Product allocation problem for an AS/RS with multiple in-the-aisle pick positions

An automated storage/retrieval system with multiple in-the-aisle pick positions is a semi-automated case-level order fulfillment technology that is widely used in distribution centers. We study the impact of product to pick position assignments on the expected throughput for different operating policies, demand profiles, and shape factors. We develop efficient algorithms of complexity O(nlog(n)) that provide the assignment that minimizes the expected travel time. Also, for different operating policies, shape configurations, and demand curves, we explore the structure of the optimal assignment of products to pick positions and quantify the difference between using a simple, practical assignment policy versus the optimal assignment. Finally, we derive closed-form analytical travel time models by approximating the optimal assignment's expected travel time using continuous demand curves and assuming an infinite number of pick positions in the aisle. We illustrate that these continuous models work well in estimating the travel time of a discrete rack and use them to find optimal design configurations.