Optimal inventory management using retail prepacks

Many types of retail items are shipped through the supply chain from the manufacturer to the stores in “prepacks,” which may consist of multiple units of the same stock keeping unit (SKU) or combinations of related SKUs packaged together. Prepacks reduce shipping and handling costs in the supply chain, but they can also increase supply - demand imbalances. This paper is the first to develop a general methodology that determines optimal replenishment policies for combinations of different prepacks. The model uses stochastic dynamic programming, and can be solved by a linear program in the steady state case. We formulate the general multi-SKU prepack case and develop specific solutions for the one-SKU and two-SKU prepack cases. A numerical analysis of various one-SKU and two-SKU prepack choices leads to some interesting insights about the optimal design of prepacks from the retailer’s standpoint. Single unit shipments are cost effective only for very low demand rates. Having multiple prepack sizes leads to significant cost savings, relative to a single prepack size. However, the incremental benefits of including larger numbers of different prepacks appear to diminish rapidly. Unless item demands are perfectly correlated, multi-SKU prepacks appear to have only a limited expected cost advantage over optimally chosen single-SKU prepacks. But multi-SKU prepacks can reduce the expected number of prepacks handled per period, which can be an important consideration for distribution centers. The best choices for multi-SKU prepacks can be counterintuitive, and some apparently attractive choices for two-SKU prepacks perform worse than one-SKU prepacks.