Expansion of variability related objective functions to due date issues
In this research, inspired by real life problems, very important scheduling areas, i.e. variability and due date related goals are considered. The focus of this study is on tardiness related objective functions in a scheduling system and the importance of the variability in tardiness and its effects on other tardiness related objectives. First the importance of minimizing variability of the positive difference between completion time of each job and its due date with the aid of some examples is explained. To measure the variability of tardiness in a flow shop scheduling system, the variance of tardiness as an objective function is considered. In this study the goal is finding a good compromise between minimizing variability in the system (variance of tardiness) and minimizing three other due date related objectives which are, total tardiness, maximum tardiness, and number of tardy jobs. One of the important advantages of the new objective function results from smoothing the difference of completion time of each job and its due date. In a situation that tardiness due to different uncertainties in the system cannot be avoided in the system, the new objective function helps to reduce the variability in the system and increase customer satisfaction in a situation that tardiness due to different uncertainties in the system cannot be avoided in the system. The enumeration analysis shows that variance of tardiness has no common behavior with other due date related objectives like total tardiness or number of tardy jobs. It means by minimizing variance of tardiness the other objective functions can be increased or decreased or it can also have no influence on the other objective functions. This shows that this new objective function should be considered next to other objective functions to minimize variability in tardiness next to other business targets. To solve this multi-objective function scheduling problem and reach a good compromise between all objective functions, two Algorithms are presented: Non-Dominated Sorting Genetic Algorithm (NSGA II) and Strength Pareto Evolutionary Algorithm (SPEA2) are presented. For the presented test problems, the numerical results show that SPEA2 has more efficient results in comparison with NSGAII; however, CPU time for NSGAII is significantly smaller than SPEA2.
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