Coordination policy for production and delivery scheduling in the closed loop supply chain

Coordinating a supply chain necessitates a synchronization strategy for reordering products and a cost-effective production and replenishment cycle time. The aim of this paper is to present an optimization framework for producing and distribution in the supply chains with a cooperating strategy. The main contribution of this paper is to integrate closed loop supply chain with open-shop manufacturing and economic lot and delivery scheduling problem (ELDSP). This integration is applied with the aim of better coordination between the members of the supply chain. This study examines the ELDSP for a multi-stage closed loop supply chain, where each product is returned to a manufacturing center at a constant rate of demand. The supply chain is also characterized by a sub-open-shop system for remanufacturing returned items. Common cycle time and multiplier policies is adopted to accomplish the desired synchronization. For this purpose, we developed a mathematical model in which a manufacturer with an open-shop system purchases raw materials from suppliers, converts them into final products, and sends them to package companies. Given that the ELDSPR is an NP-hard problem, a simulated annealing (SA) algorithm and a biography-based optimization (BBO) algorithm is developed. Two operational scenarios are formulated for the simulated annealing algorithm, after which both the algorithms are used to solve problems of different scales. The numerical results show that the biography-based optimization algorithm excellently performs in finding the best solution to the ELDSPR.