A Linear Goal Programming Method for Solving Chance-Constrained Multiobjective Problems with Interval Data Uncertainty

Abstract

This paper presents a goal programming (GP) method for modeling and solving multiobjective decision-making problems having interval parameter sets and a set of chance constraints in uncertain environments. In the proposed approach, planned interval goals defined for the objective goals are converted into standard linear goals in GP by using interval arithmetic technique and introducing under- and over-deviational variables to each of them. The chance constraints are also converted into deterministic equivalents and Taylor series approximation technique is used to transform the defined quadratic constraints into linear form to solve the problem effectively by employing linear GP method. Then, from the optimistic point of view of decision-maker, the framework of interval-valued GP is addressed to design goal achievement function for minimizing possible deviations concerned with achievement of goals within their target intervals specified in the decision situation. The approach is illustrated by a numerical example.