Abstract
We consider the distributor’s pallet loading problem where a set of different boxes are packed on the smallest number of pallets by satisfying a given set of constraints. In particular, we refer to a real-life environment where each pallet is loaded with a set of layers made of boxes, and both a stability constraint and a compression constraint must be respected. The stability requirement imposes the following: (a) to load at level k+1 a layer with total area (i.e., the sum of the bottom faces’ area of the boxes present in the layer) not exceeding α times the area of the layer of level k (where α≥1), and (b) to limit with a given threshold the difference between the highest and the lowest box of a layer. The compression constraint defines the maximum weight that each layer k can sustain; hence, the total weight of the layers loaded over k must not exceed that value. Some stability and compression constraints are considered in other works, but to our knowledge, none are defined as faced in a real-life problem. We present a matheuristic approach which works in two phases. In the first, a number of layers are defined using classical 2D bin packing algorithms, applied to a smart selection of boxes. In the second phase, the layers are packed on the minimum number of pallets by means of a specialized MILP model solved with Gurobi. Computational experiments on real-life instances are used to assess the effectiveness of the algorithm.
Highlights
The distributor’s pallet loading problem (DPLP) is a topic of wide interest for operational research and companies that deal with logistics, transport, and storage, in addition to production that leads to small and medium-sized packaging.The problem is to find the optimal loading of parallelepiped-shaped boxes, not necessarily with the same sizes, on the fewest possible number of pallets, with predefined dimensions and weight limit
We refer to a real-life environment where each pallet is loaded with a set of layers made of boxes, and both a stability constraint and a compression constraint must be respected
DPLP is strongly NP-hard, since it is a generalization of the bin packing problem (BPP) [1,2,3,4,5,6]
Summary
The distributor’s pallet loading problem (DPLP) is a topic of wide interest for operational research and companies that deal with logistics, transport, and storage, in addition to production that leads to small and medium-sized packaging. The problem is to find the optimal loading of parallelepiped-shaped boxes, not necessarily with the same sizes, on the fewest possible number of pallets, with predefined dimensions and weight limit. For a variant of this problem, the so-called container loading problem, which differs in the fact that, in general, constraints limiting the possibilities of layers overlapping are not explicit, we refer to [20,21,22,23,24,25,26,27,28,29]. We present in this paper a two-step algorithm to solve the pallet construction problem, basing our tests on real commercial orders from a logistics company using automated robots for creating and managing pallets. For similar work we refer to [30], which introduces visibility and contiguity constraints
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