Operations scheduling in reverse supply chains: Identical demand and delivery deadlines

Abstract

This study addresses an integrated operations scheduling problem in reverse supply chains, where delivery deadlines and identical demand are involved. The supply chains consist of contracted collectors, a manufacturer, and many secondary markets. Both collectors and manufacturer are capacitated. The manufacturer remanufactures returned/used products shipped from collectors and then ships finished products directly to demand points geographically dispersed in secondary markets, following order quantity and delivery due date that each demand point requests. Each demand point orders the same quantity, which can be true in supply chain practices (i.e., grouping demand points into customer zones). Furthermore, the manufacturer is imposed penalties for late deliveries. The problem is to determine shipping quantities from collectors to the manufacturer and the assignment of collectors and demand points to the manufacturer, subject to the capacity constrains on both collectors and the manufacturer. This paper formulates the scheduling problem as a bi-criteria mixed integer program with the objective of minimizing both total shipping and penalty costs and delivery lateness. For the problem with the order sizes of one unit, the total unimodularity of its constraint matrix allows for the development of a polynomial time algorithm. The problem where order sizes are the same is solved by a dynamic programming based algorithm. The respective numerical examples are provided to verify two problems and their corresponding solution approaches.