Multi-level Nonlinear Programming Problem with Some Multi-choice Parameter

Abstract

Decentralized planning is important for modeling a real-life decision-making problem. Multi-level programming is a very powerful tool for modeling such type of decentralized planning problems. In a multi-level programming problem, the decision is taken by several decision makers who are in different levels. In this paper, we studied a multi-level nonlinear programming problem where some (or all) of the coefficients of the objectives and the constraints are multi-choice type. We propose a suitable solution procedure to solve the stated multi-level programming problem. To solve these type of problems, first we tackle each multi-choice parameter of the multi-level programming problem by using interpolating polynomial and obtain a multi-level mixed integer nonlinear programming problem. Then we use the concept of tolerance membership function for the objectives and the control variables of the decision makers and formulate a fuzzy max–min type decision model to obtain a Pareto optimal solution of the transformed multi-level programming problem. We present a numerical example to illustrate the solution procedure of the stated problem.