Inventory Model- Management Science

2. Learning objectives
compute total annual
inventory cost; and
explain when to make
an order for inventory
replacement
discuss the economic
order quantity model;

3. overview
Inventories are goods intended
for sale. They are purchased
from suppliers and sold to
customers.

4. ECONOMIC ORDER
QUANTITY (EOQ) MODEL
•The economic order quantity (EOQ) model, developed by F. W.
Harris in 1915, is a deterministic inventory model, which is
applicable when there is a constant rate of demand for a product.
• It assumes that the production is almost equal to the sales. The
inventory level, then, is almost constant.
•It also assumes that the demand for a product is independent of
the demand for other products.
•At the EOQ level, the total cost of inventory is at is optimal
level.

5. • Economic Order Quantity (EOQ) Model is developed by
F.W. Harris in 1915, a deterministic inventory model,
which is applicable when there is a constant rate of
demand for a product.
• This model answers two (2) important questions
relative to inventory management. These are:
• 1. How much goods should be ordered?
• 2. When should an order be made?

6. The EOQ model works effectively under the following assumptions:
1. The demand is considered normal and constant.
2. The ordering cost, carrying cost, and purchase price are constant
and not dependent on the quantity ordered.
3. Shortages do not exist.
4. The lead time is constant.
5. The order quantity is the same for each order.
Assumptions of the eoq model

7. Number of Goods to Order Two (2) Types of Inventory
Costs
Ordering Cost - is the cost when placing an order for a
product.
Carrying Cost - is the cost associated with maintaining an
inventory.
Number of goods to order

8. 1.EOQ formula
2. Total annual inventory cost formula
3. Total carrying cost formula
4. Average inventory level formula
5. Total ordering cost formula
Formulas Relating to
Order Quantity

9. Formulas Relating to Order Quantity
1. EOQ formula:
where:
EOQ – economic order quantity
D – annual demand
OC – ordering cost per unit
CC – carrying cost per unit

10. 2. Total annual inventory cost formula:
where:
TAIC - total annual inventory cost
TOC - total ordering cost
TCC - total carrying cost
TAIC = TOC + TCC

11. 4. Average inventory level formula:
where:
TOC - total ordering cost
D - annual demand
EOQ - economic order quantity
OC - ordering cost per unit
5. Total ordering cost formula
Thus, the total annual inventory cost (TAIC) is computed as follows
TAIC = TCC +TOC
= ( 1/2 EOQ) (CC) + (D + EOQ) (OC)

12. Illustration 1
Izzy Processing Company has an annual average requirement
of 50,000 units of its product. It has been estimated that the
ordering cost is ₱80 per order and that the carrying cost per
unit of inventory is ₱2.
.
Required. Determine the following:
1.Economic order quantity
2.Average inventory level
3.Total carrying cost
4.Total ordering cost
5.Total annual inventory cost

13. = units
Illustration 1
Izzy Processing Company has an annual average requirement of 50,000 units of its product. It has
been estimated that the ordering cost is ₱80 per order and that the carrying cost per unit of inventory
is ₱2.
Answer 1. The EOQ is computed as follows:
This means that Izzy Processing Company shall place 2,000 units of the product
every time it makes an order.
Answer 2. The AI level of the business is as follows:
=
=

14. Answer 3. The TCC is computed as follows:
It can be observed that at the EOQ level,, the TCC and TOC are equal.
Answer 4. The TOC is computed as follows:
TCC = AI x CC
= 1,000 x 2
= ₱2,000
TOC = (D / EOQ) (0C)
= (50,O00 / 2,000) x 80
= ₱2,000
Answer 5. The TAIC is computed as follows:
TAIC= TCC + TOC
= 2,000 + 2,000
= ₱4,000

15. Illustration 2
Using the same information in Illustration 1, Izzy Processing
Company is evaluating to make the following orders:
Case 1 – 400 units
Case 2 – 4,000 units
Required. Determine the following under the two orders:
1.Total carrying cost
2. Total ordering cost
3.Total annual inventory cost

16. Answer. Case 1 – 400 units
The TCC is computed as follows:
TCC = AI x CC
= (400/2) x 2
= ₱400
The TOC is computed as follows:
TOC = ( D / EOQ) (OC)
= (50,000 / 400) x 80
= ₱10,000
The TAIC is computed as follows:
TAIC = TCC + TOC
= 400 + 10,000
= ₱10,400
At the EOQ level, the TAIC is
₱4,000. Any order made higher or
lower than the EOQ will increase
the total inventory cost. It can be
observed that at 400 units, the
total inventory cost becomes
₱10,400

17. Answer. Case 2 – 4,000 units
The TCC ins computed as follows:
TCC = AI x CC
= (4,000/2) x 2
= ₱4,000
The TOC is computed as follows:
TOC = (D/ EOQ) (OC)
= (50,000 / 4,000) x 80
= ₱1,000
The TAIC is computed as follows:
TAIC = TCC + TOC
= 4,000 + 1,000
= ₱5,000
Again, the total inventory cost is
higher when the order is higher
than the EOQ, which is the optimal
level when making an order.

18. When to Place an Order Reorder Point (ROP) a point in the inventory
level that requires placing an order.
To determine the ROP, the following important factors are
considered:
Lead time - it is the time required between the placing of an order
and it's receipt by a business.
Lead time usage - is the number of units demanded or consumed
during the lead time period.
Safety Stock - the amount of inventory maintained to reduce the
risk of stock out.

19. PAGE 10 OF 12
Formulas Relating to Order Time
1. Reorder Point (ROP) formula
2. Average lead time usage (ALTU) formula
3. Average usage per unit of time (AU/UT) formula
4. Total number of orders placed in a year formula
5. Cycle time formula
Cycle time - refers to the period between orders.

20. FORMULAS RELATING TO ORDER TIME
1. Reorder point (ROP) formula:
ROP = ALTU + SS
Where:
ROP – reorder point
ALTU – average lead time usage
SS – safety stock
2. Average lead time usage (ALTU) formula:
ALTU = LT x (AU/UT)
Where:
ALTU – average lead time usage
LT – lead time
AU/UT – average usage per unit of time
3. Average usage per unit of time (AU/UT) formula
Where:
AU/UT – average usage per unit of time
D – annual demand
WD/Y – working days per year
4. Total number of orders placed I a year formula:
Where:
TNO/Y – total number of orders placed in a year
D – annual demand
EOQ – economic order quantity
5. Cycle time formula:
Where:
CT – total number of orders placed in a year
WD/Y – working days per year
EOQ – economic order quantity
D – annual demand
Cycle time refers to the period between orders.

21. Illustration 3
Hyzel Manufacturing Company has an annual average requirement of
320,000 units. It has been estimated that the ordering cost is ₱80 per
order and that the carrying cost per unit of inventory is ₱20. It has 250
working days in a year and maintains a safety stock of 6,000 units. It
observes a lead time of five days.
Required. Determine the following:
1.Economic order quantity
2. Total carrying cost
3. Total ordering cost
4. Total annual inventory cost
5.Average usage per day
6. Reorder point
7. Cycle time
8.Total number of orders in a year

22. = units
Answer 1. The EOQ is computed as follows:
Answer 2. The TCC is as follows:
Illustration 3
Hyzel Manufacturing Company has an annual average requirement of 320,000 units. It has been estimated that the ordering
cost is ₱80 per order and that the carrying cost per unit of inventory is ₱20. It has 250 working days in a year and maintains
a safety stock of 6,000 units. It observes a lead time of five days.
TCC = AI x CC
= (1,600/2) x 20
= ₱16,000
Answer 3. The TOC is as follows::
TOC = (D / EOQ)(OC)
= (320,000 / 1,600) x 80
= ₱16,000

23. CT = WD/Y x EOQ /D
= 250 x 1,600 / 320,000
= 1.25 working days
Answer 4. The TAIC is as follows:
TAIC = TCC + TOC
= 16,000 + 16,000
= ₱32,000
Answer 5. The AU/UT is as follows:
= 320,000/250
= ₱1,280 units per day
Answer 6. The ROP is computed as follows:
ROP = (AU/UT x LT) + SS
= (1,280 x 5 days) + 6,000
= 6,400 +6,000
= 12,400
Hyzel Manufacturing Company
should place an order hen its
inventory level reaches
12,400 units
Answer 7. The CT is computed as follows:
Answer 8. The TNO/Y is computed as follows:
TNO/Y = 320,000/1,600
= 200 orders

24. PAGE 10 OF 12
At a glance, Hyzel Manufacturing Company has the following
information:
Quantitative Information
1.Annual demand/requirements
2.Average working days in a year
3.Lead time
4.Economic order quantity
5. Total annual inventory cost
6.Average usage per day
7.Reorder point
8.Cycle time
9.Number of orders in a year
320,000 units
250 days
5 days
1,600 units
₱32,000
1,280 units
12,400 units
1.25 days
200 orders

25. your reference
• Aduana, Nick L. Management Science: A
Quantitative Approach to Decision-Making.
839 EDSA, South Triangle Quezon City,
Philippines.