Single Machine Scheduling Problem with Rejection to Minimize the Total Earliness plus the Total Rejection Cost

Abstract

Abstract-In the classical scheduling, it is always assumed that for any job, it should be processed. However, in the real world, things may be more flexible and the decision makers can make a higher-level decision, i.e., they can break the constrain by rejecting a job. It's not hard for the readers to find examples in the industrial and commercial fields to justify this breaking. To reject a job, of course, the decision makers should pay a corresponding penalty. In this paper, we considered single-machine scheduling problems under the job rejection constraint. A job was either rejected, in which case a rejection penalty had to be paid, or accepted and processed on the single machine. In this paper, we considered fuzziness in the job scheduling problem, i.e., due-dates of all jobs are fuzzy variables. The objective was to minimize the sum of the maximum earliness of the accepted jobs and the total rejection penalty of the rejected jobs. We found a polynomial-time solution for the problem through finding the Pareto optimal points. Index Terms-Rejected penalty, maximum earliness, Pareto optimal points, fuzzy due-date.