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Methodological Background

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Optimizing Liner Shipping Fleet Repositioning Plans

Part of the book series: Operations Research/Computer Science Interfaces Series ((ORCS,volume 57))

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Abstract

We provide background information on several key topics for understanding the models of fleet repositioning in this monograph. Section 4.1 provides background on automated planning, a well-known technique for selecting and sequencing activities in order to achieve a set of goals. We then describe partial-order planning (POP), a specific type of automated planning used and extended in this monograph, in Sect. 4.2. Next, we cover mixed-integer programming (MIP), a method for solving optimization problems with linear constraints and objectives in Sect. 4.3. Finally, we describe constraint programming (CP), a branch-and-bound technique for satisfaction and optimization problems that uses constraint propagation and backtracking search to solve combinatorial problems.

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Notes

  1. 1.

    In practice, is it often more convenient to represent actions in a more expressive form, e.g., by letting the precondition be a general expression on states \(\mathit{pre}_{a}: S \rightarrow \mathbb{B}\) and represent conditional effects like resource consumption by letting the effect be a general transition function, depending on the current state of S, \(\mathit{eff }_{a,s}: S \rightarrow S\). Such expressive implicit action representations may also be a computational advantage. We have chosen a ground explicit representation of actions because it simplifies the presentation and more expressive forms can be translated into it.

  2. 2.

    We emphasize again that in automated planning, actions can actually appear multiple times in a plan. However, for the purposes of this thesis, restricting plan actions to be a subset of all actions is sufficient. We refer to [54] for an overview of general automated planning.

  3. 3.

    In this work, we only refer to mixed-integer linear programs.

  4. 4.

    The iterated application of a MIP or an exponential expansion of structures in a problem can allow MIPs to solve automated planning problems, as in [18].

  5. 5.

    More information can be found in Paul Rubin’s blog post “Perils of ‘Big M’”, http://orinanobworld.blogspot.de/2011/07/perils-of-big-m.html

  6. 6.

    Although our definition of a neighborhood relation allows the neighborhood to be of essentially any size, | N(s) | should be small, i.e. \(\forall s \in S,\vert N(s)\vert \ll \vert S\vert \).

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Authors and Affiliations

  1. Decision Support & Operations Research Lab, University of Paderborn, Paderborn, Germany

    Kevin Tierney

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Tierney, K. (2015). Methodological Background. In: Optimizing Liner Shipping Fleet Repositioning Plans. Operations Research/Computer Science Interfaces Series, vol 57. Springer, Cham. https://doi.org/10.1007/978-3-319-17665-9_4

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