Operations and Supply Chain Management The Core

378 OPERATIONS AND SUPPLY CHAIN MANAGEMENT
∙ There are two basic types of multiple-period models, with the key distinction being what
triggers the timing of the order placement.
∙ With the fixed–order quantity model, an order is placed when inventory drops to a low level
called the reorder point.
∙ With the fixed–time period model, orders are placed at fixed intervals of time, say every two
weeks. The order quantity varies for each order.
∙ Safety stock is extra inventory that is carried for protection in case the demand for an item is
greater than expected. Statistics are used to determine an appropriate amount of safety stock
to carry based on the probability of stocking out.
∙ Inventory turn measures the expected number of times that average inventory is replaced
over a year. It can be calculated in aggregate using average inventory levels or on an
individual item basis.
Single-period problem Answers the question of how much to order when an item is purchased
only one time and it is expected that it will be used and then not reordered.
Fixed–order quantity model (Q-model) An inventory control model where the amount
requisitioned is fixed and the actual ordering is triggered by inventory dropping to a specified level
of inventory.
Fixed–time period model (P-model) An inventory control model that specifies inventory is
ordered at the end of a predetermined time period. The interval of time between orders is fixed and
the order quantity varies.
Inventory position The amount on-hand plus on-order minus backordered quantities. In the case
where inventory has been allocated for special purposes, the inventory position is reduced by these
allocated amounts.
Optimal order quantity (Q opt ) This order size minimizes total annual inventory-related costs.
Reorder point An order is placed when the inventory position drops to this level.
Safety stock The amount of inventory carried in addition to the expected demand.
Inventory turn A measure of the expected number of times that inventory is replaced over a year.
Price-break model The model is useful for finding the order quantity of an item when the price
of the item varies with the order size.
​C​ u ​
​P ≤ ​ ______
​C​ o ​ + ​C​ u ​ [11.1]
​Inventory position = On-hand + On-order − Backorder​ [11.2]
​TC = DC + __ ​ D Q ​ S + __ ​ Q ​ H​ [11.3]
2
____
​Q​ opt ​ = ​ √
​ ____ 2DS
H ​ [11.4]
​R = ¯ ​d ​L​ [11.5]
​R = ¯ ​d ​L + z​σ​ L ​ [11.6]
n
​∑
¯ i=1
​d ​ = ​
​d​ i ​
______ ​ [11.7]
n
___________
n
​∑
i=1
​σ​ d ​ = ​√ ​(​d​ i ​ − ¯ ​d ​ )​ 2 ​
___________
n
​ ​ [11.8]