A Pareto-Optimal Solution for a Multi-Objective Scheduling Problem with Periodic Maintenance Requirement

Abstract

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.