A Mathematical Model for Three-Dimensional Open Dimension Packing Problem with Product Stability Constraints

  • Cong-Tan-Trinh TruongEmail author
  • Lionel Amodeo
  • Farouk Yalaoui
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1173)


This paper presents a logistical study using a mathematical model based on the Three-dimensional Open Dimension Rectangular Packing Problem (3D-ODRPP) to optimize the arrangement of products in a packaging with the practical constraint “product stability”. The proposed model aims at seeking the minimal volume rectangular bounding box for a set of rectangular products. Our model deals with orthogonal rotation, static stability and overhang constraints of products, three of the most important real-world conditions that ensure the feasibility of solution. Literature test instances are given to demonstrate that the proposed method can find the feasible global optimum of a 3D-ODRPP. Experimental results show the improvement of solution quality in terms of box volume and packaging stability comparing to existing models in the literature.


Open dimension packing problem Mathematical model Packaging stability 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Laboratory of Optimization of Industrial Systems (LOSI)University of Technology of TroyesTroyesFrance

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