Abstract: A three-stage joint scheduling problem for manufacturers with batch-processing machines and arbitrary-size jobs is considered. The objective is to minimize total cost for production, inventory and distribution. In the production part, jobs have arbitrary sizes and are processed in batches on machines as long as the total size of jobs in a batch does not exceed the machine capacity. The processing of a batch cannot be interrupted until all the jobs in the batch are completed. Completed jobs are put in inventory before distribution. In the distribution part, products are delivered with identical vehicles of third-party logistics company. The model of the problem is presented using integer programming and it is shown to be NP-hard. A lower bound of optimal cost is derived. Designing an improved ant colony optimization method is proposed to minimize total cost. The candidate list is generated by classification of jobs to reduce the running time. In order to avoid local optimum, the pheromone is updated with a rotation scheme. The performance of the algorithm is tested by experiments where 48 levels of instances are developed and the results show the effectiveness of the proposed algorithm.

Key words: ant colony optimization, arbitrary-size jobs, batch-processing machines, joint scheduling