Srikumar ACHARYA, Mitali Madhumita ACHARYA

Generalized transformation techniques for multi-choice linear programming problems

The multi-choice programming allows the decision maker to consider multiple number ofresources for each constraint or goal. Multi-choice linear programming problem can not be solveddirectly using the traditional linear programming technique. However, to deal with the multi-choiceparameters, multiplicative terms of binary variables may be used in the transformed mathematicalmodel. Recently, Biswal and Acharya [2] have proposed a methodology to transform the multi-choicelinear programming problem to an equivalent mathematical programming model, which can accommodate a maximum of eight goals on the right hand side of any constraint. In this paper we present twomodels as generalized transformation the multi-choice linear programming problem. Using any one ofthe transformation techniques a decision maker can handle a parameter with finite number of choices.Binary variables are introduced to formulate a non-linear mixed integer programming model. Using anon-linear programming software optimal solution of the proposed model can be obtained. Finally, anumerical example is presented to illustrate the transformation technique and the solution procedure.

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1] Biswal, M.P. and Acharya, S., Solving multichoice linear programming problems by interpolating polynomials, Mathematical and Computer Modelling, 54, 1405-1412 (2011).
[2] Biswal, M.P. and Acharya, S., Transformation of multi-choice linear programming problem, Applied Mathematics and Computation, 210, 182-188 (2009).
[3] Biswal, M.P. and Acharya, S., Multi-choice multi-objective linear programming problem, Journal of Interdisciplinary Mathematics, 12, 606-637 (2009).
[4] Chang, C.-T., An efficient linearization approach for mixed integer problems, European Journal of Operational Research, 123, 652- 659 (2001).
[5] Chang, C.-T., On the mixed binary goal programming problems, Applied Mathematics and Computation, 159(3), 759-768 (2004)
[6] Chang, C.-T., Multi-choice goal programming, Omega. The Internatioanl Journal of Management Science, 35, 389-396 (2007).
[7] Chang, C.-T., Revised multi-choice goal programming problem, Applied Mathematical modelling, 32(12), 2587-2595 (2008).
[8] Dantzig, G.B., Linear programming under uncertainty, Management Science, 1, 3-4 (1955).
[9] Hiller, F., Lieberman, G., Introduction to Operations Research, McGraw-Hill, New York (1990).
[10] Kent, B.B., Bare, B., Field, R.C., Bradley, G.A., Natural resource land management planning using large-scale linear programs: the usda forest service experience with FORPLAN , Operations Research, 39(1), 13-27 (1991).
[11] Liao, C.-N., Formulating the multi-segment goal programming, Computers & Industrial Engineering, 56(1), 138-141 (2008).
[12] March, J.G., Shapira, Z., Variable risk preferences and the focus of attention, Psychological Review, 99, 172-183 (1992).
[13] Rardin, Ronald L., Optimization in Operations Research, Pearson Education, India (2005).
[14] Ravindran, A., Phillips Don, T., Solberg James, J., Operations Research Principles & Practice, second ed., John Wiley, New York (1987).
[15] Schrage, L., LINGO Release 11.0. LINDO System (Inc. 2008).