Algorithms for multi-item procurement planning with case packs

A distribution case pack contains an assortment of varying quantities of different stock keeping units (SKUs) packed in a single box or pallet, with a goal of reducing handling requirements in the distribution chain. This article studies case pack procurement planning problems that address the trade-off between reduced order handling costs and higher inventory-related costs under dynamic, deterministic demand. The properties of optimal solutions for special cases of the problem involving one and two case packs are first established and these properties are used to solve the problem via dynamic programming. For the general model with multiple predefined case packs, which is shown to be strongly NP-hard, the exact approach is generalized to solve the problem in pseudopolynomial time for a fixed number of case packs. In addition, for large-size problems, the problem formulation is strengthed using valid inequalities and a family of heuristic solutions is designed. Computational tests show that these heuristic approaches perform very well compared to the commercial mixed-integer programming solver CPLEX. In addition to providing detailed methods for solving problems with deterministic demand, strategies for addressing problems with uncertain demands are discussed.