Filtering Rules for Flow Time Minimization in a Parallel Machine Scheduling Problem

TL;DR

This paper introduces filtering rules based on a polynomial-time algorithm to improve flow time minimization in parallel machine scheduling with qualification constraints, demonstrating enhanced efficiency over existing models.

Contribution

It develops filtering rules derived from a polynomial-time algorithm for flow time minimization, improving the performance of constraint programming models in scheduling.

Findings

Filtering rules significantly improve model efficiency.

Experimental results show better competitiveness with existing methods.

Rules effectively reduce disqualifications and flow time.

Abstract

This paper studies the scheduling of jobs of different families on parallel machines with qualification constraints. Originating from semiconductor manufacturing, this constraint imposes a time threshold between the execution of two jobs of the same family. Otherwise, the machine becomes disqualified for this family. The goal is to minimize both the flow time and the number of disqualifications. Recently, an efficient constraint programming model has been proposed. However, when priority is given to the flow time objective, the efficiency of the model can be improved. This paper uses a polynomial-time algorithm which minimize the flow time for a single machine relaxation where disqualifications are not considered. Using this algorithm one can derived filtering rules on different variables of the model. Experimental results are presented showing the effectiveness of these rules. They improve the competitiveness with the mixed integer linear program of the literature.