Filtering Rules for Flow Time Minimization in a Parallel Machine Scheduling Problem
This work provides incremental improvements in scheduling efficiency for semiconductor manufacturing, specifically for problems with qualification constraints and flow time minimization.
This paper addresses the problem of scheduling jobs from different families on parallel machines, subject to qualification constraints that impose a time threshold between jobs of the same family. The objective is to minimize flow time and disqualifications. The authors propose filtering rules derived from a polynomial-time algorithm for a single-machine relaxation, which significantly improves the efficiency of an existing constraint programming model.
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.