An Exact Method and Ant Colony Optimization for Single Machine Scheduling Problem with Time Window Periodic Maintenance

Abstract

This paper considers a time window periodic maintenance strategy with different duration windows and job scheduling activities in a single machine environment. The aim is to minimize the number of tardy jobs through the integration of production scheduling and periodic maintenance intervals. A mixed-integer linear programming model (MILP) is proposed to optimize small-sized test instances. Furthermore, an ant colony optimization (ACO) algorithm is developed to solve larger sized test instances. Subsequently, to measure the efficiency of the solutions obtained by ACO, Moore's algorithm is also developed to benchmark with ACO. To test the efficiency and the effectiveness of the ACO algorithm, a set of data for small and large sized problems was generated in which several parameters were adopted and then ten replicates were solved for each combination. The small sized instances were solved by the MILP. Then, the results obtained showed that the proposed ACO was able to obtain the exact solutions within reasonable CPU times, thus, it outperformed the CPLEX solver with respect to CPU. The large sized instances were solved by the Moore's algorithm and compared to ACO. Then, the results obtained showed that the ACO outperforms Moore's algorithm for all the instances tested. It can be concluded that the developed ACOis very efficient and effective in solving the problem considered in this paper.