Flowshop with additional resources during setups: Mathematical models and a GRASP algorithm

Machine scheduling problems arise in many production processes, and are something that needs to be consider when optimizing the supply chain. Among them, flowshop scheduling problems happen when a number of jobs have to be sequentially processed by a number of machines. This paper addressees, for the first time, the Permutation Flowshop Scheduling problem with additional Resources during Setups (PFSR-S). In this problem, in addition to the standard permutation flowshop constraints, each machine requires a setup between the processing of two consecutive jobs. A number of additional and scarce resources, e.g. operators, are needed to carry out each setup. Two Mixed Integer Linear Programming formulations and an exact algorithm are proposed to solve the PFSR-S. Due to its complexity, these approaches can only solve instances of small size to optimality. Therefore, a GRASP metaheuristic is also proposed which provides solutions for much larger instances. All the methods designed for the PFSR-S in this paper are computationally tested over a benchmark of instances adapted from the literature. The results obtained show that the GRASP metaheuristic finds good quality solutions in short computational times.