A multistart biased-randomized algorithm for solving a three-dimensional case picking problem with real-life constraints

This paper introduces the three-dimensional case picking problem (3D-CPP) and proposes a multistart biased-randomized algorithm (BRA) to solve it. The 3D-CPP combines two important topics in modern warehouse logistics: the pallet loading problem and the routing of pickers in manual warehouses. The proposed optimization procedure aims at minimizing the overall distance traveled by the pickers, and is achieved by combining a routing problem (i.e., the order in which picking positions are visited) with a loading problem (i.e., the way in which cases are placed onto the pallet). We also consider additional constraints regarding the weight, vertical support, and strength of the cases. In order to solve this problem, we first propose a constructive heuristic which combines routing and packing procedures. This initial heuristic is then extended into a multistart BRA by employing a skewed probability distribution to introduce a certain degree of randomness during the solution-construction process. A series of computational experiments allow us to assess the quality of the proposed approach, through a comparison with other algorithms as well as using real-life data provided by an industrial partner.