Single Machine Scheduling with Non-monotonic Time Dependent Processing Times

In scheduling problems with time dependent processing times, most studies assume that processing time of a job is a monotonic function of its start time or position. This paper studies the single machine scheduling problem with non-monotonic time dependent processing times. The processing time of a job is defined as a piecewise linear function of its start time. If the processing of job is started at a specific time, its processing time would be at its minimum. Job processing time will be increased if it is processed either before or after that specific time. The increasing rate of processing times is job-independent. The objective is to minimize the sum of actual processing times. We present a linear programming model to minimize the sum of actual processing times. Some numerical examples are considered to illustrate the performance of the model