The min–max order picking problem in synchronised dynamic zone-picking systems

In both manual and automated warehouses, a combination of efficient zoning and picker routing plays an important role in improving travel time, congestion, and system throughput. This paper considers the order picker routing problem in a dynamic and synchronised zoning environment, where the items corresponding to each customer order are picked simultaneously in multiple zones, and zones may change between different orders. The objective is to minimise the maximum time of completing the picking activities in any zone. Using a min–max type of objective not only minimises the makespan of an order picking wave, but it also helps balance the workload of the order pickers more effectively. We present a mathematical model for the optimal solution of this problem, as well as a dynamic programming approach to find the optimal solution for the case where a zone is a set of adjacent aisles. Computational experiments on randomly generated instances show that the dynamic programming approach is able to find optimal solutions in negligible computational times.