On solving three-dimensional open-dimension rectangular packing problems. Issue 5 (4th May 2017)

• Record Type: Journal Article
• Authors: Junqueira, Leonardo; Morabito, Reinaldo
• Is Part Of: Engineering optimization. Volume 49:Issue 5(2017)
• Page Start: 733
• Page End: 745
• Publication Date: 2017-05-04
• Subjects: Global optimization -- three-dimensional rectangular packing -- grid-based position MIP formulation -- open-dimension problems -- piecewise linearization; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2016.1208010
• Languages: English
• ISSNs: 0305-215X

Abstract

ABSTRACT: In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.