Mathematical Modeling and Solving the Flexible Flow Shop Scheduling Problem with Reverse Flows and the Limitation of Access to Machines

Due to the special position of flow shop scheduling systems in production centers, these issues have received a lot of attention in recent years. One common assumption in these cases is the availability of machines on the planning horizon. In real industrial environments, a machine may be temporarily unavailable for reasons such as the need for preventative maintenance. Due to the importance of this issue, in the present study the flexible flow shop scheduling problem with reverse flows is investigated by considering the activity of preventive maintenance in which there are two flows of jobs (direct and reverse) that cover the same machines in opposite directions. An essential issue for modeling the flexible flow shop-scheduling problem is to consider the limitations of access to machines in order to perform preventive maintenance. The maintenance operation on each machine has a fixed duration and its beginning and end occur in a certain time window. For the mentioned problem, a Mixed Integer NonLinear Programing (MINLP) model is presented. The objective of this model is to minimize the maximal completion time of the jobs (i.e., the ma kespan). Due to the complexity of the model and the NP-hardness of the proposed problem, the Imperialist Competitive Algorithm (ICA) is proposed to solve large-scale problems. In order to evaluate the performance of the proposed algorithm, numerical sample problems in different sizes are solved using this algorithm, the General Algebraic Modeling System (GAMS) software as well as the genetic algorithm. Computational results demonstrate the effectiveness of the Imperialist Competitive Algorithm for the considered problem.