1. Chapter 13 - Inventory Management
Inventory is a stock of anything held to meet some future demand. It is created when the rate of receipts exceeds the rate of disbursements. These items or resources can include: raw materials, finished products, component parts, supplies, and work-in-process. The challenge is to have the right amount to achieve the competitive priorities for the business most efficiently.
An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be.
This presentation covers the material in Chapter 13 on Inventory Management.

2. Why keep inventories low?
Holding or carrying costs – variable cost of keeping items on hand. The cost to keep an item on hand for a year typically ranges from 25% to 40% of the item’s value.
Interest or opportunity cost—time value of money
Storage and handling—warehouse facilities and labor
Taxes and insurance—usually proportional to inventory value
Shrinkage
Pilferage
Obsolescence
Deterioration

3. Pressure for high inventories
Customer service: For customers that have immediate or seasonal demands, finished goods inventory can speed up delivery and reduce:
Stockouts—when standard item is not on hand when demand occurs, and sale is lost.
Backorders—customer order is not filled when promised or demanded but is filled later.
Ordering costs: Costs associated 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
Setup costs: Work orders have similar costs associated with each setup, and machines may be unproductive for several hours each time the product is switched.
Labor and equipment utilization
Transportation cost
Outbound: transportation costs can be reduced by building inventories and shipping full carloads.
Inbound: per unit inbound material transportation costs can be reduced by ordering large lot sizes.
Quantity discounts. Ordering large quantities can provide a hedge against future price increases and provide a means to obtain quantity discounts.

4. Purposes of Inventory 1. To maintain independence of operations.
2. To meet variation in product demand.
3. To allow flexibility in production scheduling.
4. To provide a safeguard for variation in raw material delivery time.
5. To take advantage of economic purchase-order size. 4

5. Types of Inventory Cycle Inventory Q + 0 Average cycle inventory = 2
Created by ordering in larger quantities so as to place orders less frequently. The longer the cycle, the bigger the lot size (Q).
A larger Q can help with customer service, ordering cost, setups, transportation rates, and purchasing cost.
Two lot-sizing principles:
Q varies directly with the elapsed time (cycle) between orders. A one-month cycle means an average Q of one month’s supply.
Cycle inventory varies from Q to 0, or an average of:
Q + 0 2
Average cycle inventory =
Demand must be constant and uniform – so realize that this is a rule of thumb; estimate

6. Types of Inventory Safety stock inventory
Helps with customer service and hidden costs of missing parts
Created by placing an order sooner than typically needed
The replenishment order most likely will arrive ahead of time, protecting against three uncertainties:
Demand
Lead time
Supply
Anticipation inventory
Used to absorb uneven rates in:
Demand
Supply
Created by smoothing output rates, stockpiling during the slack season or overbuying before a price increase or capacity shortage
Examples: manufacturers of air conditioners or greeting cards

7. Types of Inventory Pipeline (transit) inventory
Created by the time spent to move and produce inventory
All orders that have been placed but not yet received
Can be found in any one of three stages:
Inbound: scheduled receipts of purchased materials paid for but not ready to use
Within the plant: WIP inventory, including all scheduled receipts for orders sent to the shop
Outbound: finished goods that have been shipped but not yet received and paid for by the customer
Pipeline inventory: Sometimes it is 0 (nothing on order) and sometimes Q (one open order). But on the average, it is
Average pipeline inventory = DL=dL

8. Types of Inventory Cycle inventory = Q/2 = 280/2 = 140 drills
= 280/2
= 140 drills
Pipeline inventory = DL = dL
= (70 drills/week)(3 weeks)
= 210 drills

9. Types of Inventory
This slide shows the cycle and pipeline inventories expected with the new proposal.

10. Inventory Costs Holding (or carrying) costs.
Costs for storage, handling, insurance, etc.
Setup (or production change) costs.
Costs for arranging specific equipment setups, etc.
Ordering costs.
Costs of someone placing an order, etc.
Shortage costs.
Costs of canceling an order, etc. 5

11. Inventory Reduction
Managers want cost-effective ways to reduce inventories. There are basic tactics, which we call levers.
The primary lever must be activated to really cut inventory.
A secondary lever reduces the penalty cost of applying the primary lever and reduces the need to have inventory in the first place.
Cycle
Primary: Reduce lot size, Q. However, making such reductions in Q without making any other changes can be devastating.
Secondary levers
Streamline methods for placing orders and making setups.
Increase repeatability, eliminate the need for changeovers.

12. Inventory Reduction Safety stock Anticipation inventory
Primary: Place orders closer to the time when they must be received. However, this approach can lead to unacceptable customer service—unless demand, supply, and delivery uncertainties can be minimized.
Secondary levers
Improve demand forecasts, Reduce lead time, Reduce supply uncertainties, communicate with suppliers, use preventive maintenance, Capacity cushions and cross-trained workers.
Anticipation inventory
Primary: Match demand rate with production rate.
Add new products with different demand cycles
Provide off-season promotional campaigns
Offer seasonal pricing plans
Pipeline inventory
Primary: Reduce lead time.
Find more responsive suppliers, improve materials handling.
In cases where lead time varies with lot size, decrease Q.

13. Inventory Placement
Managers make in part these decisions by designating an item either as special or standard.
Special: made (or purchased) to order; just enough to cover a customer request
Standard: made (or purchased) to stock and normally available when needed
Inventory held toward the finished goods level means shorter delivery time, but higher holding costs.

14. ABC Analysis 10 20 30 40 50 60 70 80 90
100
Percentage of items
Percentage of dollar value
100 —
90 —
80 —
70 —
60 —
50 —
40 —
30 —
20 —
10 —
0 —
Class C
Class A
Class B
Step 1: Divide into three classes, according to annual dollar usage. Look for natural changes, because dividing lines not exact.
Step 2: Have close control over “A” items. Use levers, review frequently, centralized buying, inventory record accuracy.

15. Economic Order Quantity
Assumptions
Demand rate is constant
No constraints on lot size
Only relevant costs are holding and ordering/setup
Decisions for items are independent from other items
No uncertainty in lead time or supply - time from ordering to receipt is constant.
Inventory holding cost is based on average inventory. Ordering or setup costs are constant.
All demands for the product will be satisfied. (No back orders are allowed.)
Price per unit of product is constant.
This slide presents the key assumptions of the model as described in the Chapter.

16. Economic Order Quantity
On-hand inventory (units)
Time
Average
cycle
Inventory Q — 2
1 cycle
Receive order
Inventory depletion (demand rate)
Figure 13.3

17. Economic Order Quantity
By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the optimal inventory order point that minimizes total costs.
Annual cost (dollars)
Lot Size (Q)
Ordering cost (OC)
Holding cost (HC)
Total cost = HC + OC

18. Economic Order Quantity
Annual
Ordering
Cost
Annual
Holding
Cost
Total Annual Cost = +
TC = Total annual cost
D = Demand
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
Note that the lowest cost occurs when the ordering cost is approximately equal to holding cost. This is not by accident.

19. Economic Order Quantity

20. Economic Order Quantity
| | | | | | | |
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Total cost = (H) (S) D Q 2
Holding cost = (H)
Ordering cost = (S)
Annual cost (dollars)

21. Economic Order Quantity
Bird feeder costs
C = (H) (S) Q 2 D
D = (18 /week)(52 weeks) = 936 units
H = 0.25 ($60/unit) = $15
S = $ Q = 390 units
C = $ $108 = $3033
Annual cost (dollars)
| | | | | |
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Total cost = (H) (S) D Q 2
Holding cost = (H)
Ordering cost = (S)

22. Economic Order Quantity
Current
cost
3000 —
2000 —
1000 —
0 — Q 2 D Q
Total cost = (H) (S)
Annual cost (dollars) Q 2
Holding cost = (H) D Q
Ordering cost = (S)
| | | | | | | |
Current Q
Lot Size (Q)

23. Economic Order Quantity
| | | | | | | |
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Current
cost Q
Total cost = (H) (S) D 2
Holding cost = (H)
Ordering cost = (S)
Bird feeder costs
D = (18 /week)(52 weeks) = 936 units
H = 0.25 ($60/unit) = $15
S = $ Q = EOQ
C = (H) (S)
EOQ =
2DS H
Example 13.3
Annual cost (dollars)
The next series of slides presents Example The series builds in steps to the conclusion of the Example showing the development of key equations along the way.

24. Economic Order Quantity
| | | | | | | |
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Current
cost Q
Total cost = (H) (S) D 2
Holding cost = (H)
Ordering cost = (S)
Bird feeder costs
D = (18 /week)(52 weeks) = 936 units
H = 0.25 ($60/unit) = $15
S = $ Q = 75 units
C = $562 + $562 = $1124
C = (H) (S)
EOQ =
2DS H
Example 13.3
Annual cost (dollars)
We calculate and plot the EOQ and costs.
Best Q
(EOQ)

25. Economic Order Quantity
This slide shows the Solver output of the cost structure of Example 13.3

26. Economic Order Quantity
Current
cost
3000 —
2000 —
1000 —
0 —
Birdfeeder costs
Time between orders Q 2 D Q
Total cost = (H) (S)
D = (18 /week)(52 weeks) = 936 units
H = 0.25 ($60/unit) = $15
S = $ Q = 75 units
EOQ D
TBOEOQ = = 75/936 = year
TBOEOQ = (75/936)(12) = 0.96 months
TBOEOQ = (75/936)(52) = 4.17 weeks
TBOEOQ = (75/936)(365) = days
Annual cost (dollars)
Lowest
cost
| | | | | | | |
Current Q
Best Q
(EOQ)
Lot Size (Q)
Example 13.3

27. Effect of Changes What happens to EOQ when demand changes?
What happens to lot sizes if setup costs decrease?
What happens if interest rates drop?
How critical are errors in estimating D, H, and S?
Note: This would be an AWESOME quiz.

28. ICS - Continuous ReviewIP IP IP
Order
received
Order
received
Order
received
Order
received Q Q Q
On-hand inventory OH OH OH R
Order
placed
Order
placed
Order
placed
Time L L L
TBO
TBO
TBO

29. Continuous Review
Inventory control systems bring together two dimensions—how much and when. Here is one of two systems that we will fully develop.
The focus is on inventory control systems for independent demand items
Other names are: reorder point system (ROP), fixed-order quantity system, and Q system.
Tracks inventory position, which is the item’s ability to satisfy future demand.
Decision rule: Whenever a withdrawal brings IP down to the reorder point (R), place an order for Q (fixed) units.

30. Continuous Review Chicken Soup R = Average demand during lead timeIP IP IP
Order
received
Order
received
Order
received
Order
received
Chicken Soup Q Q Q
On-hand inventory
R = Average demand during lead time
= (25)(4) = 100 cases
IP = OH + SR – BO
= – 0 = 210 cases OH OH OH R
Order
placed
Order
placed
Order
placed
Time L L L
TBO
TBO
TBO
Example 13.4

31. Finding R when Demand is Uncertain
When there are uncertainties in demand, there is a need for safety stock. We thus make R the largest “reasonable” demand possible during the lead time.
R = Average demand during the lead time + Safety Stock
The average demand during the lead time is determined by customers. As a management issue, the reorder point decision is really a matter of selecting the safety stock quantity. Safety stock depends on two factors:
Service level, or cycle-level policy—the desired probability of not running out in any one cycle
Amount of uncertainty in demand—If it is small, then little safety stock needed.
Choosing an appropriate service level policy
Weigh benefits of holding safety stock against the cost of holding it.
Variability in demand during lead time measured by probability distributions. We consider two: normal and discrete

32. Uncertain Demand R On-hand inventory Time Order received Q OH placedIP R
TBO1
TBO2
TBO3 L1 L2 L3

33. Reorder Point / Safety Stock
Safety Stock/R
Safety stock = zsL
= 2.33(22) = 51.3
= 51 boxes
Reorder point = ADDLT + SS =
= 301 boxes
Probability of stockout
( = 0.15)
Cycle-service level = 85%
Average demand during lead time
zL R

34. Lead Time Distributions
Figure 13.10
st = 15 = + 75
Demand for week 1
Demand for week 2
Demand for week 3
st = 26
225
Demand for
three-week lead time

35. Lead Time Distributions
Example 13.6
st = 15 = + 75
Demand for week 1
Demand for week 2
Demand for week 3
st = 26
225
Demand for
three-week lead time
Bird feeder Lead Time Distribution
t = 1 week d = L = 2
sL = st L = = 7.1
Safety stock = zsL = 1.28(7.1) = 9.1 or 9 units
Reorder point = dL + Safety stock
= 2(18) + 9 = 45 units

36. Lead Time Distributions
Example 13.6
st = 15 = + 75
Demand for week 1
Demand for week 2
Demand for week 3
st = 26
225
Demand for
three-week lead time
Bird feeder Lead Time Distribution
t = 1 week d = L = 2
Reorder point = 2(18) + 9 = 45 units
C = ($15) ($45) + 9($15) 75 2
936
C = $ $ $135 = $

37. Periodic Review Systems
Time
On-hand inventory
IP1
IP3
IP2
Order
received IP OH
placed Q1 Q2 Q3 L P
Protection interval T

38. Periodic Review Systems
Order
received IP
TV Set - P System
IP = OH + SR – BO
Qt = T - IPt
T = 400 BO = 5
OH = 0 SR = 0
IP = – 5 = –5 sets
Q = 400 – (–5) = 405 sets
Time
On-hand inventory
IP1
IP3
IP2
Order
received IP OH
placed Q1 Q2 Q3 L P
Protection interval T
The next series of slides presents Example The series builds in steps to the conclusion of the Example showing the development of key equations along the way.

39. Periodic Review Systems
T = Average demand during the protection interval + Safety stock
= d (P + L) + zsP + L
= (18 units/week)(16 weeks) (12 units) = 123 units
EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units
t = 18 units L = 2 weeks cycle/service level = 90%
Bird feeder—Calculating P and T
P = (52) = (52) = 4.2 or 4 weeks
EOQ D 75
936
P+L = st P + L = = 12 units

40. Periodic Review Systems
Bird feeder—Calculating P and T
t = 18 units L = 2 weeks cycle/service level = 90%
EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units
P = 4 weeks T = 123 units
C = ($15) ($45) + 15($15)
4(18) 2
936
C = $540 + $585 + $225 = $1350

41. Comparison of Q and P Systems
Q Systems
Convenient to administer
Orders may be combined
IP only required at review
Individual review frequencies
Possible quantity discounts
Lower, less-expensive safety stocks
This slide builds the information presented in the text comparing the two basic types of control systems.