Configuring Traditional Multi-Dock, Unit-Load Warehouses

The development of expected-distance formulas for multi-dock-door, unit-load warehouse configurations is the focus of the dissertation. From formulations derived, the width-to-depth ratios minimizing expected distances are obtained for rectangle-shaped, unit-load warehouse configurations. Partitioning the storage region in the warehouse into three classes, the performance of a multi-dock-door, unit-load warehouse is studied when storage regions can be either rectangle-shaped or contour-line-shaped. Our first contribution is the development of formulas for expected distance traveled in storing and retrieving unit loads in a rectangle-shaped warehouse having multiple dock doors along one warehouse wall and storage racks aligned perpendicular to that wall. Two formulations of the optimization problem of minimizing expected distance are considered: a discrete formulation and a continuous formulation with decision variables being the width and depth of the warehouse for single- and dual-command travel. Based on dock door configurations treated in the literature and used in practice, three scenarios are considered for the locations of dock doors: 1) uniformly distributed over the entire width of a wall; 2) centrally located on a wall with a fixed distance between adjacent dock doors; and 3) not centrally located on a wall, but with a specified distance between adjacent dock doors. Our second contribution is the investigation of the effect on the optimal width-to-depth ratio (shape factor) of the number and locations of dock doors located along one wall or two adjacent walls of the warehouse. Inserting a middle-cross-aisle in the storage area, storage racks are aligned either perpendicular or parallel to warehouse walls containing dock doors. As with the warehouse having storage racks aligned perpendicular to the warehouse wall, discrete and continuous formulations of the optimization problem are developed for both single- and dual-command travel and three scenarios for dock-door locations are investigated. Our final contribution is the analysis of the performance of a unit-load warehouse when a storage region or storage regions can be either rectangle-shaped or contour-line-shaped. Particularly, we consider two cases for the locations of dock doors: equally spaced over an entire wall of the warehouse and centrally located on a wall, but with a specified distance between adjacent dock doors. Minimizing expected distance, the best rectangle-shaped configuration is determined and its expected distance is compared with the expected distance in its counterpart contour-line-shaped configuration