Optimizing the multi-product, multi-constraint, bi-objective newsboy problem with discount by a hybrid method of goal programming and genetic algorithm

Abstract

This article points out the real-world prevalence of the multiple-product, multiple-constraint newsboy problem with two objectives—the ‘newsstand problem’—in which there are total and incremental discounts on purchasing prices. The constraints are the warehouse capacity and the batch forms of the order placements. The first objective of this problem is to find the order quantities that maximize expected profit, and the second objective is maximizing the service rate. It is assumed that the holding and shortage costs, modelled by a quadratic function, occur at the end of the period. Moreover, the decision variables are integer. A formulation of the problem is presented and shown to be an integer nonlinear programming model. Finally, an efficient hybrid algorithm is provided to solve the model and the results are illustrated with a numerical example.

Keywords:

• inventory control
• newsboy problem
• mixed integer nonlinear programming
• goal programming
• genetic algorithm