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Exploiting Packing Components in General-Purpose Integer Programming Solvers

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Optimized Packings with Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 105))

Abstract

The problem of packing boxes into a large box is often only a part of a complex problem. For example in furniture supply chain applications, one needs to decide what trucks to use to transport furniture between production sites and distribution centres and stores, such that the furniture fits inside. Such problems are often formulated and sometimes solved using general-purpose integer programming solvers.

This chapter studies the problem of identifying a compact formulation of the multi-dimensional packing component in a general instance of integer linear programming, reformulating it using the discretisation of Allen–Burke–Mareček, and solving the extended reformulation. Results on instances of up to 10,000,000 boxes are reported.

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Acknowledgements

The views expressed in this chapter are personal views of the author and should not be construed as suggestions as to the product road map of IBM products. Some of the supporting code has been developed by Allen [2] for [3] and can be downloaded at http://discretisation.sf.net (September 30th, 2014). This material is loosely based upon an otherwise unpublished Chapter 8 of the dissertation of [26], but has been extended and improved greatly thanks to the comments of two anonymous referees, both in terms of the contents and the presentation. The author is most grateful for the referees’ thoughtful suggestions.

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Correspondence to Jakub Mareček .

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Mareček, J. (2015). Exploiting Packing Components in General-Purpose Integer Programming Solvers. In: Fasano, G., Pintér, J. (eds) Optimized Packings with Applications. Springer Optimization and Its Applications, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-319-18899-7_10

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