A multi-dock, unit-load warehouse design

Expected distance formulations are developed for a rectangle-shaped, unit-load warehouse having dock doors along one warehouse wall. Based on dock-door configurations treated in the literature and/or used in practice, three scenarios are considered: (i) equally spaced dock doors spanning a wall; (ii) equally spaced dock doors with a specified distance between adjacent dock doors, and an equal number of dock doors located on each side of the wall's centerline; and (iii) equally spaced dock doors with a specified distance between adjacent dock doors and the first dock door located a given distance to the right of the left wall. Defining the shape factor as the warehouse width divided by its depth, the shape factor minimizing expected distance is determined. Single- and dual-command travel results from discrete formulations are compared with results from closed-form expressions using continuous approximations. The optimal shape factor depends on the number and locations of dock doors. When the distance between adjacent dock doors is a function of the warehouse's width, previous research results are confirmed. However, when distances between adjacent dock doors are specified, our results differ from a commonly held belief the optimal shape factor is always less than or equal to 2.0.