Optimal Inventory Control with Retail Pre-Packs

A pre-pack is a collection of items used in retail distribution. By grouping multiple units of one or more stock keeping units (SKU), distribution and handling costs can be reduced; however, ordering flexibility at the retail outlet is limited. This paper studies an inventory system at a retail level where both pre-packs and individual items (at additional handling cost) can be ordered. For a single-SKU, single-period problem, we show that the optimal policy is to order into a band with as few individual units as possible. For the multi-period problem with modular demand, the band policy is still optimal, and the steady-state distribution of the target inventory position possesses a semi-uniform structure, which greatly facilitates the computation of optimal policies and approximations under general demand. For the multi-SKU case, the optimal policy has a generalized band structure. Our numerical results show that pre-pack use is beneficial when facing stable and complementary demands, and substantial handling savings at the distribution center. The cost premium of using simple policies, such as strict base-stock and batch-ordering (pre-packs only), can be substantial for medium parameter ranges.