Lot sizing and scheduling problem for production-delivery system with job volume and due date considerations to minimise the total cost while guaranteeing a certain customer service level

This paper considers a lot sizing and scheduling problem where jobs are processed on a batching machine, and then delivered to a customer by a capacitated transporter. Each job is associated with a due date and a volume. In order to guarantee customer service level, each job has to be delivered to customer before or on its due date. It is assumed that the job which is delivered to customer before its due date will occur an earliness penalty. The objective is to minimise the total logistics cost under two kinds of due-date conditions. We formulate the problem as a non-linear model, then develop a Tabu algorithm. To verify performance of this algorithm, we establish a dominance-related exact algorithm for the small-size problems and a lower bound for the large-size problems. Numerical experiments show that the proposed Tabu algorithm performs efficiently in terms of both solution quality and running time.