Logic-based benders decomposition for scheduling a batching machine

•A generalization of single batching machine scheduling with lateness objective.•A novel logic-based Benders decomposition algorithm.•The algorithm finds new best upper bounds in short time on literature instances.•The algorithm finds high-quality solutions on new instances from the AS/RS context. T...

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Veröffentlicht in:Computers & operations research Jg. 113; S. 104777
Hauptverfasser: Emde, Simon, Polten, Lukas, Gendreau, Michel
Format: Journal Article Paper
Sprache:Englisch
Veröffentlicht: New York Elsevier Ltd 01.01.2020
Pergamon Press Inc
Federal Reserve Bank of St. Louis
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ISSN:0305-0548, 1873-765X, 0305-0548
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Abstract •A generalization of single batching machine scheduling with lateness objective.•A novel logic-based Benders decomposition algorithm.•The algorithm finds new best upper bounds in short time on literature instances.•The algorithm finds high-quality solutions on new instances from the AS/RS context. This paper investigates the problem of scheduling a set of jobs on a single batching machine to minimize the maximum lateness, where jobs may be subject to precedence constraints and incompatibilities. Single batching machine scheduling has many applications, but this study is particularly motivated by single crane scheduling in an automated storage and retrieval system (AS/RS): given a set of transport requests, which requests should be processed together in the same dual command cycle, and in what order should the cycles be processed? Since storage and retrieval requests may refer to the same physical item, precedence constraints must be observed. Moreover, the crane may not be capable of handling multiple storage or retrieval requests in the same cycle, hence the need to account for incompatibilities. We present a novel exact algorithm based on branch & Benders cut, which is shown to solve even large instances with more than 100 jobs to optimality in many cases. For the special case without precedence constraints and incompatibilities, it improves on several best-known upper bounds from the literature.
AbstractList This paper investigates the problem of scheduling a set of jobs on a single batching machine to minimize the maximum lateness, where jobs may be subject to precedence constraints and incompatibilities. Single batching machine scheduling has many applications, but this study is particularly motivated by single crane scheduling in an automated storage and retrieval system (AS/RS): given a set of transport requests, which requests should be processed together in the same dual command cycle, and in what order should the cycles be processed? Since storage and retrieval requests may refer to the same physical item, precedence constraints must be observed. Moreover, the crane may not be capable of handling multiple storage or retrieval requests in the same cycle, hence the need to account for incompatibilities. We present a novel exact algorithm based on branch & Benders cut, which is shown to solve even large instances with more than 100 jobs to optimality in many cases. For the special case without precedence constraints and incompatibilities, it improves on several best-known upper bounds from the literature.
•A generalization of single batching machine scheduling with lateness objective.•A novel logic-based Benders decomposition algorithm.•The algorithm finds new best upper bounds in short time on literature instances.•The algorithm finds high-quality solutions on new instances from the AS/RS context. This paper investigates the problem of scheduling a set of jobs on a single batching machine to minimize the maximum lateness, where jobs may be subject to precedence constraints and incompatibilities. Single batching machine scheduling has many applications, but this study is particularly motivated by single crane scheduling in an automated storage and retrieval system (AS/RS): given a set of transport requests, which requests should be processed together in the same dual command cycle, and in what order should the cycles be processed? Since storage and retrieval requests may refer to the same physical item, precedence constraints must be observed. Moreover, the crane may not be capable of handling multiple storage or retrieval requests in the same cycle, hence the need to account for incompatibilities. We present a novel exact algorithm based on branch & Benders cut, which is shown to solve even large instances with more than 100 jobs to optimality in many cases. For the special case without precedence constraints and incompatibilities, it improves on several best-known upper bounds from the literature.
ArticleNumber 104777
Author Gendreau, Michel
Emde, Simon
Polten, Lukas
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  surname: Emde
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  organization: Technische Universität Darmstadt, Fachgebiet Management Science / Operations Research, Hochschulstraße 1, Darmstadt 64289, Germany
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  givenname: Lukas
  surname: Polten
  fullname: Polten, Lukas
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  givenname: Michel
  surname: Gendreau
  fullname: Gendreau, Michel
  email: michel.gendreau@cirrelt.net
  organization: CIRRELT and Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, Montreal H3C 3A7, Canada
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Keywords Precedence constraints
Benders decomposition
Single batching machine
Automated storage and retrieval
Maximum lateness
Language English
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Snippet •A generalization of single batching machine scheduling with lateness objective.•A novel logic-based Benders decomposition algorithm.•The algorithm finds new...
This paper investigates the problem of scheduling a set of jobs on a single batching machine to minimize the maximum lateness, where jobs may be subject to...
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StartPage 104777
SubjectTerms Algorithms
Automated storage and retrieval
Automated storage retrieval systems
Benders decomposition
Cranes
Job shops
Lateness
Maximum lateness
Operations research
Precedence constraints
Production scheduling
Scheduling
Single batching machine
Upper bounds
Title Logic-based benders decomposition for scheduling a batching machine
URI https://dx.doi.org/10.1016/j.cor.2019.104777
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