Based on these figures and the data from Table 1, constraint number 9 – laboratory space – becomes 3,930X1 + 400 X2 + 600 X3  4,000 And constraint number 10 – administrative-examination space – becomes 3,000 X4 + 800 X5 + 800 X6 – 1,500 X7  1,500 Note that constraint number 9 makes project 1 mutually exclusive of projects 2 and 3. Likewise, if project 7 is taken, project 4 becomes mutually exclusive of projects 5 and 6 in constraint number 10.

The third set of constraints included two series of 3 budget constraints each – one series for the medical group and the other for the administrators. The constraint formulations were based on project net incremental cash requirements for a single period, as listed in Table 1. The impact of neglecting future cash flows diminishes in view of third-party reimbursement practices and the eleemosynary nature of the non-profit hospital. Since the costs associated with accepted projects automatically become part of the institution’s cost base for reimbursement purposes, a significant portion of any cash flow deficits are covered by payments received from third-party guarantors. Financial viability of the projects is assured by these receipts, plus the collections from self-sponsored patients and other non-patient revenues (for this particular hospital, appropriations from the state legislature).

Funds available for investment in this period totaled Rs. 2,819,667, based on the hospital’s projected operating and capital budgets. The budget constraint statements were formulated to allocate these funds separately to each group’s primary, secondary and tertiary goal sets in the proportions given by the two sets of weights listed in Table 3. The administrative staff’s budget allocations were: 71% (of Rs. 2,819,667, or Rs. 2,001,964) to achieving primary goals; 17% (Rs. 479,343) to achieving secondary goals; and 12% (Rs. 338,630) to achieving tertiary goals. For the medical staff, 50% (Rs. 1,409,834) was allocated to primary goals, 30% (Rs. 845,900) to secondary goals, and 20% (Rs. 563,993) to tertiary goals.

Goal achievement for each project, as listed in Table 1, was assigned arbitrarily by the Executive Committee (meeting as a whole), with the advice of the individual project sponsors. Project 3, for example, lists goal achievement as being:

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Goal 2 4 5 6

Goal Classification Percent Administrative 10% Tertiary 20 Tertiary 20 Primary 50 Tertiary

4149

Medical Secondary Tertiary Tertiary Tertiary

According to Table 3 the administrative group selected goal 5 as a primary goal, and goals2, 4 and 6 as tertiary goals. Thus, for this project (from the administrators’ point of view) 20% of project 3’s benefits (and implicitly its total net costs) are directed toward achievement of primary goals, 0% toward secondary goals, and 80% toward tertiary goals.

Consequently, 20% of project 3’s net incremental cash requirements, or (.20XRs. 1,026,875=) Rs. 205,375 was listed in the administrators; primary goal budget constraint, and the remainder (Rs. 821,500) was listed in their tertiary goal constraint. The medical group’s allocation for this same project is 0% toward primary goals, 10% (Rs. 102,688) toward secondary goals, and 90% (Rs. 924,187) toward tertiary goals (see Table 3). This same procedure was followed for the other six projects, thus combining the project goal achievement percentages from the top line in Table 1, the goal set weights from Table 3, and the net incremental cash requirements for each project from the bottom line in Table 1, into six budget constraint coefficients for each project. The coefficients and the total available budget were then combined into the two sets of budget constraints shown below.

ADMINISTRATIVE STAFF BUDGET CONSTRAINTS Primary Goal 348,701X1 + 0 X2 + 205,375 X3 +4,450 X4+ 73,207 X5 + 279,252 X6 + 0 X7  2,001,964 Secondary Goals: 0X1 + 0 X2 + 0 X3 +40,050 X4+ 19,522 X5 + 0 X6 + 9,750 X7  497,343 Tertiary Goals 285,300X1 + 527,219 X2 + 821,500 X3 +44,500 X4+ 4,881 X5 + 418,878 X6 + 0 X7  338,360

MEDICAL STAFF BUDGET CONSTRAINTS Primary Goals 285,300X1 + 52,722 X2 + 0 X3 +8,900 X4+ 4,881 X5 + 0 X6 + 0 X7  1,490,834 Secondary Goals 0X1 + 52,722 X2 + 102,688 X3 +13,350 X4+ 0 X5 + 244,345 X6 + 0 X7  845,900

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Tertiary Goals 348,701X1 + 421,775 X2 + 924,187 X3 +66,750 X4+ 92,729 X5 + 453,784 X6 + 9,705 X7  563,933 The objective function in the traditional goal-programming framework is expressed as m

Minimize

 (P i 1



i

d i  Pi  d i )









Where p i are the priorities coefficients assigned to goal i, and d i , d i are the positive and negative deviations from that goal. However, because our formulation considers only negative deviations, this formulation is quite similar to the “dual” formulation of a traditional linear programming model.

RESULTS AND ANALYSIS Lengthy and often heated budget meetings between the administrative and medical staffs left little doubt that a joint determination of the hospital capital budget would be extremely difficult to achieve. This rather obvious conclusion was confirmed when we solved the formulations presented in through a strict linear programming solution technique and compared the two sets of results shown in columns (2) and (3) of Table 5. While projects 1 and 6 are common to both solutions, one hundred percent acceptance of these two projects absorbs only about Rs. 1.5 million of unallocated funds.

The problem of how to divide this residual sum between the two groups still remains.

Table 5: Deviation Structure for Unallocated Funds in the Budget Constraints Projects

X 1  ......  X 7

d1 + 1d

d 3

d 2

 1

X 1  ......  X 7

- 1d

X 1  ......  X 7

- 0d1

 1 

+ 0d

 2

+ 1d

 2 

- 1d 2

Funds Constraints Limits

+ 0d

 3

= (primary limit)

+ 0d

 3

= (secondary limit)



+ 1d 3

= (tertiary limit)

Table 6: Project Acceptance Levels (3)

(1)

(2)

(4)

Project Number

Administrative Linear Programming Solution

Medical Linear Programming Solution

Compromise Linear Programming Solution

1 2 3 4 5 6 7

0.939 0.000 0.000 0.000 1.000 0.160 1.000

1.000 0.000 0.000 0.389 0.000 0.417 0.000

0.778 0.859 1.000 0.467 1.000 1.000 1.000

(5) Compromise Mixed Integer Programming Solution 0.000 1.000 1.000 0.467 1.000 1.000 1.000

Since a joint amicable allocation of funds was not possible either in actual fact or implicitly through the linear programming solution, we merged the separate administrative and medical budget constraints into a forced compromise

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formulation, which contains all 13 constraints. Both sets of deviation variables d i were retained in constructing this formulation, thus adding 3 additional variables. Columns (4) and (5) of Table 5 present the project acceptance levels for this formulation as determined through strict linear programming and mixed integer programming solution techniques, respectively. In the latter solution, projects 4 and 5 were considered divisible above certain minimum budget levels. The interpretation of all 4 solutions is facilitated by recalling that because of space limitations, project 1 is mutually exclusive of projects 2 and 3 [since all are non-divisible] and if project 7 is accepted, project 4 is mutually exclusive of projects 5 and 6 over a project acceptance level of 46.67% of project 4 [see constraint 10].

The linear programming results of the combined administrative and medical formulations [column (4)] resolve the unallocated funds problem, but this compromise model clearly implies a weighted average of priority values and suffers from the other defects noted earlier. These budget allocations, therefore, are not likely to pleasing to either group from their respective polar positions. It has the advantage of including at least parts of all projects in the capital budget, but it violates the project mutual exclusivity and divisibility considerations.

Although these problems are resolved through the application of the mixed integer programming solution technique [column (5)], the problem of an “optimal” compromise solution remains unless equality of power between the medical and administrative staffs is assumed. In other words, the model will produce an optimal allocation of funds (in the goal programming sense) provided neither group is permitted to dominate the other in specifying the institution’s goals, assigning the goal achievement points to the several projects, and assigning reward points to the divergent positions. Let’s briefly examine each of these dimensions to the hospital capital allocation problem.

First, unless the institution’s goals are correctly specified, and an appropriate unit of measure is available to measure project contribution to goal achievement, an obvious bias will creep into the initial models. Our preliminary tests demonstrated that this misspecification is amplified through forced compromise. Second, the allocation of project goal achievement percentages must be equitably assigned. In the present application, these percentages were awarded by the Hospital’s Executive Committee. A disproportionate committee representation toward one of the polar positions would clearly bias the initial and compromise formulations. Finally, the allocation of reward points to the divergent positions must be equitable. This weighting must insure a fair representation for all participants in the institution’s sphere of activities. In our model, the divergent positions were equally weighted, but the weights can be adjusted in either direction if equality in power between or among groups is inappropriate.

Although the specifications of these dimensions in the present application may not perfectly negate these potential pitfalls, we believe our criteria measures provide the rational underpinnings for a normative approach to the capital budgeting problem in nonprofit contexts. The initial construction of each model and its subsequent revision offer significant managerial insights into both organizational and operational realities, and thereby improve the resource allocation process.

This application of the goal programming technique to the hospital capital expenditure evaluation of resources can be achieved in a nonprofit context. The criterion used in judging rationality is the minimization of perception weighted deviations from a qualitative goal set. The unique feature of this model is the translation of the qualitative institutional goals into dollar values as a common unit of measure. It permits the outcome of the capital budgeting decision to be expressed conveniently in dollar terms. Thus, while the model gives the appearance of orthodoxy with regard to capital

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budgeting decisions in the for-profit enterprise, it does not directly address either the wealth maximization problem or the problem of institutional or project financial viability. Instead, the quality of both the delivery and administration of health care is emphasized through the expert perceptions of physicians and hospital administrators.

While the model as described was implemented in a hospital context, we believe that it is general enough to enable adaptation to a wide range of nonprofit institutions. As in all mathematical allocative models, however, the results are only as good as the accuracy with which the model describes the realities of the institution. Further, one must take care to insure that the model is used as a tool in the decision process and not as a black box oracle. If properly employed, this particular version of the goal programming technique can significantly enhance the rationality of the capital budgeting process in many nonprofit contexts.

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