This paper addresses the Basic Cyclic Scheduling Problem where the processing times are affected by uncertainties. We formulate the problem as a twostage robust optimization problem with polyhedral uncertainty set. We propose three exact algorithms for solving the problem. Two of them use a negative circuit detection algorithm as a subroutine and the last one is an Howard's algorithm adaptation. Results of numerical experiments on randomly generated instances show that the Howard's algorithm adaptation yields efficient results and opens perspectives on more difficult robust cyclic scheduling problems.

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.

In this paper, we consider a cyclic job shop problem where a subset of tasks have varying processing times. The minimum processing times and maximum processing times of these tasks are known. We propose a branch and bound method that finds the schedule which minimizes the mean cycle time with respect to variations. We show that the evaluation of a schedule can be considered as a volume calculus of some polytopes. Indeed, for each schedule we can associate a set of polytopes whose volumes provide information on the variation effect on the considered schedule.