A dynamic programming approach for solving the economic lot scheduling problem with batch shipments

Abstract

This note investigates the economic lot scheduling problem (ELSP) with batch shipments. It first modifies an existing formulation of the ELSP to account both for the cases of equal-sized and geometrically increasing batch shipments, and it then adapts the popular dynamic programming approach of Bomberger to the new planning situation. In addition, the paper specifies some steps of Bomberger's solution procedure that had been formulated imprecisely in the original publication of the author. The paper compares the solution approach proposed in this note to the popular methods of Hanssmann as well as Haessler and Hogue in a numerical experiment and highlights the influence of the batch shipments on the relative performance of the solution procedures. Our results show that the proposed modification reduces the performance disadvantage of Bomberger's basic period approach, which may be interesting especially for practitioners that are interested in an easy-to-apply procedure for solving the ELSP in practice. Our changes to Bomberger's solution procedure support finding the lowest total cost solution that had not always been obtained in earlier publications.