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ECONOMIC ORDER QUANTITY (EOQ) MODEL 413

The advantage of the trial-and-error approach is that it is rather easy to do and
provides the total annual cost for a number of possible order quantity decisions. In
this case, the minimum cost order quantity appears to be approximately 2000 cases.
The disadvantage of this approach, however, is that it does not provide the exact
minimum cost order quantity.
Refer to Figure 10.3. The minimum total cost order quantity is denoted by an
order size of Q*. By using differential calculus, it can be shown (see Appendix 10.1)
The EOQ formula that the value of Q* that minimizes the total annual cost is given by the formula:
determines the optimal
order quantity by s ffiffiffiffiffiffiffiffiffiffiffiffi
balancing the annual

holding cost and the Q ¼ 2DC o (10:5)
annual ordering cost. C h

In 1915 F.W. Harris This formula is referred to as the economic order quantity (EOQ) formula and can be
derived the mathematical applied to any combination of D, C h and C o .
formula for the economic Using equation (10.5), the minimum total annual cost order quantity for Cape
order quantity. It was the
first application of Cola is:
quantitative methods to r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
the area of inventory 2ð104; 000Þ32
management. Q ¼ 2 ¼ 1824 cases
Problem 2 at the end of The use of an order quantity of 1824 in Equation (10.4) shows that the minimum
the chapter asks you to cost inventory policy for Cape Cola has a total annual cost of E3649. Note that
show that equal holding Q* ¼ 1824 balances the holding and ordering costs. Check for yourself to see that
and ordering costs is a 2
property of the EOQ these costs are equal.
model.
The When-to-Order Decision
Now that we know how much to order, we want to address the question of when to
order. To answer this question, we need to introduce the concept of inventory
position. The inventory position is defined as the amount of inventory on hand plus
the amount of inventory on order. The when-to-order decision is expressed in terms
The reorder point is of a reorder point – the inventory position at which a new order should be placed.
expressed in terms of The manufacturer of Cape Cola guarantees a two-day delivery on any order
inventory position, the
amount of inventory on placed by CBC. If we assume that CBC operates 250 days per year, the annual
hand plus the amount on demand of 104 000 cases implies a daily demand of 104 000/250 ¼ 416 cases. So, we
order. Some people think expect (two days)(416 cases per day) ¼ 832 cases of Cape Cola to be sold during the
that the reorder point is two days it takes a new order to reach the CBC warehouse. In inventory terminol-
expressed in terms of
inventory on hand. With ogy, the two-day delivery period is referred to as the lead time for a new order, and
short lead times, the 832-case demand anticipated during this period is referred to as the lead-time
inventory position is demand. So CBC should order a new shipment of Cape Cola from the manufacturer
usually the same as the when the inventory reaches 832 cases. For inventory systems using the constant
inventory on hand.
However, with long lead demand rate assumption and a fixed lead time, the reorder point is the same as the
times, inventory position lead-time demand. For these systems, the general expression for the reorder point is
may be larger than as follows:
inventory on hand.

r ¼ dm (10:6)

2
Actually, Q* from equation (10.5) is 1824.28, but because we cannot order fractional cases of cola, a Q* of 1824
is shown. This value of Q* may cause a few cents deviation between the two costs. If Q* is used at its exact value,
the holding and ordering costs will be exactly the same.

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