Constrained optimization of a newsboy problem with return policy using KKT conditions and GA

Abstract

Information Management Department, St. John's University, Tamsui, Taipei, 25135, ROC A newsboy problem model in which a vendor has limited resource is developed. It is assumed that the supplier will either sell the items to the vendor outright or offer the items to the vendor with return policy. In the latter case, the supplier buys back at certain percentage of original cost from the vendor the unsold items at the end of the selling season. The purpose of this study is to investigate how the vendor should replenish the items with return policy, constrained resources and changing procured price. Three numerical examples are provided. In one example with two constrained variables, an optimal solution is derived by using KKT (Karush-Kuhn-Tucker) conditions. The other two multiple variables examples with a minimum service level or a limited budget are solved using GA (genetic algorithm). © Springer-Verlag Berlin Heidelberg 2007.