Minimizing total absolute deviation of job completion times on a single machine with cleaning activities

Abstract

This paper considers a new single machine scheduling problem with several unavailability periods, where the machine has to be stopped in order to remove the dirt. The problem appears in the process in wafer manufacturing company. During the processing of a wafer on a specific machine, the dirt, including particle, organic materials and metal-salts, etc., on the surface of the wafer while processing, has to be taken away by a cleaning agent. Once the accumulation of dirt is over a threshold value, it is necessary to interrupt the machine processing and replace the cleaning agent in order to avoid damaging the wafer. The objective is to minimize the total absolute deviation of job completion times (TADC). The problem integrates production scheduling and cleaning activities and is strongly NP-hard. Many properties for solving the problem efficiently are explored. A mixed binary integer programming model is developed to find the optimal solution. Based on the properties explored, symmetry of the V-shaped rule, and the dynamic programming on scheduling the cleaning activities, an effective heuristic is developed. Computational results indicate that the performance of the heuristic is robust and significantly outperforms the modified TADC solution in the literature. Furthermore, the efficiency of the mixed binary integer programming model and the impact of the dirt accumulation as well as cleaning time are explored in detail.