Facility logistics, warehousing, as/rs, order fulfillment, product allocation


This dissertation focuses on developing analytical models for automated storage and retrieval system with multiple in-the-aisle pick positions (MIAPP-AS/RS). Specifically, our first contribution develops an expected travel time model for different pick positions and different physical configurations for a random storage policy. This contribution has been accepted for publication in IIE Transactions (Ramtin & Pazour, 2014) and was the featured article in the IE Magazine (Askin & Nussbaum, 2014). The second contribution addresses an important design question associated with MIAPP-AS/RS, which is the assignment of items to pick positions in an MIAPP-AS/RS. This contribution has been accepted for publication in IIE Transactions (Ramtin & Pazour, 2015). Finally, the third contribution is to develop travel time models and to determine the optimal SKUs to storage locations assignment under different storage assignment polies such as dedicated and class-based storage policies for MIAPP-AS/RS. An MIAPP-AS/RS is a case-level order-fulfillment technology that enables order picking via multiple pick positions (outputs) located in the aisle. We develop expected travel time models for different operating policies and different physical configurations. These models can be used to analyze MIAPP-AS/RS throughput performance during peak and non-peak hours. Moreover, closed-form approximations are derived for the case of an infinite number of pick positions, which enable us to derive the optimal shape configuration that minimizes expected travel times. We compare our expected travel time models with a simulation model of a discrete rack, and the results validate that our models provide good estimates. Finally, we conduct a numerical experiment to illustrate the trade-offs between performance of operating policies and design configurations. We find that MIAPP-AS/RS with a dual picking floor and input point is a robust configuration because a single command operating policy has comparable throughput performance to a dual command operating policy. As a second contribution, we study the impact of selecting different pick position assignments on system throughput, as well as system design trade-offs that occur when MIAPP-AS/RS is running under different operating policies and different demand profiles. 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. As the third and final contribution, we study the impact of dedicated and class-based storage policy on the performance of MIAPP-AS/RS. We develop mathematical optimization models to minimize the travel time of the crane by changing the assignment of the SKUs to pick positions and storage locations simultaneously. We develop a more tractable solution approach by applying a Benders decomposition approach, as well as an accelerated procedure for the Benders algorithm. We observe high degeneracy for the optimal solution when we use chebyshev metric to calculate the distances. As the result of this degeneracy, we realize that the assignment of SKUs to pick positions does not impact the optimal solution. We also develop closed-form travel time models for MIAPP-AS/RS under a class-based storage policy.

Graduation Date





Pazour, Jennifer


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Industrial Engineering and Management Systems

Degree Program

Industrial Engineering








Release Date

May 2015

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)