On the multi-product newsboy problem with two constraints

There is a growing interest in the applications of the constrained multi-product newsboy problem. In this paper, we develop a methodology to examine the dual of the solution space of this type of problem with two constraints and propose an approach to obtain the optimum batch size of each product. The approach is based on utilizing the Lagrangian Multipliers, Liebniz Rule, Kuhn–Tucker conditions, and when necessary it engages them into iterative techniques to obtain the optimum or near optimum solution values. Among the important features of the developed approach is its applicability to general probability distribution functions of products' demands. Also, it can be utilized in cases when the constraints are so tight, hence allowing the decision-maker to either delete some of the products from the original list or increase the available resources. The paper shows how the parametric functions that envelope the dual solution space are developed and includes numerical examples to illustrate the application of the proposed approach.