1. EOQ for Production not Order (EPQ)
We do not buy the product.
We produce it.
Total demand / year is D
Demand / day or consumption rate is u
Production rate is p / day

2. Example A toy manufacturer uses 48000 parts for one of its products.
Consumption rate is uniform throughout the year.
Working days are 240 / year.
The firm can produce at a rate of 800 parts / day
Carrying cost is $1 / part / year
Setup cost for production run is $45 / setup
What is the optimal production size?

3. Example

4. Instantaneous and Incremental Replenishment
Instantaneous Replenishment
Incremental Replenishment

5. EPQ: Incremental Replenishment (Production and Consumption)
p-u p u
u × ( number of working days ) = D = Total demand per year

6. EPQ: One period and One year
p-u u
One Period
One Year

7. EPQ: Ordering Cost and Carrying Cost
I max
If I can state Imax in terms of Q, then I am done.
I can easily find Economic Quantity.

8. EPQ : Production & Consumption; rate & time
How much do we produce each time? Q
How long does it take to produce Q? d1
What is our production rate per day? p
How long does it take to consume Q? d1 +d2
What is our consumption rate per day ? u
p-u u
I max d1 d2

9. EPQ : Optimal Q

10. Example A toy manufacturer uses 48000 parts for one of its products.
Consumption rate is uniform throughout the year.
Working days are 240 / year.
The firm can produce at a rate of 800 parts / day
Carrying cost is $1 / part / year
Setup cost for production run is $45 / setup
What is the optimal production size?

11. What is Run Time, What is Cycle Time

12. What is the Optimal Total Cost

13. ROP If setup time takes 2 days, at which level of inventory we
should start setup?
2(200) = 400

14. Practice
A company has a yearly demand of 120,000 boxes of its product. The product can be produced at a rate of 2000 boxes per day. The shop operates 240 days per year. Assume that demand is uniform throughout the year. Setup cost is $8000 for a run, and holding cost is $10 per box per year.
a) What is the demand rate per day
b) What is the Economic Production Quantity (EPQ)
c) What is the run time
d) What is the maximum inventory
e) What is the total cost of the system

15. Assignment 4.3b What is the demand rate per day
Demand per year is 120,000 there are 240 days per year
Demand per day = /240 = 500
u = D/240 = 500
b) What is the Economic Production Quantity (EPQ)
=16000

16. Assignment 4.3b c) What is the run time We produce 16000 units
Our production rate is 2000 per day
It takes 16000/2000 = 8 days
d1 = EPQ/p = 8 days
d) What is the maximum inventory
We produce for 8 days. Each day we produce 2000 units and we consume 500 units of it. Therefore we add to our inventory at rate of 1500 per day for 8 days. That is
Imax = 8(1500) = 12000
Imax = pd1 = 8(1500) = 12000

17. Assignment 4.3b
e) What is the total cost of the system

18. Assignment 12.c
Problem : The Dine Corporation is both a producer and a user of brass couplings. The firm operates 220 days a year and uses the couplings at a steady rate of 50 per day. u = 50. Couplings can be produced at rate of 200 per day. p=200. Annual storage cost is $1 per coupling, H=1, and machine setup cost is $35 per run, S=35. Since there are 220 days per year and u is equal to 50, yearly demand is 50(220), D=
Determine the economic run size.
Approximately how many runs per year will there be?
Compute the maximum inventory level.
Determine the cycle time, run time and pure consumption time.
Compute the total cost.