Mixed integer linear programming formulations for the permutation flow shop scheduling problem with preventive maintenance activities

Integrating the maintenance activities into the production process allows for keeping/restoring the good functional state of machines and improving the system productivity. According to the maintenance strategy adopted by a company, maintenance activities can be carried out in fixed positions/intervals or can be flexible, with an optimised maintenance approach being the key to efficient production maintenance. Consequently, the scheduling problems with maintenance activities (machine availability constraints) have received an increasing attention for both cases of fixed and flexible maintenance activities. This paper investigates the flow shop scheduling problem in the non-resumable case using an arbitrary number of preventive maintenance activities on each machine, with the optimised criterion being the makespan. Three mixed integer linear programming (MILP) models are proposed for three different problem types with respect to the considered maintenance policies within fixed-time windows, after a fixed number of finished jobs, and within an optimal preventive maintenance period. The computational results based on the randomly generated test problems demonstrate the high performance of the proposed MILP models in solving a wide range of instances, particularly, in small- and medium-scale problems.