Integrated scheduling of production and distribution to minimize total cost using an improved ant colony optimization method

• We consider an integrated scheduling of production and distribution so as to minimize the production and distribution costs.
• Jobs are processed on a single parallel-batch machine with fixed capacity B.
• They are delivered to customers by identical vehicles with a fixed capacity G.
• We proposed an improved ant colony optimization method to solve the problem.
• Computational results show that our heuristic works very well in practice.

In this paper, we consider an integrated scheduling problem of production and distribution for manufacturers. In the production part, the batch-processing machines have fixed capacity and the jobs have arbitrary sizes and processing times. Jobs in a batch can be processed together, provided that the total size of the jobs in the batch does not exceed the machine capacity. The processing time of a batch is the largest processing time of all the jobs in the batch. In the distribution part, the vehicles have identical transport capacity and all the deliveries are done by a third-party logistic (3PL) provider. The objective is to minimize the total cost of production and distribution for the manufacturer. Since the problem is NP-hard in the strong sense, we propose an improved ant colony optimization method to solve the production part, and a heuristic method for the distribution part. We derive a lower bound for the optimal total cost. We generate a large number of random data to test the performance of the proposed heuristic versus the lower bound. Our results show that the performance of the heuristic is excellent while the running time is no more than five seconds for 200 jobs.