A bi-criteria model for the inventory aggregation problem under risk pooling

Inventory aggregation, also called Risk Pooling, is one of the most efficient ways to reduce the level of safety stocks thereby reducing inventory across the supply chain. Determining the best level of aggregation is a difficult problem and needs extensive study of all the possible scenarios that can affect this decision. Minimizing costs in a supply chain is no longer the sole priority of businesses. Maintaining a high level of responsiveness is also considered equally important. The conflicting nature of these two criteria makes the solution of the problem difficult. In this paper, we develop a bi-criteria nonlinear stochastic integer programming model to determine the best supply chain distribution network to meet customer demands, where minimizing costs while maintaining high levels of responsiveness is important. We develop a two-stage optimization algorithm to solve this problem.