A mixed integer linear programming modelling for the flexible cyclic jobshop problem

This paper addresses the Cyclic Jobshop Problem in a flexible context. The flexibility feature means that machines are able to perform several kinds of tasks. Hence, a solution of the scheduling problem does not only concern the starting times of the elementary tasks, but also the assignment of these tasks to a unique machine. The objective considered in this paper is the minimisation of the cycle time of a periodic schedule. We formulate the problem as a Mixed Integer Linear Problem and propose a Benders decomposition method along with a heuristic procedure to speed up the solving of large instances. It consists in reducing the number of machines available for each task. Results of numerical experiments on randomly generated instances show that the MILP modelling has trouble solving difficult instances, while our decomposition method is more efficient for solving such instances. Our heuristic procedure provides good estimates for difficult instances.