Priority allocation rules for single machine total weighted linear and square tardiness problems

Abstract

The single machine scheduling problems minimizing total weighted tardiness and square tardiness objectives have been studied in literature for many years. Applications of the model include sequencing problems in manufacture and logistics. This paper proposes two new priority allocation rules, PAR 1 and PAR 2, for solving these two problems. Unlike most known dispatch rules and constructive algorithms, our new rules take advantage of not only the jobs’ static characters values such as the process time, the due date and the weight, but also their dynamic characters values, i.e., the slack and the values of the objective function for different choices of some jobs. At any time when a job is being selected to process, some of the unprocessed jobs are delayed while the others are not. It means that the characters of these two sorts of jobs are different from each other. So, combining these characters with the objective function’s value can obtain effective dispatch rule. Experimental analysis based on the instances from the OR-Library discloses that our priority allocation rules, PAR 1 and PAR 2, are efficient and have significant advantages over traditional approaches.