A linear programming approach for linear multi-level programming problems

Abstract

In an earlier paper, we proposed a modified fuzzy programming method to handle higher level multi-level decentralized programming problems (ML(D)PPs). Here we present a simple and practical method to solve the same. This method overcomes the subjectivity inherent in choosing the tolerance values and the membership functions. We consider a linear ML(D)PP and apply linear programming (LP) for the optimization of the system in a supervised search procedure, supervised by the higher level decision maker (DM). The higher level DM provides the preferred values of the decision variables under his control to enable the lower level DM to search for his optimum in a narrower feasible space. The basic idea is to reduce the feasible space of a decision variable at each level until a satisfactory point is sought at the last level.

Keywords:

• linear multi-level programming problem
• ideal/optimal solution
• satisfactory/compromise solution
• weighting method
• fuzzy weights
• sequential linear goal programming

Acknowledgements

This work is supported by a research grant from the All India Council for Technical Education, New Delhi. The first author is grateful to AICTE, New Delhi.