Genetic Algorithm Based Goal Programming Procedure for Solving Interval-Valued Multilevel Programming Problems

This article presents goal programming (GP)procedure for solving Interval-valued multilevelprogramming (MLP) problems by using geneticalgorithm (GA) in a hierarchical decision makingand planning situation of anorganization.Intheproposed approach, first the individual best andleast solutions of the objectives of the decisionmakers (DMs) located at different hierarchicallevels are determined by using the GA method.Then, the target intervals of each of the objectivesand decision vectors controlled by the upper-levelDMs are defined in the inexact decisionenvironment.Then, in the model formulation, theintervalvalued objectives and control vectors aretransformed into the conventional form of goal byusing interval arithmetic technique.In the goalachievementfunction, both the aspects of minsumand minmax GP formulations areadopted tominimize the lower bounds of thedefinedregretintervals for goal achievement within the specifiedinterval from the optimistic point ofview of theDMs.The potential use of the approach is illustratedby a numerical example.