Energy-aware optimization for solving distributed flexible job shop scheduling problems

Abstract

INTRODUCTION: The significance of distributed manufacturing and energy costs in today's continuously increasing globalizing world has been recognized by scholars and researchers and efforts have been taken to improve process scheduling efficiency/reduce manufacturing costs over the years. A Distributed Flexible Job-Shop Scheduling Problem (DFJSP) is a distributed scheduling problem where each factory represents a single Flexible Job-Shop Scheduling Problem where a particular job cannot be assigned to more than one factory. PURPOSE: This research aims to address the distributed flexible job shop scheduling problem (DFJSP) by minimizing the maximum completion time (makespan time) where setup times of available machines for current operation depends on the previous operation processed by it (sequence dependent setup times). METHODS: This research proposed and formulated a mixed integer linear programming (MILP) model with an early optimization termination criterion to solve the DFJSP. Furthermore, this model is extended to consider electricity consumption by introducing the objective function of energy usage in the form of processing energy, setup energy & idle energy consumption and a strategy to shutdown machines when the machines are in idle state. A constraint programming model and a meta-heuristic algorithm in the form of a combination of Genetic and NEH algorithm (NEH-GA) is proposed and compared with the MILP model. RESULTS: The results shows that the MILP model achieves optimality within reasonable time and performs better than constraint programming model when problem complexity is small whereas constraint programming tends to do better when the problem complexity is large. The proposed meta-heuristic algorithm performs the best in terms of computation time when the problem complexity is large albeit not guaranteeing an optimal solution. CONCLUSION: All three models were successful in finding solutions which reduce the total energy consumption in five out of the total fourteen problem instances. For future research studies, the current DFJSP base model can be modified to other objectives such as earliness/tardiness. Similarly, optimization models can be formulated for DFJSP considering machine breakdowns with sequence dependent setup times.