Order picking problems under weight, fragility, and category constraints

Warehouse order picking activities are among the ones that impact the most the bottom lines of warehouses. They are known to often account for more than half of the total warehousing costs. New practices and innovations generate new challenges for managers and open new research avenues. Many practical constraints arising in real-life have often been neglected in the scientific literature. We introduce, model, and solve a rich order picking problem under weight, fragility, and category constraints, motivated by our observation of a real-life application arising in the grocery retail industry. This difficult warehousing problem combines complex picking and routing decisions under the objective of minimizing the distance traveled. We first provide a full description of the warehouse design which enables us to algebraically compute the distances between all pairs of products. We then propose two distinct mathematical models to formulate the problem. We develop five heuristic methods, including extensions of the classical largest gap, mid point, S-shape, and combined heuristics. The fifth one is an implementation of the powerful adaptive large neighborhood search algorithm specifically designed for the problem at hand. We then implement a branch-and-cut algorithm and cutting planes to solve the two formulations. The performance of the proposed solution methods is assessed on a newly generated and realistic test bed containing up to 100 pickups and seven aisles. We compare the bounds provided by the two formulations. Our in-depth analysis shows which formulation tends to perform better. Extensive computational experiments confirm the efficiency of the ALNS matheuristic and derive some important insights for managing order picking in this kind of warehouses