Other Periodic-Review Inventory Models

This inventory policy follows immediately from some of the computations made in Example 3.8. In this case, Sgj- = (Idiji + z -sl = 449, which is the same as the computation of s in Example 3.8. For the (S,T) system, we know that an order will be placed every T = 4 days, so each order needs to cover uncertain demand until the next order arrives T + L = 8 days later. In the (s, S, T) system of Example 3.8, inventory levels were raised higher to allow fewer orders to be placed. Thus, utilizing the (S, T) system, ordering costs will be higher, but inventory levels will be lower. 

The final periodic-review system we consider is actually the simplest, the base-stock system. In this system, we once again place an order at each review interval, but in this case, the review interval is set equal to the smallest discrete time unit covered by the system. Thus, for this inventory system, the period and the time unit are one-in-the-same. For example, if we manage the system using days as our time units—i.e., if lead time is specified in days—then in a base-stock system, we would review the inventory position X at the start of each day and place an order of size Q = S - x, to be received L days later. Thus, for this system, the review interval is T = 1 and the base-stock level is set to Sb = fr (CSL), where F is the cdf of the DLTR distribution, which in this case is the distribution of demand over L + 1 time units. If the demand rate per time unit, D, is normally distributed, then we can compute 

Sometimes, the base-stock system is referred to as an (S - 1,S) system since the reorder point for this system is effectively s = S - 1, meaning that, as long as a non-zero demand (i.e., at least one unit of demand) occurs in the reorder interval of T = 1, we reorder to bring the inventory position back to S. 

Up to this point, we have discussed a relatively large number of issues and techniques related to the management of a single item at a single site. In all of our analysis, we have assumed either a single point (or season) of demand, or a stable (stationary), repeating series of demand values. Next, we consider situations where many demand values must be estimated over time. 

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