Inventory Management (Production and Operatio Management)

1. 12
Inventory Management

2. Independent Demand
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
Independent demand is uncertain.
Dependent demand is certain.
Inventory

3. Inventory
• Independent demand – finished goods, items
that are ready to be sold
– E.g. a computer
• Dependent demand – components of finished
products
– E.g. parts that make up the computer

4. Types of Inventories
• Raw materials & purchased parts
• Partially completed goods called
work in progress
• Finished-goods inventories
– (manufacturing firms)
or merchandise (retail stores)

5. Types of Inventories (Cont’d)
• Goods-in-transit to warehouses or
customers

6. Functions of Inventory
• To meet anticipated demand
• To smooth production
requirements
• To protect against stock-outs

7. Functions of Inventory (Cont’d)
• To help hedge against price
increases
• To permit operations
• To take advantage of quantity
discounts

8. Objective of Inventory Control
• To achieve satisfactory levels of customer
service while keeping inventory costs within
reasonable bounds
– Level of customer service
– Costs of ordering and carrying inventory

9. Effective Inventory Management
• A system to keep track of inventory
• A reliable forecast of demand
• Knowledge of lead times
• Reasonable estimates of
– Holding costs
– Ordering costs
– Shortage costs
• A classification system

10. Inventory Models
• Single period model
• Multiple period model
 Fixed order quantity model
 Fixed time period model

11. Key Inventory Terms
• Lead time: time interval between ordering and
receiving the order
• Holding (carrying) costs: cost to carry an item in
inventory for a length of time, usually a year
• Ordering costs: costs of ordering and receiving
inventory
• Shortage costs: costs when demand exceeds supply

12. Examples of holding costs
• Insurance costs
• Warehousing costs
• Spoilage/breakage losses

13. Example of Ordering Cost
• Cost to prepare a purchase requisition
• Cost to prepare a purchase order
• Cost of the labor required to inspect goods when they are
received
• Cost to put away goods once they have been received
• Cost to process the supplier invoice related to an order
• Cost to prepare and issue a payment to the supplier

14. Single period model
• A news paper boy has the following probabilities of
selling a magazine:
• No. of copies sold probabilities
10 .10
11 .15
12 .20
13 .25
14 .30
Cost of a copy is 30 paise and sale price is 50 paise. He
cannot return unsold copies. How many copies should
he order?

15. Conditional Loss Table
possible
demand probabilities possible stock action
(no. of
copies)
10
copies
11
copies
12
copies
13
copies
14
copies
10 0.1 0 30 60 90 120
11 0.15 20 0 30 60 90
12 0.2 40 20 0 30 60
13 0.25 60 40 20 0 30
14 0.3 80 60 40 20 0

16. Expected Loss Table
possible
demand probabilities possible stock action
(no. of
copies)
10
copies
11
copies
12
copies
13
copies
14
copies
10 0.1 0 3 6 9 12
11 0.15 3 0 4.5 9 13.5
12 0.2 8 4 0 6 12
13 0.25 15 10 5 0 7.5
14 0.3 24 18 12 6 0
EOL 50 35 27.5 30 45

17. Fixed-Order Quantity
Models
17

18. Fixed-Order Quantity Model:
Model Assumptions
• Demand for the product is constant and
uniform throughout the period.
• Lead time (time from ordering to receipt) is
constant.
• Price per unit of product is constant.
18

19. The Inventory Cycle
Profile of Inventory Level Over Time
Quantity
on hand
Q
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time
Reorder
point
Usage
rate
Time

20. Safety Stocks
Safety stock
buffer added to on hand inventory during lead time

21. Safety Stock
reduce risk of stockout during lead time

22. Operations Strategy
• Too much inventory
– Tends to hide problems
– Easier to live with problems than to eliminate
them
– Costly to maintain
• Wise strategy
– Reduce lot sizes
– Reduce safety stock

23. 23
Basic Fixed-Order Quantity (EOQ) Model
Formula
H
2
Q
+S
Q
D
+DC=TC
Total Annual Cost =
Annual
Purchase
Cost
Annual
Ordering
Cost
Annual
Holding
Cost
+ +
TC = Total annual cost
D = annual Demand for the item,
over the year
C = Cost per unit
Q = Order quantity
S = Cost of placing an order
or setup cost
R = Reorder point
L = Lead time
H = Annual holding and storage
cost per unit of inventory

24. Cost Minimization Goal
Order Quantity (Q)
Ordering Costs
QO
AnnualCost
(optimal order quantity)
S
Q
D
H
Q
DCTC 
2

25. Minimum Total Cost
The total cost curve reaches its
minimum where the
Carrying Cost = Ordering Cost
Q
2
H
D
Q
S=

26. Reorder Point without
Safety Stock

27. Deriving the EOQ
Using calculus, we take the derivative of
the total cost function and set the
derivative (slope) equal to zero and solve
for Q.
Q =
2DS
H
=
2(Annual Demand )(Order or Setup Cost )
Annual Holding Cost
OPT

28. 28
Deriving the EOQ
CostHoldingAnnual
Cost)SetuporderDemand)(Or2(Annual
=
H
2DS
=QOPT
Reorder point, R = d L
_
d = average daily demand (constant)
L = Lead time (constant)
_

29. 29
EOQ Example Problem Data
Annual Demand = 1,000 units
Days per year considered in average daily demand = 365
Cost to place an order = $10
Holding cost per unit per year = $2.50
Lead time = 7 days
Cost per unit = $15
Given the information below, what are the EOQ and
reorder point?

30. 30
EOQ Example Solution
Q =
2DS
H
=
2(1,000 )(10)
2.50
= 89.443 units orOPT 90 units
d =
1,000 units / year
365 days / year
= 2.74 units / day
units20or19.18=(7days)day2.74units/=Ld=Rpoint,Reorder
_

31. EOQ Example (2) Problem Data
Annual Demand = 10,000 units
Days per year considered in average daily demand = 365
Cost to place an order = $10
Holding cost per unit per year = 10% of cost per unit
Lead time = 10 days
Cost per unit = $15
Determine the economic order quantity and the reorder point.

32. EOQ Example (2) Solution
Q =
2DS
H
=
2(10,000 )(10)
1.50
= 365.148 units, orOPT 366 units
d =
10,000 units / year
365 days / year
= 27.397 units / day
units274or273.97=days)(10units/day27.397=Ld=R
_
Place an order for 366 units. When in the course of using
the inventory you are left with only 274 units, place the
next order of 366 units.

33. Reorder Point with Safety Stock
• S=Z × σLT
S= Safety Stock
Z= Number of standard deviations for a specified
service probability
σLT=Standard deviation of usage during the
lead time

34. Calculation of Safety Stock
• Standard deviation of demand is 10 units per
day, lead time is 5 days. Find safety stock at a
95 percentage probability of not stocking out?
σ5= SQRT OF [(10)2 + (10)2 +(10)2+(10)2+(10)2) = 22.36
S=Z × σLT =1.64+22.36 = 36.67 = Approx. 37.

35. Calculation of Reorder Point with
Safety Stock
• Consider an economic order quantity case
where annual demand D= 1000 units,
economic order quantity Q = 200 units, the
desired probability of not stocking out P=0.95,
the standard deviation of demand during lead
time= 25 units, and lead time L= 15 days.
Determine the reorder point. Assume that
demand is over a 250-workday year.

36. Calculation of Reorder Point with
Safety Stock

37. Fixed Time Period Model
with Safety Stock

38. Fixed Time Period Model with
Safety Stock

39. • Daily demand for the product is 10 units, with
a standard deviation of 3 units. The review
period is 30 days, and the lead time is 14 days.
Management has set a policy of satisfying 98
percentage of demand from items in stock. At
the beginning of this review period, there are
150 units in inventory. How many units should
be ordered?

41. Determinants of the Reorder Point
• The rate of demand
• The lead time
• Demand and/or lead time variability
• Stockout risk (safety stock)

42. ABC Classification System
 The Scheme
– Class B items
» Moderate in number--30-35%
» Moderate in rupee value--15-20%
» Exercise average control here
– Class C items
» Highest in number--about 50%
» Lowest in rupee value--5-10%
» Exercise the least control here
 Natural break or company policy scheme

43. ABC Classification
• Class A
– 5 – 15 % of units
– 70 – 80 % of value
• Class B
– 30 % of units
– 15 % of value
• Class C
– 50 – 60 % of units
– 5 – 10 % of value

44. ABC Classification: Example
1 $ 60 90
2 350 40
3 30 130
4 80 60
5 30 100
6 20 180
7 10 170
8 320 50
9 510 60
10 20 120
PART UNIT COST ANNUAL USAGE

45. ABC Classification:
Example (cont.)
Example 10.1
1 $ 60 90
2 350 40
3 30 130
4 80 60
5 30 100
6 20 180
7 10 170
8 320 50
9 510 60
10 20 120
PART UNIT COST ANNUAL USAGETOTAL % OF TOTAL % OF TOTAL
PART VALUE VALUE QUANTITY % CUMMULATIVE
9 $30,600 35.9 6.0 6.0
8 16,000 18.7 5.0 11.0
2 14,000 16.4 4.0 15.0
1 5,400 6.3 9.0 24.0
4 4,800 5.6 6.0 30.0
3 3,900 4.6 10.0 40.0
6 3,600 4.2 18.0 58.0
5 3,000 3.5 13.0 71.0
10 2,400 2.8 12.0 83.0
7 1,700 2.0 17.0 100.0
$85,400
A
B
C
% OF TOTAL % OF TOTAL
CLASS ITEMS VALUE QUANTITY
A 9, 8, 2 71.0 15.0
B 1, 4, 3 16.5 25.0
C 6, 5, 10, 7 12.5 60.0