Single-Machine Scheduling with Discretely Controllable Job Processing Times Subject to a Deteriorating Rate-Modifying Activity

SYNOPTIC ABSTRACT

In this article, we investigate the problem of scheduling jobs with discretely controllable processing times subject to a deteriorating rate-modifying activity on a single machine. In our problem, each job has multiple processing times to be selected. But for different processing times, different processing costs are required. In addition, we can choose a deteriorating rate-modifying activity to reduce the processing times of jobs that are scheduled subsequently. We aim to minimize the following objectives: the makespan plus the total processing cost; the total completion time plus the total processing cost; and the sum of earliness, tardiness, and common due date penalties plus the total processing cost. We show that all these goals are polynomial-time solvable followed by the numerical examples.

KEY WORDS AND PHRASES:

• scheduling
• rate-modifying activity
• discretely controllable job processing times
• polynomial-time solution

Funding

This work was supported by China Scholarship Council (201408330402), Ningbo Natural Science Foundation (2010A610102), Science Foundation of Ningbo University (XKl15D218), and K. C. Wong Magna Foundation of Ningbo University.