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The purpose of this paper is to propose a new generic hybrid Petri Net (PN) model combined with the lowest makespan cut (LMC) for job shop scheduling problems in mold manufacturing to minimize the makespan of the mold part manufacture schedule.

The LMC algorithm finds a solution close to the optimal solution. The searching of the LMC algorithm starts from the lowest estimated makespan (lowest makespan). Almost all of the lowest makespans (LM) are infeasible makespans. A shifting percentage (SP) is added to the LM to obtain the shifting makespan (SM). The SM is compared with the completion time computed from the reachability tree of the Petri Net (PN) model. If the completion time is greater than the SM, the corresponding branch is cut from the reachability graph, and the SM will be compared with another branch from the reachability tree. There are two scenarios. In the first scenario, there is no feasible solution resulting from the comparison of the completion time and the SM, because the SM is lower than all of the feasible solutions. Therefore, the SP is used to increase the SM. On the contrary, in the second scenario, there is a feasible solution: the SP is used to reduce the SM. In the first scenario, a makespan that is lower than the optimal makespan is found. In the second scenario, a makespan that is greater than the optimal makespan is found. After getting close to bounds of the optimal makespan, the least makespan found in the bounds is the best solution.

The integration of the Petri Net (PN) model and the LMC algorithm can help to improve the production efficiency. In a case study, the proposed algorithm is being compared with other heuristical methods which are practical examples of mold makespans based on the shortest and the longest processing times. The schedule or the sequence obtained by the proposed algorithm is 30% less than the other methods.

This research will consider scheduling multiple mold. The mold design and the mold testing phase are not considered.

The time to produce a mold is very important. Reducing the mold production time will provide more time for mold assembly and testing. The aim of LMC algorithm is minimize the makespan. The time to produce a mold is reduced by finding the best sequence of the jobs and machines.

This paper proposes the new generic hybrid Petri Net model combined with LMC for job shop scheduling problem in the case of mold making shop to optimize the makespan of mold parts scheduling.