A Bi-Criteria Single Machine Scheduling with Rate-Modifying-Activity

In this paper, we consider a single machine scheduling problem with two criteria: minimizing both total flow time with total tardiness and minimize maximum tardiness with number of tardy jobs. Unlike the classical scheduling problems, we use a job position deterioration, which means that the job processing time increases as a function of the job position. Besides deteriorated jobs, we also consider rate-modifying-activities which alter the efficiency of the deteriorating processor. This is the first paper, to combine both time dependent processing times and problems with rate-modifying-activity in the bi-criteria objectives. To solve the new type of problem, we introduce a new scheduling mathematical model which is based on one developed Ozturkoglu and Bulfin [1]. To analyze the efficiency of the mathematical model, we use three different approaches. According to computational results, up to 50 jobs can be solved in less than one minute.