PROJECT SELECTION DECISION MAKING-A GOAL PROGRAMMING APPROACH

Transcription

1 Pacific-Asian Journal of Mathematics, Volume 5, No. 2, July-December 2011 PROJECT SELECTION DECISION MAKING-A GOAL PROGRAMMING APPROACH V. SUBBAIAH, G. RAVINDRA BABU & S. D. SHARMA ABSTRACT: This paper will provide a critical review of capital budgeting and an attempt to specified for consideration of nine mutually exclusive projects with given present values of out lays for the periods and given present values of investment proposal of large scale industry. An approach using goal programming is described as a possible practical alternative. 1. INTRODUCTION Optimization techniques are those techniques which seek to maximize or minimize a function of one more variable when the variable can be independent or related in some way or the other. During the last four decades a large number of optimization techniques have emerged in the field of business, industry and government. Mathematical programming is a general class of optimization problem to maximize or minimize an objective function dealing with many interrelated variables subject to an set of restraining conditions. Such problems are usually called programming problems. These are classified according to the characteristics of the decision environment. The theoretical models of capital budgeting demonstrate the advantage of accepting all projects with positive NPV (Net Present Value) or IRP (Internal Rate of Return) greater than the cost of capital. Yet the study indicated that 80% of the companies imposed some overall capital constraints. This capital rationing was largely self-imposed by the firms rather than by external forces. Since capital rationing practices are imposed by some of the most profitable corporations, these evidences would indicate that financial executives may impose capital rationing to reflect factors other than the cost of capital. The 163 respondents in the survey were asked to rank their financial objectives in order of importance. By a large margin the firms ranked maximization of earning per share as their primary objective. But the frequently the decision rule indicated by a discounted cash flow analysis may be in direct conflict with this particular objective. A short example may serve to illustrate this point. Assume a firm has to unrelated projects in which it can invest; the capital rationing constraint makes it possible to accept only one of the projects. Project A will generalize relatively higher cash flows, but because of the depreciation and the Keywords: Capital Budgeting Goal Programming.

2 140 V. Subbaiah, G. Ravindra Babu & S. D. Sharma amortization associated with it. The accounting earning during the first years of its life will be quite small. The IRR on project A is 20%. By way of contrast project B has an IRR of only 15%, but its first year contribution to according income would be significantly greater than the project A s. The question facing the financial manager of the form is how to evaluate each of these factors. Should he blindly follow the rules of theoretical model and accept the project A, or should he introduce the next year s earning objective in to the picture? It he should consider earning, how much IRR would he deal willing to sacrifice for an additional Rs earning per share? One percent? Two per cent? May be he should accept project B instead. After all, those additional first year earnings may help the firm achieve its budget objectives. For that matter, it may also be in the beast interest of stock holders as well as, because it is well known that the market often reacts to reported growth in earnings. The difficulty of the decision-making process in further compounded as the number of projects and the size of the capital budget is increased. Imagine complexity of selecting the optimum set of projects from 150 alternatives. The preceding discussion illustrates the dilemma financial managers often face in attempting to decide among alternative investment proposals. The lack of confidence in the pure theoretical approach is blatantly apparent when a manager is confronted with a situation where the acceptance of the theoretical optimal solution has a significant adverse effect on other operational goals such as current earnings to return on investment. It is obvious that a pragmatic approach is required to benefit the operational financial manager. Yet, the recently developed and recommended discounted cash flow concepts should not be abandoned because they give the manager information as the long-run effect on objectives. What is needed is a procedure that combines the best features of both theory and practice to give the manager a workable and feasible approach. Furthermore, this procedure must be flexible so that it can be modified and adapted to meet the specific needs of any individual company. For a method to be practicable, it must allow the operational manager to state a range of objectives or factors that be considers important for his company. These relevant factors should be integrally included, not excluded from the procedure used in deciding among various investment alternatives. As implied above, these considerations could and probably should, differ from one company to another. 2. DATA OF THE PROBLEM The data specifies for consideration nine mutually exclusive projects with given present values of outlays for periods I&II and given present values of investment proposals of large-scale industry in Hyderabad.

3 Project Selection Decision Making-a Goal Programming Approach 141 The required information is given in the following Table 1 Table 1 Investment PV for outlays PV of Sales for Man-Hours project for periods investments periods for periods I II I II I II THE GOAL PROGRAMMING MODEL 3.1 The Required Goals are Developed as Follows: G1: Present Value of Investment Goal 14X X X X X X X X X 9 + d 1 = 32.4 G2: Budget ceiling goals 12X X 2 + 6X 3 + 6X X 5 + 6X X X 8 +18X 9 + d 2 = X 1 + 7X 2 + 6X 3 + 2X X 5 + 6X 6 + 4X 7 + 3X 8 + 3X 9 + d 3 = 20.0 G3: Sales Goals 14X X X X X X X X X 9 + d 4 d 4 + = X X X X X X X X X 9 + d 5 = 84.0 G4: Employment Goals 10X X X 3 + 9X X X 6 + 7X X 8 + 8X 9 + d 6 d 6 + = X X X X X X 6 + 9X X X 9 + d 7 d 7 + = 40.0 In the present model, we propose the different priority coefficient (p i ) assigned to different goals are assumed to be as follows:

4 142 V. Subbaiah, G. Ravindra Babu & S. D. Sharma Goals Table 2 priority coefficients Net present value 1 Budget constraint for period I 2 Budget constraint for period II 3 Negative deviation of sales goal 2 Negative deviation of sales goal II 3 Negative deviation Employment goal I 4 Negative deviation Employment goal II 4 Positive deviation of sales goal l 5 Positive deviation Employment goal I 6 positive deviation Employment goal II Objective Function Minimize Z = P 1 d 1 + p 2 d 2 + p 3 d 3 + p 2 d 4 + 4p 3 d 5 + p 4 d 6 + p 4 d 7 + p 5 d p 6 d p 6 d RESULT AND DISCUSSION The solution will be obtained by using OM for windows computer software may be interpreted as follows: X 1 = 0.0, X 2 = 0.0, X 3 = , X 4 = , X 5 = , X 6 = 0.0, X 7 = 0.0, X 8 = 0.0, X 9 = Goal Goal programming solution Goal constraints Total X 3 X 4 X 5 X 9 Net Present value Budget Constraints-I Budget Constraints-II Sales Goal I Sales Goal II Employment Goal I Employment Goal II Clearly the solution reveals those units of project X 3, units of project X 4, units of project X 5 and Units of project X 9 should be chosen. If the respective units of these projects are chosen four of seven goals. That is two budget constraint goals that is both for period one and two sales goals that is

5 Project Selection Decision Making-a Goal Programming Approach 143 both for period one and two would be achieved fully as desired. While the net present value goal would be over achieved as desired. In the formulation yielding a total net present value of 84.0 and the last goals. That is two employment goals relating to period one and period two are found to be over achieved requiring total man hours per day to the extent of in period one and in period two. These goals were found to be not achieved as desired since both overachievement and under achievement of these goals were considered to be undesirable in the goal programming model. The attributing factor to this solution is assignment of lower priority co-efficient to the two employment goals. One of the characteristics features which may be observed from the above is that all goals with higher priority co-efficient are achieved as desired and goals with lower priority were found to be not achieved as desired. 5. CONCLUSION A critical review of capital budgeting is done with goal programming approach and The data specified for consideration nine mutually exclusive projects with given present values of outlays for periods I&II and given present values of investment proposals of large-scale industry in Hyderabad. REFERENCES [1] Aderoba A., A Goal Programming Model for National Revenue Allocation, Industrial Engineering, 23, (1994), 3-8. [2] Alex, and E. R. B., et al., Process Synthesis and Optimization Tool for Environmental Design: Methodology and Structure, Computer and Chemical Engineering, 24(2-7), (2000), [3] Andrease, et al., A Comparision of Electricity Market Design in Net Work, Operation Research, 57, (2009), [4] Aviv Y., et al., Design for Postponement a Comprehensive Characterization of Its Benefits Under Unknown Demand Distribution, Operation Research, 49(5), (2001), [5] Blahe J., et al., A Goal Programming Approach to Strategic Resource Allocation in Acute Cane in Hospitals, European Journal of Operation Research, (2007), [6] Chang N., A Fuzzy Goal Programming Approach for the Optimal Planning of Metropolitan Solid Waste Management Systems, European Journal of Operation Research, 99(2), (1997), [7] Chino. Ter Chang, Mixed Binary Interval Goal Programming, Journal of O R Society, 57(4), (2006), [8] Gang Kou, and Yipeng, A Bibliography Analysis of Multi Criteria Decision Making in Computer Science, A Journal of Communication in Computer of Information Science, (2009),

6 144 V. Subbaiah, G. Ravindra Babu & S. D. Sharma [9] Jaewook Lee, et al., A Hybrid Approach of Goal Programming for Weapon System Selection, Portal, (2010), [10] Javad D., et al., Using Aopsis Method with Goal Programming for Best Solution of Strategic Plans in B.Sc Model, A Journal of American Science, 6(30), (2010). V. Subbaiah Department ofmathematics, Meerut College, Meerut, U.P., India. G. Ravindra Babu Department of Computer Science and Engineering, Sri Chaitanya College of Engineering and Technology, Shariguda (village), Ibrahim Patnam (Mandal), RR (dist), Hyderabad, AP, India. S. D. Sharma Department ofmathematics, Meerut College, Meerut, U.P., India.