On the optimal lot-sizing and scheduling problem in serial-type supply chain system using a time-varying lot-sizing policy

In this paper, we solve the optimal sequencing, lot-sizing and scheduling decisions for several products manufactured through several firms in a serial-type supply chain so as to minimise the sum of setup and inventory holding costs while meeting given demand from customers. We propose a three-phase heuristic to solve this NP-hard problem using a time-varying lot- sizing approach. First, based on the theoretical results, we obtain candidate sets of the production frequencies and cycle time using a junction-point heuristic. Next, we determine the production sequences for each firm using a bin-packing method. Finally, we obtain the production times of the products for each firm in the supply chain system by iteratively solving a set of linear simultaneous equations which were derived from the constraints. Then, we choose the best solution among the candidate solutions. Based on the numerical experiments, we show that the proposed three-phase heuristic efficiently obtains feasible solutions with excellent quality which is much better than the upper-bound solutions from the common cycle approach.