The multiechelon inventory model in Example 12.10 requires about 595 items of on-hand or pipeline inventory, on average, to satisfy the fill rate constraint, even though the mean total demand per week is only 450. See how this changes as the amount of uncertainty decreases. Specifically, make the standard deviations of demand smaller and then run RISK Optimizer (with exactly the same settings). You can make the standard deviations as small as you like. Does the mean total system inventory get closer to 450?

Example 12.10

MANAGING INVENTORY AT LEE SUPPLY

Lee Supply has three retail stores that are supplied by a central warehouse. For this example, the focus is on a single product sold at the stores. At the beginning of each week, each store requests a quantity of this product from the warehouse, and such shipments arrive at the beginning of the following week (one-week lead time). Similarly, at the beginning of each week, the warehouse orders a quantity of this product from an overseas manufacturer, and such shipments arrive in three weeks (three-week lead time). Weekly demands at each retailer are independent, normally distributed, random variables, and any demands that cannot be met from on-hand inventory are backordered and satisfied as soon as possible. The means and standard deviations of demand can vary across retailers, but they are constant through time. All ordering policies are characterized by an order-up-to quantity Q, where each retailer and the warehouse can have a different Q. For a retailer, this works as follows. At the beginning of a week, the retailer checks the beginning inventory (after the arrival of the order from the previous week and after satisfying any backorders from the previous week) and subtracts the mean demand. This difference is its expected inventory by the end of the week. It then places an order large enough to raise this difference to Q. For example, if Q = 180, the beginning inventory is 150, and the mean demand is 140, the retailer will place an order for 180 - (150 - 140) = 170 it items from the warehouse. Depending on its own on-hand inventory, the warehouse might or might not be able to satisfy all retailer requests. If it has enough on hand, it satisfies the requests completely. However, if it doesn't have enough on hand, it allocates proportionally. For example, suppose the three retailer requests are for 150, 200, and 100 items, and the warehouse has only 360 items on hand, or 80% of the total requested. Then each retailer gets 80% of its request (rounded to the nearest integer). Finally, the ordering policy for the warehouse, again determined by an order-up-to quantity Q, works as follows. The warehouse calculates the sum of its current and pipeline inventory (the latter being shipments on the way from the manufacturer) and subtracts the total it is about to send to the retailers this week. Then it orders enough to raise this difference to Q. The company would like to choose the four Q values to minimize the average total inventory in the system over time, while assuring that there is a large probability of having a high fill rate (the percentage of demand met on time). How should it proceed?

Objective To develop a simulation model that allows the company to evaluate the total system inventory and the fill rate for any values of the order-up-to quantities, and then to choose "good" values of these quantities.