In most distribution centers, products are received from the suppliers in units of pallet, stored in a rack, moved to the picking area for replenishment, picked according to customer orders, and shipped to customers. In some distribution centers, however, replenishment is made in not a whole pallet but only a portion of a pallet load, mainly due to the limited space in the order-picking area; as a result, partially loaded pallets occupy cells in the rack. As the number of slow-moving items increases, more cells are occupied by partially loaded pallets so that fewer empty cells are available for storing full, incoming pallets. This will necessitate the construction or leasing of additional storage space, which will entail significant cost. As an alternative, we propose pallet consolidation, which involves moving a partial load to another partially-loaded pallet in order to create one empty cell in the rack. In this paper, we define three pallet consolidation problems; formulate each problem as a binary integer programming model; and present heuristic algorithms for the problems. The average performance of each of the proposed heuristics is evaluated using simulation.