Job-shop production scheduling with reverse flows

In this paper, we present a modeling approach for the NP-hard scheduling problem Job-shop with reverse flows. This problem is characterized by two flows that cover the same machines but in opposite senses. The objective is to minimize the maximum completion time of the jobs. We start by providing a mathematical formulation and we analyze the complexity and some particular cases of the problem. Then, we propose a heuristic method for solving the NP-hard 3-machine case, which we evaluate by conducting tests on Taillard´s benchmark. These tests give satisfying results and show that the heuristic ensures good performance when the two flows have close numbers of jobs.