A Constraint Programming model for fast optimal stowage of container vessel bays

► We study the container stowage problem within subsections of container vessel bays. ► A representative model of the problem is introduced. ► Integer and Constraint Programming approaches to solve these problems are compared. ► We do extensive testing with instances derived from real stowage plans....

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Vydáno v:	European journal of operational research Ročník 220; číslo 1; s. 251 - 261
Hlavní autoři:	Delgado, Alberto, Jensen, Rune Møller, Janstrup, Kira, Rose, Trine Høyer, Andersen, Kent Høj
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.07.2012 Elsevier Elsevier Sequoia S.A
Témata:	Applied sciences Assignment problem Combinatorial analysis Constraint Programming Container ships Container vessel stowage planning Containers Exact sciences and technology Flows in networks. Combinatorial problems Ground, air and sea transportation, marine construction Integer Programming Inventory control, production control. Distribution Marine and water way transportation and traffic Mathematical programming Operational research and scientific management Operational research. Management science Optimization Optimization techniques Planning Programming Scheduling, sequencing Slot planning Solvers Stowing Studies Vessels Slot planning Container vessel stowage planning Constraint Programming Integer Programming Constraint satisfaction Combinatorial optimization Modeling Constrained optimization Integer programming Production management Container Container ship NP hard problem Economic impact Medium term Planning Maritime transportation Stowage State constraint
ISSN:	0377-2217, 1872-6860
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Abstract	► We study the container stowage problem within subsections of container vessel bays. ► A representative model of the problem is introduced. ► Integer and Constraint Programming approaches to solve these problems are compared. ► We do extensive testing with instances derived from real stowage plans. ► Our test instances are solved as required for application by the industry. Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for large container vessels within a few minutes. It decomposes the problem into a master planning phase that distributes the containers to bay sections and a slot planning phase that assigns containers of each bay section to slots. In this paper, we focus on the slot planning phase of this approach and present a Constraint Programming and Integer Programming model for stowing a set of containers in a single bay section. This so-called slot planning problem is NP-hard and often involves stowing several hundred containers. Using state-of-the-art constraint solvers and modeling techniques, however, we were able to solve 90% of 236 real instances from our industrial collaborator to optimality within 1second. Thus, somewhat to our surprise, it is possible to solve most of these problems optimally within the time required for practical application.
AbstractList	Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for large container vessels within a few minutes. It decomposes the problem into a master planning phase that distributes the containers to bay sections and a slot planning phase that assigns containers of each bay section to slots. In this paper, we focus on the slot planning phase of this approach and present a Constraint Programming and Integer Programming model for stowing a set of containers in a single bay section. This so-called slot planning problem is NP-hard and often involves stowing several hundred containers. Using state-of-the-art constraint solvers and modeling techniques, however, we were able to solve 90% of 236 real instances from our industrial collaborator to optimality within 1 second. Thus, somewhat to our surprise, it is possible to solve most of these problems optimally within the time required for practical application. Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for large container vessels within a few minutes. It decomposes the problem into a master planning phase that distributes the containers to bay sections and a slot planning phase that assigns containers of each bay section to slots. In this paper, we focus on the slot planning phase of this approach and present a Constraint Programming and Integer Programming model for stowing a set of containers in a single bay section. This so-called slot planning problem is NP-hard and often involves stowing several hundred containers. Using state-of-the-art constraint solvers and modeling techniques, however, we were able to solve 90% of 236 real instances from our industrial collaborator to optimality within 1 second. Thus, somewhat to our surprise, it is possible to solve most of these problems optimally within the time required for practical application. [PUBLICATION ABSTRACT] ► We study the container stowage problem within subsections of container vessel bays. ► A representative model of the problem is introduced. ► Integer and Constraint Programming approaches to solve these problems are compared. ► We do extensive testing with instances derived from real stowage plans. ► Our test instances are solved as required for application by the industry. Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for large container vessels within a few minutes. It decomposes the problem into a master planning phase that distributes the containers to bay sections and a slot planning phase that assigns containers of each bay section to slots. In this paper, we focus on the slot planning phase of this approach and present a Constraint Programming and Integer Programming model for stowing a set of containers in a single bay section. This so-called slot planning problem is NP-hard and often involves stowing several hundred containers. Using state-of-the-art constraint solvers and modeling techniques, however, we were able to solve 90% of 236 real instances from our industrial collaborator to optimality within 1second. Thus, somewhat to our surprise, it is possible to solve most of these problems optimally within the time required for practical application.
Author	Delgado, Alberto Jensen, Rune Møller Rose, Trine Høyer Janstrup, Kira Andersen, Kent Høj
Author_xml	– sequence: 1 givenname: Alberto surname: Delgado fullname: Delgado, Alberto email: alde@itu.dk organization: IT University of Copenhagen, Rued Langgaards Vej 7, 2300 Copenhagen S, Denmark – sequence: 2 givenname: Rune Møller surname: Jensen fullname: Jensen, Rune Møller email: rmj@itu.dk organization: IT University of Copenhagen, Rued Langgaards Vej 7, 2300 Copenhagen S, Denmark – sequence: 3 givenname: Kira surname: Janstrup fullname: Janstrup, Kira email: kj@transport.dtu.dk organization: Copenhagen University, Universitetspark 5, 2100 Copenhagen Ø, Denmark – sequence: 4 givenname: Trine Høyer surname: Rose fullname: Rose, Trine Høyer email: m01thr@math.ku.dk organization: Copenhagen University, Universitetspark 5, 2100 Copenhagen Ø, Denmark – sequence: 5 givenname: Kent Høj surname: Andersen fullname: Andersen, Kent Høj email: kent@imf.au.dk organization: Århus University, Ny Munkegade 118, 8000 Århus C, Denmark
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Snippet	► We study the container stowage problem within subsections of container vessel bays. ► A representative model of the problem is introduced. ► Integer and... Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach...
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SubjectTerms	Applied sciences Assignment problem Combinatorial analysis Constraint Programming Container ships Container vessel stowage planning Containers Exact sciences and technology Flows in networks. Combinatorial problems Ground, air and sea transportation, marine construction Integer Programming Inventory control, production control. Distribution Marine and water way transportation and traffic Mathematical programming Operational research and scientific management Operational research. Management science Optimization Optimization techniques Planning Programming Scheduling, sequencing Slot planning Solvers Stowing Studies Vessels
Title	A Constraint Programming model for fast optimal stowage of container vessel bays
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