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

• Published in: European journal of operational research Vol. 220; no. 1; pp. 251 - 261
• Main Authors: Delgado, Alberto, Jensen, Rune Møller, Janstrup, Kira, Rose, Trine Høyer, Andersen, Kent Høj
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: 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
• DOI: 10.1016/j.ejor.2012.01.028

► 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.