Multi-objective stochastic integer linear programming with fixed recourse

Abstract

The real life decision problems have three main properties. The first one is to have conflicting objectives in the problem structure, the second one is the stochasticity in the description of problem parameters in contexts where the probability distribution of random parameters is known and the last one is due to involvement of integer decision variables which increased dimension of the problem. Multi-objective nature with discrete variables and imprecise parameters make the mathematical expression of the problem harder to solve with the traditional approaches. An efficient algorithm is developed, via extending the well-known L-shaped method using generalised benders decomposition to efficiently handle the integer variables in the first stage and the integer recourse in the second stage of the model formulation. The proposed solution method able to identify all efficient integer feasible solutions converge in a finite number of iterations. A numerical example and a computational implementation are also included for illustration.