A Tabu Search Approach for Lot Sizing and Scheduling Problem with Arbitrary Job Sizes and Due Date Considerations

Abstract

This article deals with a lot sizing and scheduling problem in which each job is associated with an arbitrary due date and an arbitrary volume. The jobs are firstly processed on a batching machine which can process a batch of jobs simultaneously, and then delivered to a customer by a transporter which has a limited capacity. Each batch to be processed by the machine occurs a setup cost as well as a setup time, each batch to be delivered by the transporter occurs a delivery cost as well as a delivery time. Delay is not allowed. It is assumed that the job which is delivered to customer before its due date will incur a customer inventory cost. The objective is to minimize the sum of the setup, delivery and customer inventory cost. We firstly show that this problem is NP-hard, and then proposed a Tabu search approach to solve this problem. To verify performance of this proposed heuristic algorithm, we compare it with lower bounds for the problems. Numerical experiments show that the proposed Tabu search approach can find near optimal solutions in reasonable computational time.