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

Abstract : 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.