MILP Modeling and Optimization of Energy-Efficient Distributed Flexible Job Shop Scheduling Problem

With the global warming problem and increasing energy cost, manufacturing firms are paying more and more attention to reducing energy consumption. This paper addresses the distributed flexible job shop scheduling problem (DFJSP) with minimizing energy consumption. To solve the problem, firstly, a novel mixed integer linear programming (MILP) model is developed to solve small-scaled problems to optimality. Due to the NP-hardness of DFJSP, we then propose an efficient hybrid shuffled frog-leaping algorithm (HSFLA) for solving DFJSP, particularly for large-sized problems. HSFLA combines the shuffled frog-leaping algorithm (SFLA) with powerful global search ability and variable neighborhood search (VNS) with good local search ability. Moreover, in HSFLA, the encoding method, the decoding method, the initialization method and the memetic evolution process are specifically designed. Finally, numerical experiments are conducted to evaluate the performance of the proposed MILP model and HFSLA.