A New CP-Approach for a Parallel Machine Scheduling Problem with Time Constraints on Machine Qualifications

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 lose 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 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 (CP) 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.

Single and Parallel Machine Scheduling with Variable Release Dates

“…Recent works [11,20] developed new formulations for the unrelated case (which it is clearly a special case of the identical case) and arc-flow formulations [27] for the P m |r j | w j F j case. Recently, [33,36] examined Constraint Programming methods for parallel machines scheduling problems although not for the particular case of P m |r j | w j F j . Other researchers (e.g.…”

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

“…In the following section, the part of the CP model of [7] which is useful for this work is recalled. This part corresponds to a Parallel Machine Scheduling Problem (PMSP) with family setup times.…”

“…In this paper, 19 instance sets are generated with The naming scheme for the different solving algorithms is described in Table 1. The first letter represents the model where ILP model, CP O model and CP N model denotes respectively the ILP model and CP model of [7], and the CP model detailed in Section 2.2. The models are implemented using IBM ILOG CPLEX Optimization Studio 12.10 [4].…”

“…Several solution methods has been defined for PTC [7,10,11]. In particular, the authors of [7] present two pre-existing models: a Mixed Integer Linear Program (MILP) and a Constraint Programming (CP) model.…”

“…Several solution methods has been defined for PTC [7,10,11]. In particular, the authors of [7] present two pre-existing models: a Mixed Integer Linear Program (MILP) and a Constraint Programming (CP) model. Furthermore, they define a new CP model taking advantage of advanced CP features to model machine disqualifications.…”