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PERIODIC REVIEW MODEL WITH PROBABILISTIC DEMAND 441

another decision variable; that is, instead of ordering at every periodic review, a
reorder point is established. If the inventory on hand at the periodic review is at or
below the reorder point, a decision is made to order up to the replenishment level.
However, if the inventory on hand at the periodic review is greater than the reorder
level, such an order is not placed, and the system continues until the next periodic
review. In this case, the cost of ordering is a relevant cost and can be included in a
cost model along with holding and stock-out costs. Optimal policies can be reached
based on minimizing the expected total cost. Situations with lead times longer than
the review period add to the complexity of the model. The mathematical level
required to treat these more extensive periodic review models is beyond the scope
of this text.

NOTES AND COMMENTS

1 The periodic review model presented in this section was used to initiate an order whenever the
is based on the assumption that the lead time for reorder point was reached. The safety stock for
an order is less than the periodic review period. this model was based on the probabilistic
Most periodic review systems operate under this demand during the lead time. The periodic
condition. However, the case in which the lead time review model presented in this section also
is longer than the review period can be handled by determined a recommended safety stock.
defining H in Equation (10.38) as the inventory However, because the inventory review was
position, where H includes the inventory on hand only periodic, the safety stock was based on
plus the inventory on order. In this case, the order the probabilistic demand during the review
quantity at any review period is the amount needed period plus the lead-time period. This longer
for the inventory on hand plus all outstanding period for the safety stock computation means
orders needed to reach the replenishment level. that periodic review systems tend to require a
2 In the order-quantity, reorder point model larger safety stock than continuous review
discussed in Section 10.7, a continuous review systems.

Summary

In this chapter we introduced a number of inventory models:
l The basic inventory problem for an organization is to balance the need for having enough inventory to
meet expected demand but to keep the associated inventory costs at a minimum.
l The key costs involved in inventory are ordering costs, holdings costs and, in some situations,
backorder costs. In practice it can be difficult to calculate costs accurately.
l The basic economic order quantity (EOQ) model determines the quantity of inventory to order each
time that will minimize total inventory costs. The model also provides details on the re-order time.
l The EOQ model can be adapted to determine the economic production lot size and also to deal with
quantity discounts.
l Inventory models can be developed for situations where demand is probabilistic and not deterministic
and for multiperiod situations.

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