Modeling and Optimization for Multi-Objective Nonidentical Parallel Machining Line Scheduling with a Jumping Process Operation Constraint

Abstract

This paper investigates the nonidentical parallel production line scheduling problem derived from an axle housing machining workshop of an axle manufacturer. The characteristics of axle housing machining lines are analyzed, and a nonidentical parallel line scheduling model with a jumping process operation (NPPLS-JP), which considers mixed model production, machine eligibility constraints, and fuzzy due dates, is established so as to minimize the makespan and earliness/tardiness penalty cost. While the physical structures of the parallel lines in the NPPLS-JP model are symmetric, the production capacities and process capabilities are asymmetric for different models. Different from the general parallel line scheduling problem, NPPLS-JP allows for a job to transfer to another production line to complete the subsequent operations (i.e., jumping process operations), and the transfer is unidirectional. The significance of the NPPLS-JP model is that it meets the demands of multivariety mixed model production and makes full use of the capacities of parallel production lines. Aiming to solve the NPPLS-JP problem, we propose a hybrid algorithm named the multi-objective grey wolf optimizer based on decomposition (MOGWO/D). This new algorithm combines the GWO with the multi-objective evolutionary algorithm based on decomposition (MOEA/D) to balance the exploration and exploitation abilities of the original MOEA/D. Furthermore, coding and decoding rules are developed according to the features of the NPPLS-JP problem. To evaluate the effectiveness of the proposed MOGWO/D algorithm, a set of instances with different job scales, job types, and production scenarios is designed, and the results are compared with those of three other famous multi-objective optimization algorithms. The experimental results show that the proposed MOGWO/D algorithm exhibits superiority in most instances.

Identical Parallel Machine Scheduling Considering Workload Smoothness Index

“…Constraints ( 9) and (10) give the processing sequence of jobs on each machine. Constraint (11) gives the range of the variables.…”

“…Large Job Instances (n ≥ 50) Below, we further test the performance of the proposed two heuristic algorithms together with the previous list scheduling algorithms with large job input instances. Especially, we consider two scenarios with regard to the variation range of the processing times of jobs, i.e., p j ∈ [5,10] or p j ∈ [8,10]. Similar to the case of small job input instances, three instances are generated for each combination (m, n), and the average results are reported in Tables 2 and 3, where the running time is in seconds.…”

“…For the solution quality, we observe by Tables 2 and 3 that the objective value of the solution obtained by any of the heuristic algorithms increases proportionally in the number of machines, while the number of jobs has no significant impact on the objective value. Moreover, when the job processing time is scaled in [8,10], the average performance of LSA RPT is even better than that of LSA LPT . That is to say, compared to small-scale numerical experiments, LSA LPT lost its power to solve large-scale instances.…”

“…Various optimization objectives, including the makespan and the total completion time, have been well addressed in previous studies [4][5][6][7]. In addition to the above classical objectives, workload balance between the machines together with the corresponding operators is also a major aspect of decision making in manufacturing industry [8][9][10]. It contributes to reducing the idleness and work-in-process and removing bottlenecks [8,11].…”