Mathematics of Pooling

In Chapters 4 and 5 we develop the mathematical models and analysis of systems that are designed to take advantage of the pooling of inventories. In Chapter 4, the analysis pertains to uncapacitated systems. We start by studying the newsvendor problem in which one or more items are managed at a single location. We then extend the basic newsvendor model to a multi-echelon distribution system. We discuss one of the key difficulties in managing such systems, the possibility of having too much inventory at one location and no inventory at another location, which is called system imbalance. We make various assumptions about unit costs, holding costs, fixed ordering costs, and demand uncertainty and rates in these extensions. We close the chapter by developing a multi-echelon model and algorithm for setting stock levels for an on-line retailer.