An exact dynamic programming algorithm for the precedence-constrained class sequencing problem

•Dynamic programming algorithm for precedence-constrained class sequencing problem.•Based on sub-procedures tailored to the structure of the problem.•New lower bounding technique.•Algorithm solves large instances to proven optimality. This article discusses the precedence-constrained class sequencin...

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Published in:Computers & operations research Vol. 124; p. 105063
Main Authors: Bürgy, Reinhard, Hertz, Alain, Baptiste, Pierre
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.12.2020
Pergamon Press Inc
Subjects:
Algorithms
Constraint modelling
Dynamic programming
Identical family setup times
Integer programming
Job shops
Lower bounds
Mixed integer
One-machine scheduling
Operations research
Polynomials
Precedence constraints
Scheduling
Sequencing
Precedence constraints
One-machine scheduling
Dynamic programming
Sequencing
Identical family setup times
ISSN:0305-0548, 0305-0548
Online Access:Get full text
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Summary:•Dynamic programming algorithm for precedence-constrained class sequencing problem.•Based on sub-procedures tailored to the structure of the problem.•New lower bounding technique.•Algorithm solves large instances to proven optimality. This article discusses the precedence-constrained class sequencing problem (PCCSP). In scheduling terms, this is a single-machine problem with precedence constraints and family setups with the goal of minimizing the number of setups. From a practical perspective, PCCSP covers a wide range of applications such as, for example, scheduling problems in systems with job families where multipurpose processors need retooling to switch from a job of one family to a job of another family. Previous research has shown that PCCSP is NP-hard and that no polynomial-time algorithm with constant worst-case performance exists unless P=NP. So far, only little research has been conducted on the development of specific computational methods for PCCSP. This article bridges this gap by proposing a dynamic programming algorithm for solving PCCSP exactly. It comprises specialized lower bound computations, node merging and precedence reasoning algorithms, and heuristics that successfully exploit the problem’s structure. Based on extensive numerical experiments, we analyze the algorithm in detail and show that it outperforms mixed-integer programming and constraint programming models.
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ISSN:0305-0548
0305-0548
DOI:10.1016/j.cor.2020.105063