1. EOQ for production lots EOQ with quantity discount Safety Stock Periodic review system
----

2. Model II: EOQ for Production Lots
Inventory Management
Used to determine the order size, production lot.
Differs from Model I because orders are assumed to be supplied or produced at a uniform rate (p) rather than the order being received all at once.
06 July 2012
KLE College of Pharmacy, Nipani.

3. Production Order Quantity Model
Inventory level
Time
Part of inventory cycle during which production (and usage) is taking place
Demand part of cycle with no production
Maximum inventory t
Figure 12.6

4. Model II: EOQ for Production Lots
Inventory Management
It is also assumed that the supply rate, p, is greater than the demand rate, d
The change in maximum inventory level requires modification of the TSC equation
TSC = (Q/2)[(p-d)/p]C + (D/Q)S
The optimization results in
06 July 2012
KLE College of Pharmacy, Nipani.

5. Example: EOQ for Production Lots
Inventory Management
Highland Electric Co. buys coal from Cedar Creek Coal Co. to generate electricity. CCCC can supply coal at the rate of 3,500 tons per day for $10.50 per ton. HEC uses the coal at a rate of 800 tons per day and operates 365 days per year.
06 July 2012
KLE College of Pharmacy, Nipani.

6. Example: EOQ for Production Lots
Inventory Management
HEC’s annual carrying cost for coal is 20% of the acquisition cost, and the ordering cost is $5,000.
What is the economical production lot size?
b) What is HEC’s maximum inventory level for coal?
06 July 2012
KLE College of Pharmacy, Nipani.

7. Example: EOQ for Production Lots
Inventory Management
Economical Production Lot Size
d = 800 tons/day; D = 365(800) = 292,000tons/year
p = 3,500 tons/day
S = $5,000/order., C = .20(10.50)= $2.10/ton/year
= 42, tons per order
06 July 2012
KLE College of Pharmacy, Nipani.

8. Example: EOQ for Production Lots
Inventory Management
Total Annual Stocking Cost (TSC)
TSC = (Q/2)((p-d)/p)C + (D/Q)S
= (42,455.5/2)((3, )/3,500)(2.10)
+ (292,000/42,455.5)(5,000)
= 34, ,388.95
= $68,777.90
Note: Total Carrying Cost
equals Total Ordering Cost
06 July 2012
KLE College of Pharmacy, Nipani.

9. Model III: EOQ with Quantity Discounts
Under quantity discounts, a supplier offers a lower unit price if larger quantities are ordered at one time
This is presented as a price or discount schedule, i.e., a certain unit price over a certain order quantity range
This means this model differs from Model I because the acquisition cost (ac) may vary with the quantity ordered, i.e., it is not necessarily constant
. . . more

10. Model III: EOQ with Quantity Discounts
Under this condition, acquisition cost becomes an incremental cost and must be considered in the determination of the EOQ
The total annual material costs (TMC) = Total annual stocking costs (TSC) + annual acquisition cost
TSC = (Q/2)C + (D/Q)S + (D)ac
. . . more

11. Model III: EOQ with Quantity Discounts
To find the EOQ, the following procedure is used:
1. Compute the EOQ using the lowest acquisition cost.
If the resulting EOQ is feasible (the quantity can be purchased at the acquisition cost used), this quantity is optimal and you are finished.
If the resulting EOQ is not feasible, go to Step 2
2. Identify the next higher acquisition cost.

12. Model III: EOQ with Quantity Discounts
3. Compute the EOQ using the acquisition cost from Step 2.
If the resulting EOQ is feasible, go to Step 4.
Otherwise, go to Step 2.
4. Compute the TMC for the feasible EOQ (just found in Step 3) and its corresponding acquisition cost.
5. Compute the TMC for each of the lower acquisition costs using the minimum allowed order quantity for each cost.
6. The quantity with the lowest TMC is optimal.

13. Example: EOQ with Quantity Discounts
A-1 Auto Parts has a regional tire warehouse in Atlanta. One popular tire, the XRX75, has estimated demand of 25,000 next year. It costs A-1 $100 to place an order for the tires, and the annual carrying cost is 30% of the acquisition cost. The supplier quotes these prices for the tire:
Q ac
1 – 499 $21.60
500 – 1,

14. Example: EOQ with Quantity Discounts
Economical Order Quantity
This quantity is not feasible, so try ac = $20.95
This quantity is feasible, so there is no reason to try ac = $21.60

15. Example: EOQ with Quantity Discounts
Compare Total Annual Material Costs (TMCs)
TMC = (Q/2)C + (D/Q)S + (D)ac
Compute TMC for Q = and ac = $20.95
TMC2 = (891.93/2)(.3)(20.95) + (25,000/891.93)100
+ (25,000)20.95
= 2, , ,750
= $529,355.80
… more

16. Example: EOQ with Quantity Discounts
Compute TMC for Q = 1,000 and ac = $20.90
TMC3 = (1,000/2)(.3)(20.90) + (25,000/1,000)100
+ (25,000)20.90
= 3, , ,500
= $528, (lower than TMC2)
The EOQ is 1,000 tires
at an acquisition cost of $20.90.

17. SAFETY STOCK Is required to be considered in some conditions
They Arise
because
In practical situation
Demand of items may fluctuate at any point of time
And also suppliers always need some lead time to supply the goods

18. Lead time can easily be provided to supplier by placing order before inventory become zero.
e.g.
Lead time is 10 days , so order can be placed 10 days before it becomes zero. Let the uniform consumption of inventory be 50 units per day therefore during the 10days of lead time 500 units will be consumed . Hence ROL can be fixed at 500 units. A
Stock out may occur sometime due to either excessive consumption or due to undue stretching of lead time
We know stock out is undesirable for the various reasons so to avoid it extra stock is maintained throughout thr year. This is called as Safety Stock

19. Inventory decreases at constant rate
Inventory Level
Re order level Q
500 units
Lead Time
10days
First Order
Second Order
Goods Received
Lead time being provided by fixing a reorder level
Lead

20. Inventory decreases at constant rate
Inventory Level
Re order level Q
500 units
7 days
Lead Time
10days
First Order
Second Order
Goods Received
Excessive consumption of inventory during the lead time, leading to stock out
Lead

21. Inventory decreases at constant rate
Inventory Level
Re order level Q
500 units
7 days
Lead Time
Second Order
Safety Stock
800 units
Goods Received
Safety Stock avoids a stock out caused by excessive consumption of inventory during lead time

22. Let’s do one practical But let’s have one understanding
A low level of safety stock can lead to a stock out. On the other hand a high level of safety stock unnecessarily ties up capital. Therefore we need to determine the optimum level of safety stock. Which should neither be low nor high.
Let’s do one practical

23. Safety stock involves two types of costs:
1. CC carrying cost of safety stock
2. SC stock out cost
These cost are inversely related to each other
CC safety stock ∞ 1/Stock out cost
High the safety stock high CC low the chance of SC.
Research shows that the total cost of safety stock is minimum only when
CC safety stock = SC safety stock
Let’s take an example keeping normal lead time constant .
Demand during lead time may vary leading to possibility of stock out.

24. Practical- CASE of NESTLE
A local chocolate distributor at Ghaziabad deals with a popular brand called chocostick. The normal lead time taken by the supplier of chocostick is 10 days . The normal consumption of inventory during the lead time is 500 units per day. there are 10 inventory cycles per year. The CC is Rs.1 per unit per year. The stock out cost is Rs.2. per unit short. Mr. Ram the sales man gives you a consumption pattern of chocostick ( based on his past 100 observations)
Find the optimum level of safety stock for chocostick.
Consumption during lead time (units)
Probability
1000
.01
2000
.03
3000
.07
4000
.14
5000
.61
6000
.04
7000
8000
1.00

25. Crux of the case:
See they have given normal lead time of supplier and also consumption during the lead time that too at normal rate.
He had analyzed the pattern of the demand during lead time .
He understand one fact very clearly stock out will cost double of the carrying cost.
So normal consumption of chocostick during the lead time = 10 days X 500 units/day=5000 units
As per observations out of 100 consumption during lead time is 5000 unit or less 86 times.(86 = )
Therefore if no safety stock is maintained there is an 86% chance that a stock out will not happen.
But still the problem is HOW MUCH safety stock.

26. Let’s understand the crux of the other part
CASE 1. No safety stock: then stock out will be there only when DDLT exceeds 5000 units. i.e 6000/7000/8000 with stock out of 1000/2000/3000
CASE units of safety stock : then stock out at DDLT exceeds 6000 units
CASE units of safety stock : then stock out at DDLT exceeds 7000 units
CASE units of safety stock: then stock out will only when DDLT exceeds to 8000 units.
So to arrive at the optimum safety stock you need to understand that at what level of safety stock your inventory cost i.e carrying as well as stock out cost will be minimum.

27. Lead time consumption leading to stock out
NO. of units short
Probability
Expected annual stock out cost. (RS.)
Case1.
6000
1000
.04
10X1000X.04X2 = 800
7000
2000
.07
10X2000X.07X2 = 2800
8000
3000
.03
10X3000X.03X2 = 1800
Case 2.
10X1000X.07X2 = 1400
10X2000X.03X2 = 1200
Case 3.
10X1000X.03X2 = 600
600.00

28. Comparison Safety stock levels (units) CC of safety stock (Rs.)
Stock out Cost
(Rs.)
Total safety Stock Cost(Rs.)
1000
2000
600.00
3000

29. Safety Stock(other method)
Use safety stock to protect against stockouts when demand or lead time is not constant.(based on service level)
Safety stock = z x s’d
z is from Standard Normal Distribution Table and is based on P = Probability of being in-stock during lead time.
ROP = expected demand during lead time + safety stock
= d x LT + z x s’d , S’d= Sd * square root of LT
Average Inventory Level (AIL) = regular stock + safety stock Q
AIL =
+ z x s’d 2

30. monthly demand forecast(d) = 11,107 units
Standard deviation (sd) = 3,099 units
Lead time (Lt) = 1.5 months
Probability of available inventory =75%
Sol:
ROP= d*LT + Z(s’d)
s’d=sd L = 3,099 * =3,795
Z= from area under the standard normal distribution
ROP=11107 *1.5 +(0.67*3,795)= 19,203

32. Periodic Review System
Figure Periodic review system: units in stock versus time

33. Target Level or Maximum Inventory Level
Total of the:
demand (D) during the review period (R)
+ demand (D) during the lead time (L)
+ safety stock (SS)
T = D(R + L) + SS

34. Periodic Review - Order Quantity
When it is time to place an order
Order the difference between the target level (T) and the quantity on hand (I ).
Q = T - I

35. Periodic Review System
Used when:
there are many small issues from stock e.g. grocery stores
many items are ordered from one source
many items are ordered together to fill a truck or a production run

36. Periodic Review - Example Problem
A harware company stocks nuts and bolts and orders them from a local supplier once every two weeks (10 working days). Lead time is two days. The company has determined that the average demand for 1/2 inch bolts is 150 per week (5 working days), and it wants to keep a safety stock of three day’s supply on hand. An order is to be placed this week, and stock on hand is 130 bolts.
a. What is the target level?
b. How many 1/2 inch bolts should be ordered this time?
Let: D= demand per unit time = 150 / 5 = 30 per working day
L = lead time = 2 days
R = review period = 10 days
SS = safety stock = 3 day’s supply = 90 units
I = inventory on hand = 130 units

37. Periodic Review - Example Problem Continued
Target level T = D(R + L) + SS
= 30(10 + 2) + 90
= 450 units
Order quantity Q = T - I =
= 320 units
Place an order now for 320 units which will arrive in 2 days.

38. Pull Inventory Control - Repetitive Ordering
For perpetual (continual) demand.
Treat each stocking point independently.
Consider 1 product art 1 location.
Reorder Periodic
Determine: Point System Review System
How much to order: Q T-I
When to (re)order: ROP t