1. Bus Adm 370 - Chp 12 Inventory Mgmt.
CHAPTER 12
Inventory Management

2. Bus Adm 370 - Chp 12 Inventory Mgmt.
Agenda
Inventory Management?
Inventory
Reasons for holding/avoiding inventory
Objective of inventory management
Continuous (perpetual) inventory counting system
Constant demand and lead time : EOQ Model
Uncertain demand and constant lead time
Economic Production Model (EPQ)
Single-Period Model (newsboy Problem)
First class (50mins): no video, slide 1-18, 2nd class (50mins), slides (finish EOQ plus one EOQ exercise, 3rd class( 50 mins) (uncertain demand, EPQ plus 1 uncertain demand exercise)

3. What is
Inventory Management?

4. Bus Adm 370 - Chp 12 Inventory Mgmt.
Inventory: A stock or store of goods.
Inventory is created when
receiving rate exceeds usage rate
incoming raw material exceeds production consumption
production exceeds demand
Inventory can be measured in
physical units
money
Firms typically stock many items in inventory.
Many of the items a firm carries in inventory relate to the kind of business it engages in.

5. Bus Adm 370 - Chp 12 Inventory Mgmt.
Inventory Examples
Manufacturing firms carry supplies of raw materials, purchased parts, finished items, spare parts, tools,....
Department stores carry clothing, furniture, stationery, appliances,...
Hospitals stock drugs, surgical supplies, life-monitoring equipment, sheets, pillow cases,...
Supermarkets stock fresh and canned foods, packaged and frozen foods, household supplies,...
Not all items in inventory are items to be sold.

6. Why might we want to build inventories?
a. Customer service: For customers that have immediate or
seasonal demands, finished goods inventory can speed up
delivery and reduce stockouts and backorders.
b. Ordering costs: Costs associated with purchasing, follow-up,
receiving, and paperwork are incurred each time an order is
placed. By ordering in larger quantities, the resulting inventory
provides a means of obtaining and handling materials in
economic lot sizes.
c. Setup costs: Production orders have similar costs associated with each setup, and machines may be unproductive for several hours each time the product is switched.
> Labor and time to make changeover
> May include scrap and rework

7. Why might we want to build inventories? (cont’d)
c. Stabilizing output rates: Inventories can be used to cover peaks
in demand, level production activities, stabilize employment, and
improve labor relations.
d. Transportation costs: Transportation costs can be reduced by
building inventories and shipping full truckloads.
e. Quantity discounts. Ordering large quantities can provide a
hedge against future price increases and provide a means to
obtain quantity discounts.

8. Why might we want to avoid inventories?
a. Collectively called “inventory holding cost.” The cost to keep an item on hand for a year typically ranges from 25
percent to 40 percent of the item’s value.
b. Cost components
Interest or opportunity cost of capital — time value of money
Storage and handling—warehouse facilities and labor
Taxes and insurance—usually proportional to inventory value
Shrinkage
- Pilferage
- Obsolescence
- Deterioration

9. Objective of Inventory Management
Bus Adm Chp 12 Inventory Mgmt.
Objective of Inventory Management
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Right goods, right place, right time, right quantity
Goal: matching supply with demand!

10. Basic Inventory Management Questions
Bus Adm Chp 12 Inventory Mgmt.
Basic Inventory Management Questions
How much to order
When to order?
Purchase Order
Description
Qty.
Microwave
1000

11. Effective Inventory Systems?

12. Effective Inventory Management
Bus Adm Chp 12 Inventory Mgmt.
Effective Inventory Management
1. A reliable forecast of demand
2. Knowledge of lead times and lead time variability
3. Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
4. A classification system
5. An inventory Counting system
Types
2. A reliable forecast of demand that includes an indication of possible forecast error.
3. Knowledge of lead times and lead time variability.
4. Reasonable estimates of inventory holding costs, ordering costs, and shortage costs.
5. A classification systems for inventory items.

13. 1. Demand Forecast & 2. Lead Time
Need reliable estimates of the amount and timing of demand
Lead Time: Time interval between placing and receiving the order
- Lead time variability: the greater
the potential variability, the greater
the need for additional stock to
reduce the risk of a shortage
between deliveries

14. Bus Adm 370 - Chp 12 Inventory Mgmt.
3. Inventory Costs cont.
b. Holding (carrying) cost: Physically holding item in storage.
- Holding costs are stated in either way:
a percentage of unit price
a dollar amount per unit
c. Shortage costs: Costs resulting when demand exceeds supply.
- It is often difficult to quantify shortage costs.
Holding cost also include opportunity costs having funds tied up in inventory.
interest
insurance
taxes
depreciation
obsolescence
warehouse costs (heat, light, rent, security)
opportunity costs
deterioration
spoilage
theft
breakage
One objective of Inventory Control is to minimize
the sum of these costs by balancing them.

15. 4. Classification Systems
ABC Classification System: Classifying inventory according to some measure of importance and allocating control efforts accordingly.
A - very important
B - mod. important
C - least important
Annual
$ value
of items A B C
High
Low
Few
Many
Number of Items

16. Class B is between the two extremes
Uses of ABC Approach
Class A typically contains about 10-20% of the items and 60-70% of the annual dollar value
Receive close attention: frequent reviews make sure customer service levels
Class C contains about 50-60% of the items, but only 10-15% of the dollar value
Receive only loose control, usually order in large quantities
Class B is between the two extremes

17. 5. Inventory Counting Systems - Types
Periodic system: Physical count of items made at periodic intervals (weekly, monthly)
- Good: Economics of scale
- Bad: Lack of control between reviews, carry extra stock to protect against shortages between reviews
Continuous (perpetual) system: System that keeps track of removals from inventory continuously, thus monitoring current levels of each item. Fixed quantity is ordered when a certain level is reached
- Good: keep constant count of inventory, fixed order quantity
Bad: higher record keeping cost, periodic inventory counting is still required
Two-bin system: Two containers of inventory; reorder when the first is empty
- Good: simple, cheap, need not record each withdrawal
- Bad: reorder card may not be turned in for some reasons

18. Self Test
1. The objective of inventory management is to minimize the cost of holding inventory.
2. The overall objective of inventory management is to achieve satisfactory levels of customer service while keeping inventory costs reasonable.
3. In the A-B-C approach, C items typically represent about 15 percent of the number of items, but 60 percent of the dollar usage.
4. The two basic issues in inventory are how much to order and when to order. F T F T

19. Continuous (perpetual) System with Constant Demand and Lead Time
– EOQ (basic)

20. Basic Economic Order Quantity Model (EOQ)
Assumptions:
1. Ordering in batch from supplier.
2. Only one product is involved.
3. Constant demand rate. Demand is spread evenly throughout the year.
4. Constant lead time. Lead time does not vary much for a long enough time.
5. Single delivery for each order.
6. A single flat unit price from the supplier.
Standard goods

21. System Performance Measures for any Q
D = 400 units/year, H= 1.5 $/unit/year , S = $50 /order
Q = 100 units
Average (cycle) inventory
average (cycle) inventory =
annual inventory holding cost
number of orders per year =
annual ordering cost =
length of order cycle =
annual total cost (C) = holding cost + ordering cost Q
order cycle

22. System Operations and Cost Trade-off
 D=400, h=1.5, S=50
Q=100
Q=200
Average (cycle) inv. 50
100
number of orders / yr 4 2
annual inv. holding cost 75
150
annual ordering cost
200
annual total cost
275
250
Tradeoff:
The higher Q, the higher inventory holding cost, but the lower ordering cost.
Question: Where to strike the balance? What’s best Q?
On-hand inventory
Time (year) 1
Q=200
Q=100
On-hand inventory
Time (year) 1

23. EOQ is the order quantity that minimizes the total cost
Annual cost (dollars)
Holding cost =
Ordering cost =
D=400, H=1.5, S=50
Q=100, TC =275
Q=200, TC=250
EOQ=163, TC=245
Lot Size (Q)

24. How much to order? When to order? EOQ Model Answer: EOQ =
where D = annual demand, H = annual unit holding cost
When to order?
Instantaneous replenishment, i.e. lead time =0
Answer: when the inventory = 0
Constant replenishment lead time = L
Answer ?

25. EOQ Model – Reorder point (ROP)
Let L = the time “periods” (say, days) for a replenishment
order to arrive,
d = demand per unit time period.
When to order?
Answer: when the on-hand inventory is equal to the reorder point: ROP = d*L ( = demand during lead time)
Order
received
Order
placed
On-hand inventory
ROP L
Time

26. Example 1 D = 800 * 12 = 9600 /yr Match! S = $75 /order
Demand for a certain radial tires at a tire company is 800 units per month. Each tire costs the company $80. Ordering costs are $75, and the annual carrying costs are 20 percent of the purchase price. Lead time is 5 days and assume the company operates 288 days a year.
D = 800 * 12 = 9600 /yr
S = $75 /order
P = $80, r = 0.20
H = rP = $80 * 0.2 = $16 /unit · yr
Match!

27. Solution to Example 1
1. How many tires should the manager order in each lot?
2. What is the company's average inventory of this tire?
3. How often will an order be placed (length of order cycle)?

28. Solution to Example 1 (Cont.)
4. How many times per year will an order be placed?
5. How much does the company spend annually on ordering costs?
6. How much does the company spend annually on holding (carrying) costs?

29. Solution to Example 1 (Cont.)
7. What is the total annual cost if the EOQ quantity is ordered? OR
The ordering and carrying costs are equal at the EOQ

30. Solution to Example 1 (Cont.)
8. What is the reorder point (ROP)?

31. Continuous (perpetual) System with Uncertain Demand and Constant Lead Time

32. Bus Adm 370 - Chp 12 Inventory Mgmt.
Continuous System – Uncertain Demand
constant lead time = L
Order
received
Order
received
Order
received
Order
received Q Q Q
On-hand inventory
ROP
Order
placed
Order
placed
Order
placed
Observations from the previous graph:
- Inventory level is not a straight/smooth line within any
cycle.
- Inventory levels at the order receiving epochs are
different from cycle to cycle, even though order
placements are trigged by the same reorder point
and order quantities are the same.
- Inventory cycles have different lengths.
Time L L L

33. Continuous System – Uncertain Demand
constant lead time = L
How much to order?
Answer: EOQ =
where E[D] = average (expected) annual demand, H = annual unit holding cost
When to order?
Reorder Point (ROP)?

34. Continuous Review – Uncertain Demand
constant replenishment lead time = L
What should be the reorder point (ROP) :
If ROP = average (expected) demand during lead time, we have a 50% chance stocking out during the inventory cycle.
So, to have a cycle-service level higher than 50%, we need a higher ROP. The part of ROP above the average demand during lead time is safety stock:
ROP = average demand during lead time + safety stock
Service Level =
Prob. (demand is filled
by on-hand inventory)
=1-Prob(stockout)
Cycle-service level > 50%
Probability of stock-out
Average demand during lead time
Safety
Stock
ROP

35. Calculation of Reorder Point (ROP)
If demand during lead time is Normal distributed with a mean (average) value of and standard deviation of , then the required safety stock for a given cycle-service level can be expressed as the number (z) of standard deviation;
ROP = average demand during lead time + safety stock =
where, z can be found from a Normal Distribution Table.
Cycle-service level
ROP

36. Cycle service level
0.90
0.80
.9918
.999 z
1.28
0.84
2.40
3.08

37. Calculation of
Often demand distribution data is not expressed in terms of replenishment lead time. Suppose we know that the demand per “time period” (say, week) is Normal distributed with a mean value of and a standard deviations of
The inventory replenishment lead time is L time periods. Then, the demand during lead time will be Normal distributed with a mean value of
and standard deviation of

38. Example 2
The Discount Appliance Store uses a continuous review system. One of the company’s items has the following characteristics:
Demand = 10 units/wk (assume 52 weeks per year)
Ordering/setup cost (S) = $45/order
Holding cost (H) = $12/unit/year
Lead time (L) = 3 weeks
Standard deviation in weekly demand = 8 units
Cycle-service level = 70%
a. What is the optimal order quantity for this item?
b. What is the desired safety stock?
What is the desired reorder point R?

39. Example 2 (solution) safety stock (ss) =
a. The optimal order quantity is the EOQ:
D = (10/wk)*(52 wk/yr) = 520 /yr;
b. Safety stock:
For a cycle-service level of 70%, z = (from Normal Table)
safety stock (ss) =
c. Reorder point (R):
average demand during lead time:
R = average demand during lead time + safety stock
= z = = 37

40. Bus Adm 370 - Chp 12 Inventory Mgmt.
Summary of Continuous Inventory System
Use EOQ model
When: inventory level drops to ROP
If lead time is 0, ROP =0
If lead time L > 0, ROP=L*d
How much: EOQ formula,
yes
Is demand deterministic? no
When: inventory position drops to/below ROP
How much: EOQ formula,

41. Economic Production Quantity (EPQ)

42. Basic Economic Production Quantity Model (EPQ)
Assumptions:
1. Produces in batch and production rate is constant.
2. Only one product is involved.
3. Constant demand rate. Demand is spread evenly throughout the year.
4. Constant lead time. Lead time does not vary much for a long enough time.
5. Usage occurs continually, but production occurs periodically.
6. Capacity to produce a part exceeds the part's usage rate.
Standard goods

43. Economic Production Quantity (EPQ)
Maximum
Inventory
Imax
Slope= Production rate p
Slope= Production rate p – usage rate u
Slope= - usage rate u
Usage rate u is demand rate D in terms of the time measure same as production rate p.
e.g. (a) D = 200 units / week, p = 50 units / day  u = 200/5 = 40 units / day
(b) D = 5 units / hr, p = 8 units / hr  u = 5 units / hr.

44. Economic Production Quantity (EPQ)
Maximum
Inventory
Imax

45. Economical Production/Optimal Run quantity
Tradeoff: higher production /run quantity, higher holding (carrying) cost, but lower setup costs. How much to produce each run is optimal? Answer: EPQ
Production cycle time
Run time
(time of producing in a cycle)
S – setup cost, H – unit holding cost, D – demand, p – production rate, u – usage rate

46. Example 3
A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate 800 per day. The toy trucks are assembled uniformly over entire year. Carrying cost is $1 per wheel a year. Setup costs for a production run of wheels is $45. The firm operates days per year.

47. Solution to Example 3
1. What is the optimal size of a production run?
2. What is the length of each production run?
3. What is cycle time for the optimal run size?

48. Solution to Example 3 (Cont.)
4. What is the maximum inventory level? the average inventory level?
5. What is the average annual cost for holding inventory? for setting up production?
TC = $1800

49. Single-Period Model
-- Newsboy Problem

50. Fashion goods Single-Period Model Assumptions:
1. Only one product is involved.
2. Uncertain bulk demand realizes in a selling season. We have a demand distribution estimated from past pattern and belief of future trend.
3. A single order arrives before selling season.
4. Excess inventory is salvaged after selling season.
Fashion goods

51. Newsboy Problem – An Example
Bus Adm Chp 12 Inventory Mgmt.
Newsboy Problem – An Example
Example: A newsboy can buy copies of a newspaper for 25 cents early in the morning each day and sell them for 85 cents during the day. He is paid 5 cents for unsold copies.
Underage cost (shortage cost): the marginal cost of under-stocking one unit.
Cunderage = = $0.60 per copy
Overage cost (excess cost): the marginal cost of over-stocking one unit.
Coverage = = $0.20 per copy
Cunderage =

52. This percentage is called “Newsboy critical fractile”
Newsboy Solution
The goal:
Identify the order quantity that minimizes the sum of underage and overage costs
Newsboy solution – optimal stocking quantity
Te cost minimum order quantity guarantees a service level (percentage of chance that demand is satisfied)
This percentage is called “Newsboy critical fractile”

53. Newsboy Problem – An Example
Example: The newsboy has an underage cost of $ 0.60/unit, and an overage cost of $0.20/unit. The demand is approximately normal with a mean of 1000 copies per day (µ=1000) and standard deviation of 10 copies per day (σ=10).
Service Level = Prob. (demand is filled by on-hand inventory)
=1-Prob(stockout)