Cargo Analytical Integration in Space Engineering: A Three-dimensional Packing Model

Fasano, Giorgio

doi:10.1057/9780230372924_11

Cited by 15 publications

(14 citation statements)

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“…Since sub-optimal solutions are sufficient in most real-world cases, some MIP-based heuristics have been implemented to look into quick satisfactory (sub-optimal) solutions (Fasano 1999.…”

Section: Mip-based Heuristic Approachmentioning

confidence: 99%

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A MIP approach for some practical packing problems: Balancing constraints and tetris-like items

Fasano

2004

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This paper considers packing problems with balancing conditions and items consisting of clusters of parallelepipeds (mutually orthogonal, i.e. tetris-like items). This issue is quite frequent in space engineering and a real-world application deals with the Automated Transfer Vehicle project (funded by the European Space Agency), at present under development. A Mixed Integer Programming (MIP) approach is proposed. The three-dimensional single bin packing problem is considered. It consists of orthogonally placing, with possibility of rotation, the maximum number of parallelepipeds into a given parallelepiped. A MIP formulation of the problem is reported together with a MIP-based heuristic approach. Balancing conditions are furthermore examined, as well as the orthogonal placement (with rotation) of tetris-like items into a rectangular domain.

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“…Since sub-optimal solutions are sufficient in most real-world cases, some MIP-based heuristics have been implemented to look into quick satisfactory (sub-optimal) solutions (Fasano 1999.…”

Section: Mip-based Heuristic Approachmentioning

confidence: 99%

“…Mixed Integer Programming (MIP, see Nemhauser and Wolsey 1988) in some cases represents a valuable alternative (Fasano 1999;Mathur 1998;Padberg 1999). This approach seems quite suitable to solve some classes of non-standard packing problems with additional conditions (e.g.…”

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confidence: 99%

A MIP approach for some practical packing problems: Balancing constraints and tetris-like items

Fasano

2004

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“…Remark 3 The introduction of an ad hoc objective function has been described at a quite detailed level in Fasano (1999) and the reader is referred there for a deeper analysis. The non-intersection constraints (4) of the Basic Model are reformulated in an LP-relaxed form.…”

Section: Procedures Logicmentioning

confidence: 99%

“…static balancing, separation planes, prefixed orientation/position of some items) of the 3D-Packing Problem to solve. An LP-relaxation of the σ variables is performed dropping their integrality conditions and an ad hoc objective function (Fasano 1999) aimed at minimising the intersection between items is adopted (together with a reformulation of constraints (4), see Fasano 1999). In this phase intersections between items are admitted, while all the other basic and additional constraints must be respected.…”

Section: Procedures Logicmentioning

confidence: 99%

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MIP-based heuristic for non-standard 3D-packing problems

Fasano

2007

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Abstract. This paper is the continuation of a previous work (Fasano 2004), dedicated to a MIP formulation for non-standard three-dimensional packing issues, with additional conditions. The Single Bin Packing problem (Basic Problem) is considered and its MIP formulation shortly surveyed, together with some possible extensions, including balancing, tetris-like items and non-standard domains. A MIP-based heuristic is proposed to solve efficiently the Basic Problem or any possible extension of it, susceptible to a MIP formulation. The heuristic is a recursive procedure based on a non-blind local search philosophy. The concept of abstract configuration, concerning the relative positions between items, is introduced: the relative positions of items, determined by any abstract configuration, give rise to a feasible solution in an unbounded domain. The heuristic generates a sequence of good abstract configurations and solves, step by step, a reduced MIP model by fixing the relative positions of items, corresponding to the current abstract configuration.

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