• An important class of simulation problems involves inventory systems. A simple inventory system is shown in Figure 2.11.

• This inventory systems has a periodic review of length N, at which time the inventory level is checked. An order is made to bring the inventory up to level M. At the end of the first review period, an order quantity, $Q_1$, is placed.

• In this inventory system, the lead time (i.e.., the length of time between the placement and receipt of an order) is zero

• Demands are not usually known with certainty, so the order quantities are probabilistic. Demand is shown as being uniform over the period in Figure 2.11.

• In actuality, demand are not usually uniform and do fluctuate over time. One possibility is that demands all occur at the beginning of the cycle.

• Another is that the lead time is random of some positive length.

• Notice that, in the second cycle, the amount in inventory drops below zero, indicating a shortage.

• In Figure 2.11, these units are backordered; when the order arrives, the demand for the backordered items is satisfied first. To avoid shortages, a buffer, or safety, stock would need to be carried.

• Carrying stock in inventory has an associated cost attributed to the interest paid on the funds borrowed to buy the items (this also could be considered as the loss from not having the funds available for other investment purposes).

• Other costs can be placed in the carrying or holding cost column: renting of shortage space, hiring of guards, and so on. An alternative to carrying high inventory is to make more frequent reviews and, consequently, more frequent purchases or replenishments.

• This has an associated cost: the ordering cost. Also, there is a cost in being short. Customers could get angry, with a subsequent loss of good will.

• Larger inventories decrease the possibilities of shortages. These costs must be traded off in order to minimize the total cost of an inventory system.

• The total cost (or total profit) of an inventory system is the measure of performance. This can be affected by the policy alternatives.

Various costs involved in the inventory system are

1. Holding cost: This is related to the cost of keeping items of inventory over a period of time.

2. Shortage cost :It is related with the cost of not having available inventory when demanded.

3. Setup cost: The cost associated with order is called setup cost.