Page 605 - Introduction to Business

CHAPTER 16 Managing Business Operations 579

For example, if the annual demand for an item is D 600 units and the quan-
tity procured in each order is Q 30 units, then the number of orders per year
would be N D/Q 600/30 20, and the average inventory level will be L Q/2
30/2 15 units.
We now have that
AOC ON OD/Q
AHC HL HQ/2
TAC OD/Q HQ/2

The operations manager would like to find the value of Q that minimizes TAC.
Because L Q/2, the operations manager is also implicitly finding the value of L
that minimizes TAC.
For example, if the annual demand for an item is D 600 units, the ordering
cost is O $90 per order, the annual holding cost is h 30 percent of the item’s
value, the item’s value is V $100, and the item is sold in boxes of 10 units, then to
find the value of Q that minimizes TAC, the operations manager would perform the
calculations presented in Exhibit 16.14. In these calculations, H hV (0.30)(100)
30. When the number of boxes procured per order is 1 and thus the number of
units procured per order is 10, we can calculate the following:
N D/Q 600/10 60
L Q/2 10/2 5
AOC ON (90)(60) $5400
AHC HL (30)(5) $150
TAC AOC AHC $5400 $150 $5550
The other calculations in Exhibit 16.14 are performed similarly.
Observe that the minimum TAC is $1800, which is achieved by L 30 units,
resulting from procuring 6 boxes per order or, equivalently, procuring 60 units per
order. Any average inventory level lower or higher than 30 units will lead to higher
total annual ordering and holding costs. The operations manager has thus found an
inventory level that is not too low or too high. Of special interest is that the mini-
mum TAC occurs when the AOC and the AHC are equal, or balanced, in our exam-
ple at $900 each. This is always the case in this model.
reality What do you think would happen if companies stopped carrying
CH ECK inventory?

EXHIBIT 16.14
Finding the Optimal Inventory Level

Number of Quantity Number of Average Annual Annual Total Annual
Boxes Procured in Orders Inventory Ordering Holding Ordering and
Procured Each Order per Year Level Cost Cost Holding Cost
per Order Q N L AOC AHC TAC
1 10 60 5 $5400 $ 150 $5550
2 20 30 10 $2700 $ 300 $3000
3 30 20 15 $1800 $ 450 $2250
4 40 15 20 $1350 $ 600 $1950
5 50 12 25 $1080 $ 750 $1830
6 60 10 30 $ 900 $ 900 $1800
7 70 9 35 $ 771 $1050 $1821
8 80 8 40 $ 675 $1200 $1875
9 90 7 45 $ 600 $1350 $1950
10 100 6 50 $ 540 $1500 $2040

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