MILP methods for the S-stage flexible flow shop scheduling problem

Abstract

This paper studies the flexible flow shop (FFS) NP-hard scheduling problem with the availability constraints to minimise the makespan. We used implicitly Branch and Bound through developing three different new mixed integer linear programming (MILP) to model the problem based on different definitions of the decision variables. We studied the efficiency of the model proposed in terms of a computational resolution and of the quality of the linear lower bound by using ILOG-Cplex solver. The experimentations which are carried out show that we can optimally solve the problems up to ten jobs and within four stages using three parallel machines per stage within several minutes of process time (CPU). We find that two proposed MILP show good results in terms of the quality of the linear lower bound obtained by the relaxation of the integrity constraints of this model.