Abstract
This paper studies an integrated scheduling problem for a single-item, make-to-order supply chain system consisting of one supplier, one capacitated transporter and one customer. Specifically, we assume the existence in the production stage of an intermediate inventory that works as a buffer to balance the production rate and the transportation speed. Jobs are first processed on a single machine in the production stage, and then delivered to the pre-specified customer by a capacitated vehicle in the delivery stage. Each job has a due date specified by the customer, and must be delivered to the customer before its due date. Moreover, it is assumed that a job that is finished before its departure date or arrives at the customer before its due date will incur a stage-dependent corresponding inventory cost (WIP inventory, finished-good inventory or customer inventory cost). The objective is to find a coordinated production and delivery schedule such that the sum of setup, delivery and inventory costs is minimised. We formulate the problem as a nonlinear model in a general way and provide some properties. We then derive a precise instance from the general model and develop a heuristic algorithm for solving this precise instance. In order to evaluate the performance of the heuristic algorithm, we propose a simple branch-and-bound (B&B) approach for small-size problems, and a lower bound based on the Lagrangian relaxation method for large-size problems. Computational experiments show that the heuristic algorithm performs well on randomly generated problems.
Acknowledgements
The authors would like to thank the two anonymous reviewers of this paper for their helpful comments and suggestions that have improved the quality of the paper.