Date of Graduation


Document Type


Degree Name

Master of Science in Industrial Engineering (MSIE)

Degree Level



Industrial Engineering


John A. White

Committee Member

Russell D. Meller

Second Committee Member

Letitia M. Pohl


Philosophy, Religion and theology, Facility logistic, Warehouse design


This thesis develops expected travel distance expressions for both single- and dual-command operations in a unit-load warehouse design with multiple docks. Storage racks are aligned perpendicular to the wall containing docks. Results are presented for continuous and discrete formulations. Because of the importance of how docks are located on a wall, different dock locations are investigated, including uniformly distributed docks along one wall, specified distances between adjacent docks located symmetrically about the mid-point of a warehouse wall, and any distribution of locations along one wall. Among the results obtained, we find that the width-to-depth ratio of the storage area (commonly called shape factor) that minimizes expected distance traveled is a function of the number of docks and their locations. We find that the spacing between adjacent docks and the distance the first dock is from either the left end of the wall containing the docks or the centerline of the warehouse can significantly affect the optimal shape factor. Two cases are treated for the distance between adjacent docks: a) the distance is a function of the width of the storage area or the width of the storage area is a function of the number of docks and the distance between them and b) the distance is a fixed value. In the former case, our results are consistent with those obtained by others; however, in the latter case, some of our results will be surprising to many who have studied similar design problems.