A matheuristic for flexible job shop scheduling problem with lot-streaming and machine reconfigurations
针对多品种小批量生产中批量流和机器重构带来的调度难题，提出一种结合混合整数线性规划和变邻域搜索的数学启发式方法，用于最小化总加权拖期，并通过基准算例和实际案例验证了其有效性。
Multi-variety and small-batch production mode enables manufacturing industries to expeditiously satisfy customers' personalised demands, where a large amount of identical jobs can be split into several sublots, and be processed by reconfigurable machines with multiple machining technics. However, such highly flexible manufacturing environments bring some intractable problems to the production scheduling. Mathematical programming and meta-heuristic methods become less efficient when a scheduling problem contains both discrete and continuous optimisation attributes. Therefore, matheuristic, which combines advantages of the two methodologies, is regarded as a promising solution. This paper investigates a flexible job shop scheduling problem with lot-streaming and machine reconfigurations (FJSP-LSMR) for the total weighted tardiness minimisation. First, a monolithic mixed integer linear programming (MILP) model is established for the FJSP-LSMR. Afterwards, a matheuristic method with a variable neighbourhood search component (MH-VNS) is developed to address the problem. The MH-VNS adopts the classical genetic algorithm (GA) as the framework, and introduces two MILP-based lot-streaming optimisation strategies, LSO1 and LSO2, to improve lot-sizing plans with varying degrees. Four groups of instances are extended from the well-known Fdata benchmark to evaluate the performance of proposed MILP model, LSO1 and LSO2 components, and MH-VNS. Numerical experimental results suggest that LSO1 and LSO2 are efficient in different scenarios, and the proposed MH-VNS can well balance the solution quality and computational costs for reasonably integrating the GA- and MILP-based local search strategies. In addition, a complicated FJSP-LSMR case is abstracted from a real-world shop floor for processing large-sized structural parts to further validate the MH-VNS.