1. 12/27/2017
Inventory Management
LO20–1: Explain how inventory is used and understand what it costs.
LO20–2: Analyze how different inventory control systems work.
LO20–3: Analyze inventory using the Pareto principle.
TRA 3151, FGCU

2. Outline The Importance of Inventory Functions of Inventory
Types of Inventory
Managing Inventory
ABC Analysis
Inventory Models
Independent vs. Dependent Demand
Holding, Ordering, and Setup Costs

3. Outline – Continued Inventory Models for Independent Demand
The Basic Economic Order Quantity (EOQ) Model
Minimizing Costs
Reorder Points
Probabilistic Models and Safety Stock
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4. Amazon.com
Amazon.com started as a “virtual” retailer – no inventory, no warehouses, no overhead; just computers taking orders to be filled by others
Growth has forced Amazon.com to become a world leader in warehousing and inventory management
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5. Amazon.com
Each order is assigned by computer to the closest distribution center that has the product(s)
A “flow meister” at each distribution center assigns work crews
Lights indicate products that are to be picked and the light is reset
Items are placed in crates on a conveyor, bar code scanners scan each item 15 times to virtually eliminate errors
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6. Amazon.com
Crates arrive at central point where items are boxed and labeled with new bar code
Gift wrapping is done by hand at 30 packages per hour
Completed boxes are packed, taped, weighed and labeled before leaving warehouse in a truck
Order arrives at customer within days
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7. Importance of Inventory
One of the most expensive assets of many companies representing as much as 50% of total invested capital
Operations managers must balance inventory investment and customer service
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8. Inventory
Inventory can be visualized as stacks of money sitting on forklifts, on shelves, and in trucks and planes while in transit.
For many businesses, inventory is the largest asset on the balance sheet at any given time.
Inventory can be difficult to convert back into cash.
It is a good idea to try to get your inventory down as far as possible.
The average cost of inventory in the United States is 30 to 35 percent of its value.

9. Definitions
Inventory: the stock of any item or resource used in an organization
Includes raw materials, finished products, component parts, supplies, maintenance/repair items, and work-in-process
Service: Unsold seats, unsold tickets, unoccupied hotel rooms or hospital beds
Work-in-process
Undergone some change but not completed
A function of cycle time for a product

10. Inventory system: the set of policies and controls that monitor levels of inventory
Determines what levels should be maintained, when stock should be replenished, and how large orders should be.
Purposes of Inventory:
To maintain independence of operations
To meet variation in product demand
To allow flexibility in production scheduling
To provide a safeguard for variation in raw material delivery time
To take advantage of economic purchase order size

11. Inventory Management
The objective of inventory management is to strike a balance between inventory investment and customer service
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12. Demand Types
Independent demand – the demands for various items are unrelated to each other
For example, a workstation may produce many parts that are unrelated but meet some external demand requirement. Cars, appliances, computers, and houses are examples of independent demand inventory
Dependent demand – the need for any one item is a direct result of the need for some other item
Usually a higher-level item of which it is part. Tires stored at a Goodyear plant are an example of a dependent demand item

13. Inventory Costs Costs Holding (or carrying) costs
Costs for storage, handling, insurance over time
Setup (or production change) costs
Costs for arranging specific equipment setups, so cost to prepare a machine or process for manufacturing an order
Ordering costs
Costs of placing an order and receiving goods
Shortage costs
Costs of running out

14. Cost (and range) as a Percent of Inventory Value
Holding Costs
Category
Cost (and range) as a Percent of Inventory Value
Housing costs (building rent or depreciation, operating costs, taxes, insurance)
6% (3 - 10%)
Material handling costs (equipment lease or depreciation, power, operating cost)
3% ( %)
Labor cost
3% (3 - 5%)
Investment costs (borrowing costs, taxes, and insurance on inventory)
11% (6 - 24%)
Pilferage, space, and obsolescence
3% (2 - 5%)
Overall carrying cost
26%
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15. Cost (and range) as a Percent of Inventory Value
Holding Costs
Category
Cost (and range) as a Percent of Inventory Value
Housing costs (building rent or depreciation, operating costs, taxes, insurance)
6% (3 - 10%)
Material handling costs (equipment lease or depreciation, power, operating cost)
3% ( %)
Labor cost
3% (3 - 5%)
Investment costs (borrowing costs, taxes, and insurance on inventory)
11% (6 - 24%)
Pilferage, space, and obsolescence
3% (2 - 5%)
Overall carrying cost
26%
Holding costs vary considerably depending on the business, location, and interest rates. Generally greater than 15%, some high tech items have holding costs greater than 40%.
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16. Supply Chain Inventory Models

17. Inventory Models Single-period model
Used when we are making a one-time purchase of an item
Fixed-order quantity model
Used when we want to maintain an item “in-stock,” and when we restock, a certain number of units must be ordered
Fixed–time period model
Item is ordered at certain intervals of time

18. Inventory Systems – Comparison
Single-period inventory model
One-time purchasing decision (e.g., vendor selling T-shirts at a football game)
Seeks to balance the costs of inventory overstock and under stock
Multi-period inventory models
Fixed-order quantity models
Event triggered (e.g., running out of stock)
Fixed-time period models
Time triggered (e.g., monthly sales call by sales representative)

19. Inventory Control-System Design Matrix

20. Inventory Management
Inventory accuracy – refers to how well the inventory records agree with physical count
Cycle counting – a physical inventory-taking technique in which inventory is counted on a frequent basis rather than once or twice a year

21. ABC Analysis based on Pareto principle
Divides inventory into three classes based on annual dollar volume
Class A - high annual dollar volume
Class B - medium annual dollar volume
Class C - low annual dollar volume
Used to establish policies that focus on the few critical parts and not the many trivial ones
Other criteria such as quality, design changes, high unit cost can be used instead of dollar volume

22. Percent of Number of Items Stocked Percent of Annual Dollar Volume
ABC Analysis
Item Stock Number
Percent of Number of Items Stocked
Annual Volume (units) x
Unit Cost =
Annual Dollar Volume
Percent of Annual Dollar Volume
Class
#10286
20%
1,000
$ 90.00
$ 90,000
38.8% A
#11526
500
154.00
77,000
33.2%
#12760
1,550
17.00
26,350
11.3% B
#10867
30%
350
42.86
15,001
6.4%
#10500
12.50
12,500
5.4%
72%
23%

23. Percent of Number of Items Stocked Percent of Annual Dollar Volume
ABC Analysis
Item Stock Number
Percent of Number of Items Stocked
Annual Volume (units) x
Unit Cost =
Annual Dollar Volume
Percent of Annual Dollar Volume
Class
#12572
600
$ 14.17
$ 8,502
3.7% C
#14075
2,000
.60
1,200
.5%
#01036
50%
100
8.50
850
.4%
#01307
.42
504
.2%
#10572
250
150
.1%
8,550
$232,057
100.0% 5%

24. ABC Analysis A Items 80 – 70 – 60 – Percent of annual dollar usage
80 –
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | |
Percent of inventory items
A Items
B Items
C Items

25. ABC Classification

26. Need to determine when and how much to order
Multi-Period Models
Fixed-Order Quantity
Fixed-Time Period
Inventory remaining must be continually monitored
Has a smaller average inventory
Favors more expensive items
Is more appropriate for important items
Requires more time to maintain – but is usually more automated
Is more expensive to implement
Counting takes place only at the end of the review period
Has a larger average inventory
Favors less expensive items
Is sufficient for less-important items
Requires less time to maintain
Is less expensive to implement

27. Multi-Period Models – Comparison

28. Multi-Period Models – Process

29. Fixed-Order Quantity Models – 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.
Inventory holding cost is based on average inventory.
Ordering or setup costs are constant.
All demands for the product will be satisfied.

30. Fixed-Order Quantity Model
Always order Q units when inventory reaches reorder point (R).
Inventory is consumed at a constant rate, with a new order placed when the reorder point (R) is reached once again.
Inventory arrives after lead time (L). Inventory is raised to maximum level (Q).

31. Total cost of holding and setup (order) Optimal order quantity (Q*)
Minimizing Costs
Objective is to minimize total costs
Annual cost
Order quantity
Total cost of holding and setup (order)
Setup (or order) cost
Minimum total cost
Optimal order quantity (Q*)
Holding cost
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32. Economic Order Quantity (EOQ)
The optimal order quantity (Qopt) occurs where total costs are at their minimum

33. Example 20.2

34. Number of units in each order Setup or order cost per order
The EOQ Model
Annual setup cost = S D Q
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual setup cost = (Number of orders placed per year)
x (Setup or order cost per order)
Annual demand
Number of units in each order
Setup or order cost per order =
= (S) D Q
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35. Inventory Usage Over Time
Inventory level
Time
Average inventory on hand Q 2
Usage rate
Order quantity = Q (maximum inventory level)
Minimum inventory
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36. The EOQ Model Q = Number of pieces per order
Annual setup cost = S D Q
Annual holding cost = H Q 2
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual holding cost = (Average inventory level)
x (Holding cost per unit per year)
Order quantity 2
= (Holding cost per unit per year)
= (H) Q 2
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37. The EOQ Model 2DS = Q2H Q2 = 2DS/H Q* = 2DS/H
Annual setup cost = S D Q
Annual holding cost = H Q 2
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Optimal order quantity is found when annual setup cost equals annual holding cost D Q
S = H 2
Solving for Q*
2DS = Q2H
Q2 = 2DS/H
Q* = 2DS/H
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38. An EOQ Example Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units
Determine optimal number of needles to order
D = 1,000 units
S = $10 per order
H = $.50 per unit per year
Q* =
2DS H
Q* =
2(1,000)(10)
0.50
= 40,000 = 200 units
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39. Expected number of orders
An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order
H = $.50 per unit per year
= N = =
Expected number of orders
Demand
Order quantity D Q*
N = = 5 orders per year
1,000
200
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40. Expected time between orders Number of working days per year
An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year
= T =
Expected time between orders
Number of working days per year N
T = = 50 days between orders
250 5
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41. An EOQ Example Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
Total annual cost = Setup cost + Holding cost
TC = S H D Q 2
TC = ($10) ($.50)
1,000
200 2
TC = (5)($10) + (100)($.50) = $50 + $50 = $100
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42. An EOQ Example Management underestimated demand by 50%
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
1,500 units
TC = S H D Q 2
TC = ($10) ($.50) = $75 + $50 = $125
1,500
200 2
Total annual cost increases by only 25%
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43. An EOQ Example Actual EOQ for new demand is 244.9 units
D = 1,000 units Q* = units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
1,500 units
TC = S H D Q 2
Only 2% less than the total cost of $125 when the order quantity was 200
TC = ($10) ($.50)
1,500
244.9 2
TC = $ $61.24 = $122.48
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44. Lead time for a new order in days Number of working days in a year
Reorder Points
EOQ answers the “how much” question
The reorder point (ROP) tells “when” to order
ROP =
Lead time for a new order in days
Demand per day
= d x L
d = D
Number of working days in a year
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45. Reorder Point Curve Q* Resupply takes place as order arrives
Inventory level (units)
Time (days) Q*
Resupply takes place as order arrives
Slope = units/day = d
ROP (units)
Lead time = L
Figure 12.5
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46. Number of working days in a year
Reorder Point Example
Demand = 8,000 iPods per year
250 working day year
Lead time for orders is 3 working days
d = D
Number of working days in a year
= 8,000/250 = 32 units
ROP = d x L
= 32 units per day x 3 days = 96 units
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47. Probabilistic Models and Safety Stock
Used when demand is not constant or certain
Use safety stock to achieve a desired service level and avoid stockouts
ROP = d x L + ss
Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit x the number of orders per year
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48. Establishing Safety Stock Levels
Safety stock – refers to the amount of inventory carried in addition to expected demand.
Safety stock can be determined based on many different criteria.
A common approach is to simply keep a certain number of weeks of supply.
A better approach is to use probability.
Assume demand is normally distributed.
Assume we know mean and standard deviation.
To determine probability, we plot a normal distribution for expected demand and note where the amount we have lies on the curve.

49. Fixed-Order Quantity Model with Safety Stock
Demand is variable, but follows a known distribution/
After the reorder is placed, demand during the lead time may be higher than expected, consuming some (or all) of the safety stock

50. Example 20.4 For 95% probability, z = 1.64. Excel: Reorder Point
For 95% probability, z = 1.64.
Policy – place a new order for 936 units whenever stock falls to 388 units on hand. This results in a 95% probability of not stocking out during the lead time.
Excel: Reorder Point

51. Reorder Point with a Safety Stock (Buffer added to the inventory on hand during lead time)
point, R Q LT
Time
Inventory level
Safety Stock
Safety stock: additional amount of inventory kept over and above the average
amount required to meet demand

52. Probabilistic Demand
Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined
ROP = demand during lead time + ZsL
where Z = number of standard deviations
sL = standard deviation of demand during lead time
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53. Probabilistic Demand Risk of a stockout (5% of area of normal curve)
Probability of no stockout 95% of the time
Mean demand 350
Risk of a stockout (5% of area of normal curve)
ROP = ? kits
Quantity
Safety stock
Number of standard deviations z
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54. Safety Stock Example Number of Units Probability 30 .2 40 ROP  50 .3
ROP = 50 units Stockout cost = $40 per frame
Orders per year = 6 Carrying cost = $5 per frame per year
Number of Units
Probability 30 .2 40
ROP  50 .3 60 70 .1
1.0
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55. Safety Stock Example
ROP = 50 units Stockout cost = $40 per frame
Orders per year = 6 Carrying cost = $5 per frame per year
Safety Stock
Additional Holding Cost
Stockout Cost
Total Cost 20
(20)($5) = $100 $0
$100 10
(10)($5) = $ 50
(10)(.1)($40)(6) = $240
$290
$ 0
(10)(.2)($40)(6) + (20)(.1)($40)(6) = $960
$960
A safety stock of 20 frames gives the lowest total cost
ROP = = 70 frames
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56. Probabilistic Demand Inventory level Time Safety stock 16.5 units
ROP 
Place order
Inventory level
Time
Minimum demand during lead time
Maximum demand during lead time
Mean demand during lead time
ROP = safety stock of 16.5 = 366.5
Receive order
Lead time
Normal distribution probability of demand during lead time
Expected demand during lead time (350 kits)
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57. Probabilistic Example
Average demand = m = 350 kits
Standard deviation of demand during lead time = sdLT = 10 kits
5% stockout policy (service level = 95%)
Using Appendix I, for an area under the curve of 95%, the Z = 1.65
Safety stock = ZsdLT = 1.65(10) = 16.5 kits
Reorder point = expected demand during lead time + safety stock
= 350 kits kits of safety stock
= or 367 kits
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58. Fixed-Period (P) Systems
Orders placed at the end of a fixed period
Inventory counted only at end of period
Order brings inventory up to target level
Only relevant costs are ordering and holding
Lead times are known and constant
Items are independent from one another
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59. Fixed-Period Systems Inventory is only counted at each review period
May be scheduled at convenient times
Appropriate in routine situations
May result in stockouts between periods
May require increased safety stock
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60. Fixed-Time Period Model
Time periods are equal, but ending inventory varies.
Reorder quantity varies, depending upon ending inventory level. Beginning inventory is always the same.

61. Fixed-Time Period Model

62. Example 20.5

63. Inventory Control and Supply Chain Management
Average inventory – expected amount of inventory over time
Inventory turns – number of times inventory is cycled through over time – a measure of how efficiently inventory is used
Fixed Order Quantity:
D = 1,000 units
Q = 300 units
SS = 40 units
Inventory Turn = 1,000 / (300/2) +40
= 1,000/190 = turns per year
Fixed Time Period:
Weekly demand(d) = 50 units
Review Cycle (T) = 3 weeks
SS = 30 units
Inventory Turn= 52(50)/(50(3)/2 + 30
= 52(50)/105 = 2600/105 = 24.8 turns /year

64. Single Period Model Applications
Overbooking of airline flights
Ordering of clothing and other fashion items
One-time order for events – e.g., t-shirts for a concert

65. Single Period Inventory Model
Consider the problem of deciding how many newspapers to put in a hotel lobby
Too few papers and some customers will not be able to purchase a paper, and profits associated with these potential sales are lost.
Too many papers and the price paid for papers that were not sold during the day will be wasted, lowering profit.

66. Solving the Newspaper Problem
Consider how much risk we are willing to take of running out of inventory.
Assume a mean of 90 papers and a standard deviation of 10 papers.
Assume we want an 80 percent chance of not running out.
Assume that the probability distribution associated of sales is normal, stocking 90 papers yields a 50 percent chance of stocking out.

67. Solving the Newspaper Problem
From Appendix G, we see that we need approximately 0.85 standard deviation of extra papers to be 80 percent sure of not stocking out.
Using Excel, “=NORMSINV(0.8)” =

68. Single-Period Inventory Models

69. Example 20.1 Overestimating cancellation: More overbooking
Underestimating cancellation: Less overbooking
Overestimating cancellation: More overbooking

70. Example 20.1
From Appendix G, we see that our desired level falls about 0.55 standard deviations below the mean (z = -0.55)
Using Excel, “=NORMSINV(0.2857)” =

71. Problem 7 Purchasing cost= $0.2 /card Revenue: $2.15 / card
Demand = 2,000; standard deviation 500
What is the optimal production quantity?
Cu = 2.15 – .2 = 1.95
Co = .2, Cu/(Co+Cu) = 1.95/( ) =
From the standard normal table, Z-value is 1.325; Prob. of being in stock = 0.907
So, optimal production quantity = 2, (1.325) = , e.g cards

72. Problem 10 Purchasing cost= $0.25 / newspaper
Revenue: $1.00 / newspaper
Demand = 250; standard deviation 50
How many copies should you buy?
Cu = = 0.75
Co = .25, Cu/(Co+Cu) = 0.75/( ) = 0.75
Prob. of being in stock (service level) = From the standard normal table, Z-value is 0.67;
So, optimal quantity = (0.67) = 283.5, e.g. 284 papers
What is the probability of running out of stock?
1- P = = 0.25

73. Problem 7 Purchasing cost= $0.2 /card Revenue: $2.15 / card
Demand = 2,000; standard deviation 500
What is the optimal production quantity?

74. Problem 10 Purchasing cost= $0.25 / newspaper
Revenue: $1.00 / newspaper
Demand = 250; standard deviation 50
How many copies should you buy?