1. Example ( In terms of Percentage)
CNG-LPG company in Karachi, purchases 5000 compressors a year at Rs.8,000 each. Ordering costs are Rs. 500 and Annual carrying costs are 20 % of the purchase price. Compute the Optimal price and the total annual cost of ordering and carrying the inventory.

2. Example ( In terms of Percentage)
Data
D=Demand =5,000
S=Ordering= Rs. 500
H=Holding/Carrying Cost=0.2 X 8,000=Rs.1600

3. Example 3 ( In terms of Percentage)
Q0= Sq Root of ( 2(5,000)(500)/(1600))
= 55.9=56 Compressors
TC= Carrying costs + Ordering Costs
=Q0/2 ( H) + D/Q0 (S)
= 56/2 ( 1600) /56 (500)
= 28 ( 1600)+ 44,643
=44,800+44,643=Rs. 89,443

4. Economic Production Quantity (EPQ)
Production done in batches or lots
Capacity to produce a part exceeds the part’s usage or demand rate.
Assumptions of EPQ are similar to EOQ except orders are received incrementally during production.

5. Economic Production Quantity
Usage
Production
& Usage
Production
& Usage
Usage
Inventory Level

6. Economic Production Quantity Assumptions
Only one item is involved
Annual demand is known
Usage rate is constant
Usage occurs continuously
Production rate is constant
Lead time does not vary
No quantity discounts

7. Economic Production Quantity Assumptions
The basic EOQ model assumes that each order is delivered at a single point in time.
If the firm is the producer and user, practical examples indicate that inventories are replenished over time and not instantaneously.
If usage and production ( delivery) rates are equal, then there is no buildup of inventory.

8. Economic Production Quantity Assumptions
Set up costs in a way our similar to ordering costs because they are independent of lot size.

9. Economic Production Quantity Assumptions
The larger the run size, the fewer the number of runs needed and hence lower the annual setup.
The number of runs is D/Q and the annual setup cost is equal to the number of runs per year times the cost per run ( D/Q)S.

10. Economic Production Quantity Assumptions
Total Cost is
TC min= Carrying Cost+ Setup Cost
= ( I max/2)H+ (D/Q0)S
Where I max= Maximum Inventory

11. Economic Run Size

12. Economic Production Quantity Assumptions
Where p= production rate
U = usage rate

13. Economic Production Quantity Assumptions
The Run time ( the production phase of the cycle) is a function of the run size and production rate
Run time = Q0/p
The maximum and average inventory levels are
I max = Q0/p (p-u)
I average= I max/2

14. Example (Economic Run Size)
A firm in Sialkot produces 250,000 each world class footballs for both domestic and international markets . It can make footballs at a rate of 2000 per day. The footballs are manufactured uniformly over the whole year. Carrying cost is Rs. 100 per football and Setup cost for a production run is Rs The manufacturing unit operates for 250 days per year.

15. Example 4 Economic Run Size
Determine the
Optimal Run Size.
Minimum total annual cost for carrying and setup cost.
Cycle time for the Optimal Run Size.
Run time

16. Example 4 Economic Run Size
Determine the
Optimal Run Size.
= Sq Root (2 X 250,000 X 2500/100 )( Sq Root (2 000 / ))
2500( sqroot2X2)=5000 footballs.

17. Example 4 Economic Run Size
Minimum total annual cost for carrying and setup cost.
= Carrying Cost + Set up Cost
=( I max/2)H+ ( D/Q0)S
Where I max= Q0/p ((p-u))=5000/2000(1000)
=2500 footballs
Now TC= 2500/2 X (250,000/5000 )(2500)
=1250 X ,000
=125, ,000
= Rs. 250,000

18. Example 4 Economic Run Size
Cycle time for the Optimal Run Size.
Q0/U=5000/1000= 5 days
Run time
Q0/p=5000/2000= 2.5 days

19. Quantity Discount
Price reductions for large orders are called Quantity Discounts.

20. Total Costs with Purchasing Cost
Annual
carrying
cost
Purchasing
TC = + Q 2 H D S
ordering PD

21. Total Costs with PD Cost Adding Purchasing cost doesn’t change EOQ
TC with PD
TC without PD PD
Quantity
Adding Purchasing cost doesn’t change EOQ

22. Example
The maintenance department of a large cardiology hospital in Islamabad uses about 1200 cases of corrosion removal liquid, used for maintenance of hospital. Ordering costs are Rs 100, carrying cost are Rs 20 per case, and the new price schedule indicates that

23. Example
orders of less than 50 cases will cost Rs 1250 per case, 50 to 79 cases will cost Rs 1150 per case , 80 to 99 cases will cost Rs 1050 per case and larger costs will be Rs 1000 per case.
Determine the Optimal Order Quantity and the Total Cost.

24. Example D=1200 case. S= Rs. 100 per case H=Rs.20 per case Range Price
1 to Rs 1250
50 to Rs 1150
80 to Rs 1050
100 or more Rs 1000

25. Example Compute the Common EOQ=Sq Root ( 2DS/H)
= Sq Root ( 2 X 100 X 1200/20)
=Sq Root (12000)
=109.5=110 cases which would be brought at 1000 per oder
The total Cost to Purchase 1200 cases per year would be
TC= Carrying Cost+ Order Cost+ Purchase Cost
=(Q/2)H+(D/Q0)S+PD
=(110/2)20+(1200/110) X 1000
= ,000
=Rs. 1,202,191

26. When to Reorder with EOQ Ordering
Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered.
Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.
Service Level - Probability that demand will not exceed supply during lead time.

27. Example
An apartment complex in Quetta requires water for its home use.
Usage= 2 barrels a day
Lead time= 5 days
ROP= Usage X Lead Time
= 2 barrels a day X 7 = 14 barrels

28. Determinants of the Reorder Point
The rate of demand
The lead time
Stock out risk (safety stock)
Demand and/or lead time variability

29. Example
An owner of a Montessori equipment firm in Karachi, determined from historical records that demand for wood required for Montessori equipment averages 25 tones per anum. His operations management expertise allowed him to determine the demand during lead that could be described by a normal distribution that has a mean of 25 tons and a standard deviation of 2.5 tons.

30. Fixed-Order-Interval Model
Orders are placed at fixed time intervals.
Order quantity for next interval?
Suppliers might encourage fixed intervals.
May require only periodic checks of inventory levels.
Risk of stock out.