Scheduling with Proportional Linear Deteriorating and a Maintenance Activity

Abstract

In this paper, we consider single machine scheduling with proportional linear deteriorating in which the processing time of a job depends on its starting time in a sequence. We assume that a maintenance activity is performed in a schedule. After a maintenance activity, machine will revert to its initial condition. The objective is to find simultaneously the optimal sequence for jobs and the position of a maintenance activity to minimize the makespan. A polynomial time algorithm is provided to solve the problem.