A travel-time model for a person-onboard order picking system

The design of an order picking system in a distribution center depends on several decisions, where a key decision is determining the optimal storage system configuration (the number, length, and height of the storage aisles). To make this decision, a throughput model that considers vertical, as well as horizontal, travel is needed. In this paper we extend prior research that considers horizontal travel for a given number and length of the storage aisles so that we are also able to consider the height of the aisles as well. Such a model will provide a more accurate estimate of the throughput of an order picker and it will also permit an examination of the tradeoff between the length and height of the aisles. The analytical model we develop to estimate throughput is based on probability models and order statistics results assuming random storage. It is intended for person-onboard order picking systems and we consider both Tchebychev and rectilinear travel. We illustrate the use of our travel-time model by incorporating it into a simple, cost-based optimization model to recommend the height of a one-pallet-deep storage system.