Pallet Loading Problem Model Based on Nested Loop Algorithm

Abstract

This model is based on the problem B in the Mathematical Modeling Contest of North China Electronic Power University in 2015. It works out solutions for non-overlapping box arrangement with load-bearing limits and without bearing limits, which can finally solve the practical loading problem of overlapping of multi-type boxes considering bearing limits. About the mentioned practical problem, it is actually a two-dimensional layout problem. In this paper, models for integer layout in unified direction are established by integer programming. First, select an area-undetermined rectangle in the lower-left corner of the pallet and pack boxes X in it in unified direction. Then divide the residual area into two pars, B and C, and pack boxes Y in each part in unified direction. The layout of the residual area is concerned with the size of the lower-left corner. To reduce discussions, the maximum area utilization of B and C is set as constraint which will be considered comprehensively, the minimum of the whole oddments of three areas be set as objective function, thus four layout methods can be obtained. Then exchange the box types in the selected rectangle and the residual area, there comes another four layout methods. By analyzing the packing and division methods of the eight layout, the optimal solution can be concluded.