Joint Machine Selection and Buffer Allocation in Large Split and Merge Manufacturing Systems

This study focuses on the simultaneous optimization of machines and buffers in split and merge production systems. The objective was to minimize the total investment cost under a minimum throughput rate and maximum cycle time constraints. It is challenging to solve this type of stochastic resource allocation problem due to the phenomenon of the combinatorial explosion search space and the inability to obtain closed-form expressions for the optimization model. In this paper, a decomposition-coordination method (DCM) is proposed to optimize the machine types used, the number of machines, and the capacities of buffers of general feed-forward topology systems efficiently and accurately. Instead of directly targeting large-scale systems, the DCM decomposes the original system into several small decoupled systems with added coordination variables and then separately optimizes each decomposed system. An optimal or near-optimal solution is obtained after several iterations of the decoupled system optimization and coordination variable updating. Moreover, we develop a simulated annealing algorithm and non-dominated sorting genetic algorithm-II as benchmark algorithms and provide a parameter calibration analysis of the two metaheuristics. Finally, comprehensive numerical experiments are performed to demonstrate the performances of the DCM, and a multifactorial experimental analysis is conducted to determine the influence of the split and merge system parameters on the performances of the DCM. The results confirmed that the scale of the system, complexity of topology, cycle time constraint, traffic intensity, price ratio, and their interactions significantly influenced the total cost obtained from the DCM, whereas the scale of the system, traffic intensity, and price ratio significantly affected the computation time.