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Figure is an idealized depiction of inventory levels of an item over time

Inventory build-up and depletion

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1. The figure shows initially the inventory level of an item dropping steadily because of usage of this item. When the inventory level is at a certain level, called the ‘reorder point’, a purchase order is issued for this item

2. After the passage of a certain length of time, called the ‘lead time’, this order is filled and the inventory level increases by the amount of the order, Q. This cycle of inventory depletion and order fulfilment repeats itself.

3. Note also that in the diagram the inventory level is kept above a certain amount, called the ‘safety stock’.

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In this system, inventory levels are continuously monitored, and orders are

issued when the inventory is depleted to a predetermined level, called the

reorder point (ROP), as shown in Figure . The order quantity is calculated

on the basis of the EOQ formula, as given above.

The reorder point is set as follows. When an order is issued at the reorder

point, it is gradually depleted to the safety stock (SS) level over the lead

time L (see Figure ). The use of inventory over the lead time L is D × L,

since the annual demand is D Thus the reorder point is given by

Calculating the annual costs to buy this item is straightforward, since the usage per year is D units and the price per unit is p ($).

•Purchase cost = p × D

Annual holding cost is the amount of money spent in renting the space to hold the inventory

Calculation of the annual holding cost is based on the average inventory held. From Figure, the maximum inventory held is SS + Q, decreasing gradually to minimum inventory level, SS. Thus the average inventory held is:

•Average inventory level = (SS + Q + SS)/2 = SS + Q/2

•And the annual holding cost = (SS + Q/2) CH

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Since D is the annual usage of the item, and each time an order is

placed for this item the number of items purchased per order is Q,

the number of orders placed over the whole year is D/Q. The annual

order processing cost includes the cost of identifying the supplier,

preparing a purchase order, chasing it, and receiving the item.

If S is the order processing cost per order, we can calculate the annual

order processing cost:

•Annual order processing cost = (D/Q) S

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Adding these three costs the total annual inventory costs associated with this item are calculated below

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The Fine Garments Company sells fashion clothing. The forecasted

annual demand for their premium leather jacket is 1200. The order-

processing cost per order is $25, and inventory holding cost is

$50/item/year. How many leather jackets should they order in one

shipment?

Answer

Fine Garments should order 35 leather jackets each time they place an order on their supplier in order to minimise their annual inventory costs.