Optimizing job release and scheduling jointly in a reentrant hybrid flow shop

In a reentrant manufacturing system, job release and scheduling are of great importance. However, the two decisions have been made separately in the past. This study mainly aims at optimizing job release and scheduling jointly in a reentrant hybrid flow shop (RHFS-OJRSJ) with unrelated parallel machines. To promote energy conservation and emission reduction, a mathematical model for minimizing the makespan and total energy consumption is proposed. Due to the frequent reentrances of jobs and the complexity of the RHFS-OJRSJ problem, it is a strongly NP-hard problem. To effectively solve the RHFS-OJRSJ problem, an improved multi-objective evolutionary algorithm based on inverse optimization and decomposition (IMOEA/IOD) is proposed. First, the improved multi-objective evolutionary algorithm based on decomposition is employed to search the solution space. Second, a genetic algorithm is integrated to determine an initially best job release plan, based on which the scheduling problem can be encoded. Third, in the decoding, inverse optimization is introduced to further optimize the job release plan. Finally, to avoid falling into a local optimum and ensure population diversity, an adaptive neighborhood updating strategy is proposed. The experimental results demonstrate that the IMOEA/IOD algorithm bridges the gap of the job release and scheduling problem and the proposed algorithm can effectively solve the RHFS-OJRSJ problem.