Multi-choice stochastic bi-level programming problem in cooperative nature via fuzzy programming approach


1 School of Applied Sciences and Humanities, Haldia Institute of Technology, Purba Midnapore, 721 157, Haldia, India

2 Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, 721 102, Midnapore, India


In this paper, a Multi-Choice Stochastic Bi-Level Programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general transformation technique with the help of binary variables is used to transform the multi-choice type cost coefficients of the objective functions of Decision Makers(DMs). Then the transformed problem is considered as a deterministic multi-choice bi-level programming problem. Finally, a numerical example is presented to illustrate the usefulness of the paper.