Designing packing boxes to minimize number of box types

Abstract

In a product packing procedure, many types of packing boxes may be used if a factory has several kinds of goods or products. The cost spent for many types of boxes is added to the manufacturing cost. However, it would be more efficient in the aspects of the cost reduction and the production management if we can design reasonable box sizes and can minimize the number of box types for packing goods. In this work, we propose a heuristic rectangular box design algorithm for packing each kind of rectangular goods when the number of goods per box is given. The objective of this algorithm is to design the rectangular boxes with the shapes close to cubes as much as possible under the given bounds. Furthermore, we propose a heuristic method and an integer linear programming model for minimizing the number of types of packing boxes. A smaller box could be substituted by a larger one only when the percentage change on each size of both boxes (with respect to the larger box) does not exceed a given value. Example problems are given to illustrate the use of the proposed heuristic and model.