MILP formulation and genetic algorithm for flow shop scheduling problem with missing operations

Abstract

The purpose of this research is to formulate and solve general flow shop scheduling problems with missing operations in which the objective function is to minimise the maximum completion time (Makespan). Missing operations assumption refers to the fact that at least one job does not visit one machine. We first propose a mixed integer linear programming (MILP) model for the problem that can generates non-permutation schedules. The MILP Model can be used to compute optimal solution for the small-sized problems. In addition, we have presented an adapted genetic algorithm that can be used to generate non-permutation schedule with relatively good solutions in short computational time. Considering of non-permutation schedules is necessary to pass some machine when we have missing operations assumption. To verify the effectiveness of the presented approach, computational experiments are performed on a set of well-known classical flow shop scheduling (without missing operation) benchmark problems. The results show that the performance of the approach is suitable and can reaches good-quality solutions within a reasonable computational time. Thus, we use the genetic algorithm to solve large-sized flow shop scheduling problems with missing operations.