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

This article presents goal programming (GP) procedure for solving Interval-valued multilevel programming (MLP) problems by using genetic algorithm (GA) in a hierarchical decision making and planning situation of an organization. In the proposed approach, first the individual best and least solutions of the objectives of the decision makers (DMs) located at different hierarchical levels are determined by using the GA method. Then, the target intervals of each of the objectives and decision vectors controlled by the upper-level DMs are defined in the inexact decision environment. Then, in the model formulation, the interval valued objectives and control vectors are transformed into the conventional form of goal by using interval arithmetic technique. In the goal achievement function, both the aspects of minsum and minmax GP formulations are adopted to minimize the lower bounds of the defined regret intervals for goal achievement within the specified interval from the optimistic point of view of the DMs.The potential use of the approach is illustrated by a numerical example.