The distributed permutation flowshop scheduling problem

This paper studies a new generalization of the regular permutation flowshop scheduling problem (PFSP) referred to as the distributed permutation flowshop scheduling problem or DPFSP. Under this generalization, we assume that there are a total of F identical factories or shops, each one with m machines disposed in series. A set of n available jobs have to be distributed among the F factories and then a processing sequence has to be derived for the jobs assigned to each factory. The optimization criterion is the minimization of the maximum completion time or makespan among the factories. This production setting is necessary in today’s decentralized and globalized economy where several production centers might be available for a firm. We characterize the DPFSP and propose six different alternative Mixed Integer Linear Programming (MILP) models that are carefully and statistically analyzed for performance. We also propose two simple factory assignment rules together with 14 heuristics based on dispatching rules, effective constructive heuristics and variable neighborhood descent methods. A comprehensive computational and statistical analysis is conducted in order to analyze the performance of the proposed methods