A Mixed Integer Mathematical Programming Optimization Model for the NP-Hard Industrial Processes Scheduling Problem

This paper investigates single machine scheduling problem with unequal release times and deterioration jobs where the objective function of it is minimal makespan. A mixed integer mathematical programming optimization model is developed for the problem which belongs to the NP-hard problem. The model is tested on examples and compared with a heuristic algorithm introduced by Lee et al.. Moreover, the branch-bound algorithm proposed by Lee et al. also can obtained optimal solutions the same as the results from CPLEX but the CPU time of it for 28 jobs even needs more than 2 hours, thus, the results between them are not compared. According to results of computational tests, it is showed that the proposed model is very effective in solving problems because it can obtain optimal solutions within a short time. Therefore, it is very useful and valuable for decision maker who requires the optimal solutions.

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