Network configuration distributed production scheduling problem: A constraint programming approach

Nowadays, many massive factories are forced to distribute their products in several manufacturing units. This issue has caused the emergence of a novel category of problems called distributed production scheduling, which is vital in today's growing world. In this paper, the distributed production scheduling problem by considering network configuration with two echelons is addressed. The first and second echelon factories have different job configurations and have a hybrid flow shop and a flexible job shop environment, respectively. For this problem, A bi-objective mixed integer linear programming (MILP) model is presented to minimize the maximum completion time of jobs and transportation costs between the selected factories in two echelons, respectively. Consequently, the epsilon constraint method is used to deal with this bi-objective model. In addition, since distributed scheduling problems are classified as NP-Hard problems, it is very challenging to solve them for largesized instances. For this reason, a constraint programming model (CP) is also proposed. To evaluate the performance of the proposed MILP model and CP model, a total of 180 numerical instances are randomly generated in small, medium, and large sizes. The obtained results demonstrate the significant ability of the constraint programming approach in solving complex distributed scheduling problems even for large-sized instances with 30 jobs, 10 stages/operations for each job, 6 machines for each stage/operation, and 4 factories at each echelon in a reasonable time and proof that the CP model can outperform the MILP model in this problem.