A new CP-approach for a parallel machine scheduling problem with time constraints on machine qualifications

TL;DR

This paper introduces a new constraint programming approach for scheduling jobs on parallel machines with dynamic qualification constraints, outperforming existing models especially when minimizing disqualifications.

Contribution

A novel CP model for machine qualification constraints that better captures disqualification dynamics and improves scheduling performance.

Findings

The new CP model outperforms ILP and existing CP models for disqualification objectives.

The CP model is competitive with existing models when minimizing flow time.

Experiments demonstrate the effectiveness of the new CP approach in complex scheduling scenarios.

Abstract

This paper considers the scheduling of job families on parallel machines with time constraints on machine qualifications. In this problem, each job belongs to a family and a family can only be executed on a subset of qualified machines. In addition, machines can lose their qualifications during the schedule. Indeed, if no job of a family is scheduled on a machine during a given amount of time, the machine loses its qualification for this family. The goal is to minimize the sum of job completion times, i.e. the flow time, while maximizing the number of qualifications at the end of the schedule. The paper presents a new Constraint Programming (CP) model taking more advantages of the CP feature to model machine disqualifications. This model is compared with two existing models: an Integer Linear Programming (ILP) model and a Constraint Programming model. The experiments show that the new CP model outperforms the other model when the priority is given to the number of disqualifications objective. Furthermore, it is competitive with the other model when the flow time objective is prioritized.