We will extend the results of the last chapter in three ways. First, we will consider multi-stage systems. These systems are characterized by multiple locations where inventory management decisions have to be made. Recall that in the last chapter, there was only a single stage, that is, the ordering and inventory management decisions involved only one location. Second, we will work with the reorder interval as the decision variable over which cost is optimized instead of the order quantity. We continue to assume that demand occurs at a deterministic and stationary rate. Thus, once we know the reorder interval, we can easily determine the corresponding order quantity. Therefore, the two decision variables are equivalent; our preference for the reorder interval is due to practical reasons, as we explain below. Third, instead of determining the optimal solution, we will develop algorithms that determine reorder intervals that are easier to use in practice but are not necessarily optimal. However, we will establish that the worst possible cost will not be higher than the optimal cost by more than 6%. These inventory management policies that we will develop are referred to as power-of-two (PO2) policies. As we explained in Chapter 1, many of the inventory management models are applicable in production systems as well. In inventory systems, these models are used to determine the optimal order quantity and reorder interval; in production systems the objective is to find the lot size and the reorder interval between consecutive production runs. The PO2 policies that we will study in this chapter can be applied both in production and inventory systems. We will discuss the specific applications while studying various types of multi-stage systems. The first advantage of the use of the reorder interval is motivated by a production system. Clearly, while planning production, it is natural to think in terms of producing items once every planning period (for example, shift, week, or month). When working with the order quantity as the decision variable, the corresponding reorder interval may be any real number; remember the relationship from last chapter, T = Q/λ. It could be