Inventory management with actual palletized transportation costs and lost sales

Pallets are widely used for bulk shipping in the United States and Europe. In response to the call for more comprehensive research on inventory management that incorporates practical freight rates, this study investigates optimal inventory replenishment decisions by explicitly considering palletized shipping rates and lost sales in multi-product multi-period inventory system facing stochastic demand. We first introduce a stepwise transportation cost function that accurately captures real-world palletized less-than-truckload (LTL) and truckload (TL) shipment costs by accounting for both pallet quantity and truck capacity. We then formulate two novel inventory models that consider palletized freight transportation costs and the coexistence of LTL and TL shipments, with one model excluding lost sales and the other specifically incorporating lost sales. We apply both models to a wholesaler based in the Midwest, U.S., and analyze the effects of varying shipping rates and lost sales on inventory decisions. Our results show that the inclusion of lost sales in the inventory replenishment model can potentially reduce total costs for the company. Interestingly, our findings contradict prevailing industry practices of maximizing truck capacity, revealing that filling up the “free” space on a truck may increase total logistics costs. This holds true even when shipping rates are relatively high and lost sales are considered. Furthermore, our results suggest that joint optimization of transportation and inventory decisions may not be necessary when shipping costs are small relative to inventory costs and lost sales are not considered. However, as shipping rates increase and lost sales are factored in, a joint optimization that accounts for all factors can yield much greater savings.