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1.3 A Simple Inventory System

The inputs to program ssq1, the arrival times and the service times, can have any positive real value — they are continuous variables. In some models, however, the input variables are inherently discrete. That is the case with the (trace-driven) discrete-event simulation model of a simple inventory system constructed in this section. As in the previoussection, we begin with a conceptual model then move to a specification model and, finally, to a computational model. 1.3.1 CONCEPTUAL MODEL

Definition 1.3.1 An inventory system consists of a facility that distributes items from its current inventory to its customers in response to a customer demand that is typically random, as illustrated in Figure 1.3.1. Moreover, the demand is integer-valued(discrete) because customers do not want a portion of an item.* Because there is a holding cost associated with items in inventory, it is undesirable for the inventory level to be too high. On the other hand, if the inventory level is too low, the facility is in danger of incurring a shortage cost whenever a demand occurs that cannot be met. Figure 1.3.1. Simple inventory system diagram.
.... ..................................................... ................................................... . ..

demand items

.... . .................................................... ................................................... . ..

order

customers
.... ....... ........................................... ................................................... .. . ...

facilitysupplier
... ....... ........................................... ................................................... .. . ....

items

As a policy, the inventory level is reviewed periodically and new items are then (and only then) ordered from a supplier, if necessary.** When items are ordered, the facility incurs an ordering cost that is the sum of a fixed setup cost independent of the amountordered plus an item cost proportional to the number of items ordered. This periodic inventory review policy is defined by two parameters, conventionally denoted s and S. • s is the minimum inventory level — if at the time of review the current inventory level is below the threshold s then an order will be placed with the supplier to replenish the inventory. If the current inventory level is at or aboves then no order will be placed. • S is the maximum inventory level — when an order is placed, the amount ordered is the number of items required to bring the inventory back up to the level S. • The (s, S) parameters are constant in time with 0 ≤ s < S. * Some inventory systems distribute “items” that are not inherently discrete, for example, a service station that sells gasoline. With minormodifications, the model developed in this section is applicable to these inventory systems as well. ** An alternate to the periodic inventory review policy is a transaction reporting inventory policy. With this policy, inventory review occurs after each demand instance. Because inventory review occurs more frequently, significantly more labor may be required to implement a transaction reporting inventorypolicy. (The scanners at a grocery store, however, require no extra labor). The transaction reporting policy has the desirable property that, for the same value of s, it is less likely for the inventory system to experience a shortage.

1.3 A Simple Inventory System

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A discrete-event simulation model can be used to compute the cost of operating the facility. In some cases, the values ofs and S are fixed; if so, the cost of operating the facility is also fixed. In other cases, if at least one of the (s, S) values (usually s) is not fixed, the cost of operating the facility can be modified and it is natural to search for values of (s, S) for which the cost of operating the facility is minimized. To complete the conceptual model of this simple (one type of item) inventory system...
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