Scheduling to minimize the makespan in large-piece one-of-a-kind production with machine availability constraints

This paper addresses a job shop scheduling problem, in which the jobs belong to the large-piece one-of-a-kind production (LP-OKP) model, and the machines are subject to availability constraints (Jm(LP-OKP), hjk |r-a |Cmax). The objective is considered to minimize the makespan. The scheduling model is derived from real industries, such as ship building industry, power plant building industry, steel-structure building industry and so on, and represents a more realistic and complex situation. In this study, two different scheduling algorithms of a slack-based mixed integer linear programming (MILP) model and a time slot-based search method are proposed to solve the scheduling problem. The experiments are implemented on CPLEX and search scheduling platform, respectively. The results reveal that the slack-based MILP model and time slot-based search method give better solutions than the rule-based algorithm. The deviation of objective optimal value results show that the slack-based MILP model and time slot-based search method can improve the makespan solution by 0.7% and 5.6%, respectively. And the percentage improvement of CPU time results show that they can shorten the CPU time by 74.5% and 12.9%, respectively. We found that the performance of the time slot-based search method is significantly competitive as compared to the slack-based MILP model but its CPU time is significantly higher than that of the slack-based MILP model.