Matheuristics for the flowshop scheduling problem with controllable processing times and limited resource consumption to minimize total tardiness

Abstract

This paper addresses the problem of scheduling jobs in a flowshop layout where the machines can operate at different speeds and require an amount of a resource that is a non-decreasing function of its speed. Furthermore, there is a limit in the maximum amount of the resource that can be consumed, so the problem serves to model either a constraint on the energy or raw material employed in the process, or on the maximum amount of pollutant that can be emitted. In contrast to the classical permutation flowshop scheduling problem, in the variant under study the processing times are controllable, there is an specific resource consumption, and each job has a due date. The objective function considered is the minimization of the total tardiness of the jobs. Given the NP-hard nature of this problem, we focus onto developing approximate solution procedures that can yield high-quality solutions with a reasonable CPU effort. More specifically, we develop a fast solution procedure to build an initial solution and two hybrid matheuristics based on mixed-integer linear programming formulations of the problem. The first one combines a relax-and-fix approach with the generation of heuristic cutting planes, while the second one relaxes some decision variables in the first stage and fixes other decision variables in the final stage. The computational experience carried out show that our proposals outperform the mathematical models as well as an approximate procedure proposed for a related problem.