Hub production scheduling problem with mold availability constraints

This research delves into a scheduling challenge inherent in the wheel hub casting process, a critical stage in automotive wheel manufacturing. The process involves shaping molten metal into specific wheel hub designs using dedicated molds. Diverse customer demands necessitate a unique mold for each wheel hub design, posing a scheduling challenge due to the limited availability of these expensive and long-lasting molds. There are 2 machines available for casting. Each wheel hub design requires a specific mold. These molds are expensive, longlasting, and need periodic maintenance. The objective function is to minimize the total time (makespan) to complete all casting jobs. Only one job requiring a specific mold can be processed at a time (due to mold limitations). Molds are unavailable during maintenance periods. The challenge lies in scheduling jobs considering both machine availability and mold constraints to minimize the overall production time. We formulate a mathematical model using mixed integer programming to precisely represent the problem and its constraints. Inspired by the Longest Processing Time (LPT) rule, we propose a heuristic named LRTPT to efficiently schedule jobs on the two machines. For large-scale problems, we employ a novel SIAIS algorithm to find near-optimal solutions effectively. We also present a dedicated branch and bound algorithm specifically tailored to solve smaller-sized instances of the problem. This algorithm leverages two lower bounds and several dominance properties to expedite the search for the optimal solution. To evaluate the effectiveness of our proposed approaches, we conduct a series of comprehensive experiments. The results demonstrate that the branch and bound algorithm significantly outperforms the widely used optimization solver CPLEX for smaller problems. Furthermore, the SIAIS algorithm proves to be more efficient than existing scheduling heuristics.