A Mathematical Model for the Flexible Job Shop Scheduling Problem With Availability Constraints

Abstract

We tackle the Flexible Job Shop Problem (FJSSP) subject to availability constraints due to maintenance tasks on machines. Previous studies explored meta-heuristic methods to address this problem and solved small-sized instances generated from classical FJSSP benchmark. We first introduce a new benchmark, comprising more than 2000 instances, for the problem based on the well-known FJSSP benchmarks. A mixed integer model is then developed to solve this problem. We carry out a computational study on the proposed benchmark and analyze its performances. Results show that our model can solve small and medium size instances efficiently. We also observe important variation in complexity depending on the class of instance which makes the proposed benchmark interesting to evaluate our approach and further improve the solving process in future works.