1. Statistical Inventory Management
“Education in Pursuit of Supply Chain Leadership”
dp&c
Chapter8
Chapter 8
Statistical Inventory Management

2. Learning Objectives Understand the demand driver
Define the concepts of stock replenishment
Describe the replenishment review interval
Review the basic terms of statistical inventory replenishment
Review the basic inventory replenishment techniques
Detail the basic of the reorder point
Work with reorder point lead time and safety stock
Explore min/max and periodic review methods

3. Learning Objectives (cont.)
Define order quantity techniques
Calculate the economic order quantity (EOQ)
Detail the assumption of the EOQ technique
Calculate order quantity discounts
Perform order quantity joint replenishment
Determine the transportation EOQ
Discuss replenishment by item class
Discuss the application of lean to statistical order management

4. Statistical Inventory Management
Chapter 8
Statistical Inventory Management
Statistical Inventory Replenishment Concepts

5. Understanding the Demand Driver
Independent Demand
The demand for an item that is unrelated to the demand for other items. Demand for finished goods, parts required for destructive testing, and service parts requirements are examples of independent demand
Dependent Demand
Demand that is directly related to or derived from the bill of material structure for other items or end products. Such demands are therefore calculated and need not and should not be forecast
APICS Dictionary, 13th edition

6. Characteristics of Dependent Demand
Demand for these items is independent of company inventory decisions.
Demand for these items is subject to a level of random variation.
These items are usually planned and managed without reference to other items.
Planning for these items usually involves the use of forecasting techniques designed to foretell future demand based on past historical usage.
These items are best planned with some form of safety or reserve stock to counterbalance variation in forecasting.
The critical question for inventory availability is one of quantity rather than timing.

7. Characteristics of Dependent Demand
Dependent demand items are always planned and managed in relation to other items as detailed in the bills of material (BOMs) in which they are specified
Replenishment quantities for production inventories can be precisely determined by establishing the demand on “parent” level assemblies and then using the BOM structure to calculate exactly the “children” item requirements and due dates
Future demand for production inventories should not be forecasted
Management inventory planning decisions directly impact the demand for these items
Dependent demand items rarely use safety or reserve stocks
The critical question for inventory availability is one of timing rather than quantity

8. BOM Structure Example Independent Demand A Dependent Demand B C
(Service Part)
Dependent
Demand D E
Dependent
Demand
Dependent
Demand

9. Concept of Inventory Replenishment
The theory behind inventory replenishment management is that for each item, an optimal stocking and ordering quantity can be determined either statistically or through some form of experience, or even intuition. The object is to ensure that the optimum stocking level for each item in the inventory is maintained at the targeted service level without creating excess stock.

10. “Saw-Tooth Chart”

11. Replenishment Review Interval
Continuous Review System
The inventory level on-hand and on-order for this system is checked whenever a change in inventory level occurs and when the reorder point is reached a restocking order is released
Periodic Review System
In this model an order is placed every “n” time periods. The order quantity is variable and essentially replaces the items consumed during the current time period

12. Continuous and Periodic Review Systems
Issue
Continuous
Periodic
Lower maintenance expense X
Ordering by item family
Lower inventory investment
Replenishment predictability
Overall control
Fast-moving items
Low cost bulk items
Higher customer service levels
Use of computer required
Lower purchase order costs

13. Replenishment Trigger
Basic Replenishment Technique Terms
Demand
Determines the rate at which an item’s inventory is consumed
Determines the average amount of inventory on hand for a product sufficient to satisfy demand during the lead time
Cycle Stock
Safety Stock
Determines the extra inventory a company decides to hold in addition to cycle stock
Determines the available inventory on-hand balance at which a replenishment order is triggered
Replenishment Trigger
On-Hand Balance
Determines the current available quantity of an item

14. Basic Replenishment Technique Terms (cont.)
Review Interval
Determines the point in time inventory balance records should be reviewed for possible replenishment
Determines the span of time from the moment the need for resupply is identified until it has been received
Lead Time
Reorder Quantity
Determines the replenishment quantity to restore inventory above the trigger point
Determines the standard quantity in which items are either manufactured or purchased
Lot Size

15. Statistical Inventory Management
Chapter 8
Statistical Inventory Management
Inventory
Replenishment Techniques

16. Replenishment Ordering Techniques
Visual Review
Replenishment determined by physically reviewing the inventory on-hand balance
Two-Bin
Fix order system using two containers: one for picking and one for reserve
Periodic Review
A fixed review cycle is established and replenishment occurs at the time of review
Order Point
A targeted quantity is statistically determined that is used as the trigger for replenishment
TPOP
A computerized method that time phases demand and replenishment activities
Lean
Replenishment is triggered using non-computer tools, such as a kanban card

17. Statistical Inventory Management
Chapter 8
Statistical Inventory Management
Reorder Point Systems

18. Order Point Technique
The order point calculation consists in determining if there is enough inventory on hand to satisfy Demand during the Lead Time plus Safety Stock
OP = Demand x Lead Time
+ Safety Stock

19. Order Point – Basic Model
Demand
Inventory
Quantity
Stockout point
Time

20. Reorder Point - Exercise
Objective: Calculate a reorder point
Data: Average demand per week is 100 units, the replenishment lead time is 2 weeks, and the safety stock is 50 units
Formula: ROP = D x LT + SS
where:
ROP = Reorder point
D = Demand
LT = Lead time
SS = Safety stock
Solution: 100 x = 250 units

21. Reorder Point Using Trend
Objective: Calculate a reorder point using trend
Data:
Past week’s demand = 205 units
The a factor = 0.1
Prior period’s smoothed average =
Prior period’s trend = 0.58
Lead time = 2 weeks
Solution:
New smoothed average demand = a(Dt) + (1 – a) (Dt-1) = 0.1 x x =
The difference is Dt1 – Dt = – = 3.05
The trend is Trendt-1(1 – a) + a x Differencet = 0.82

22. Reorder Point Using Trend – Exercise (cont.)
Solution:
New expected period demand is ((Trendt(1 – a) / a) + Smoothed averaget = 0.82 x 0.9/ =
New forecast of reorder point demand is expected period demand x LT = x 2 = 370 units

23. Cyclical Order Point Using Trend
Objective: Calculate a cyclical reorder point using trend
Data:
13 months of past data
The a factor = 0.1
The (1-a) / a factor = 9.0
Current month’s demand = 145 units
Current base series = (calculated by using the surrounding quarter demand from the previous year.)
Solution:
New demand ratio = current demand / current base series = 145 / =
New average ratio = (1-a) x Previous average ratio + (a x Current demand ratio) = (.9 x 1.098) + (.1 x ) =

24. Cyclical Order Point Using Trend (cont.)
Solution:
The difference is Current demand ratio – Current average ratio = – = .011.
New trend is (1-a) x Previous trend + (a x Current difference) = (.9 x .0034) + (.1 x .011) =
New expected ratio is Current period average ratio + (1-a) / a + Current trend = =
New expected demand is Current expected ratio x current base series = x =

25. Defining Lead Time Oder Review Order Prep Order Transmission
The time it takes for review and selection of items for replenishment order action
Oder Review
Order Prep
Time to generate the order and review for quantity discounts
Order Transmission
Time to print, verify, and transmit order to the supply source
Time for supplier order processing, pick and pack, and shipment to the ordering source
Supplier Processing
Time spent receiving, checking, quality control, and staging the order
Receiving
Time spent in item movement, put-away, and any final information recording
Item Restocking

26. Defining Safety Inventory
Expected demand Q
A quantity of stock planned to be in inventory to protect against fluctuations in demand or supply
Q / 2
Cycle
Inventory S
Safety Stock
APICS Dictionary, 13th edition T
Time
Q = 250 units
Q /2 = 250 units / 2 = 125 units
S = 125 units / 2 = 63 units
Q/2 + S = 313 units

27. Normal Distribution - Diagram
1,000 1σ
= 285 units
715
1,285
600
1,350
430
1,570
145
1,855 +/ - 1σ
68.27% +/ - 2σ
95.45% +/ - 3σ
99.73%

28. Calculating the Safety Stock – Part 1

29. Calculating the Standard Deviation – Part 2
Two methods possible:
Squared Deviation: å (
Actual
Demand –
Forecast) 2
SD =
number of periods - 1
Formula:
a.) Squared deviation = 841,001 / 9 =
b.) Standard Deviation (1s) = 93, = units
2. MAD Method
a.) Mean Absolute Deviation (MAD) = 2649 / 10 = 264.9
b.) Standard Deviation (1s) = x 1.25 = units

30. Reorder Point with Safety Stock Calculation
Objective: Calculate a reorder point with safety stock
Data:
Demand per week = 1,000 units
Lead time = 2 weeks
Customer service level (CSL) = 98%
Standard deviation (s) =
Unit cost = US$235.00
Solution:
Demand during lead time = 1,000 x 2 weeks = 2,000 units
Safety stock (SS) = CSL x (s) = NORMSINV (.98) x = units
ROP = 2,000 units units = 2, units
SS cost = US$235 x = US$147,535 (rounded)

31. Safety Stock Using Probability
Objective: Calculate safety stock using probability
Data:
Demand per week = 1,000 units
Lead time = 2 weeks
Carrying cost/unit = US$30
Cost of stock out/unit = US$100
Optimum number of replenishment orders per year = 26
Current reorder point = 2,000 units
Demand above 2,000 units during reorder point period:
Number of units
Probability
2,000
2,100
2,200
2,300
2,400
24%
15% 8% 2% 1%

32. Safety Stock Using Probability (cont.)
Solution:
Safety
Stock
Carrying Cost
+ Stock out Cost =
Total
Cost
2,000
(100 * .15 * US$100 * 26) +
(200 * .08 * US$100 * 26) +
(300 * .02 * US$100 * 26) +
(400 * .01 * US$100 * 26) = US$106,600
US$106,600
2,100
100 * US$30 = US$3,000
(100 * .08 * US$100 * 26) +
(200 * .02 * US$100 * 26) +
(300 * .01 * US$100 * 26) = US$39,000
US$42,000
2,200
200 * US$30 =
US$6,000
(100 * .02 * US$100 * 26) +
(200 * .01 * US$100 * 26) = US$10,400
US$16,400
2,300
300 * US$30 =
US$9,000
(100 * .01 * US$100 * 26) = US$2,600
US$11,600
2,400
400 * US$30 =
US$12,000
Calculate safety stock carrying cost by multiplying the carrying cost times the safety stock
Calculate stock out cost: the sum of the units stocked out x the probability x the unit cost x the number of orders per year

33. Supply Uncertainty and Safety Stock
Objective: Calculate safety stock with supply uncertainty
Data:
Average daily demand (D) = 250 units
Lead time (LT) = 9 days
Standard deviation of demand (sD) = 85 units
Customer service level (CSL) = 95%
Standard deviation of lead time (sLT) = 5 days
Formula:

34. Supply Uncertainty and Safety Stock (cont.)
Solution:
Solve for standard deviation of demand during the lead time: sL = = 1,275.74
Solve for safety stock (SS):
SS = sL x CSL = x 1.65 = 2,105 (rounded)
New order point calculation:
250 (D) x 9 (LT) + 2,105 (SS) = 4,355 units

35. Min/Max Order System Definition: Minimum quantity calculation:
Called the min/max system because the inventory position should always be a quantity located between the minimum and maximum stocking values
Minimum quantity calculation:
Use the standard reorder point equation
Maximum quantity calculation:
Function of the average daily demand, lad time, and the standard deviation
Formula:
(Demand x lead time) + (customer service level x standard deviation x square root of the lead time)

36. Min/Max Order System – Example
Objective: Calculate min/max order quantity
Data:
Average daily demand (D) = 50 units
Lead time (LT) = 4 days
Standard deviation of demand (sD) = 20 units
Customer service level (CSL) = 98%
Min quantity = 125 units
Solution:

37. Periodic Review – Overview
Definition:
Items are reviewed periodically and replenishment orders are launched at each review. The order quantity contains sufficient stock to bring the inventory position up to a target inventory level
Uses:
Used when it is difficult to record withdrawals and additions of stock on a continuous basis
Used when items are ordered in families
Used for items with a limited shelf life
Significant economies can be gained by ordering in bulk

38. Periodic Review System TechniqueA
Safety Stock
Review Cycle 3 2 1
Lead
Time
Target
Inventory
Order
Quantity
Demand
Review
Point
Quantity
Replenishment
Receipt

39. Periodic Review Calculation
Equations:
Order review cycle = dividing an item’s units sold annually by the standard lot quantity
Target inventory level (TI) =
TI = (D(L + T)) + (SSsD )
where
D = the demand rate
L = item lead time
T = the review period
SS = item safety stock

40. Periodic Review Calculation – Example
Objective: Calculate a periodic review replenishment
Data:
Average weekly demand (D) = 1,000 units
Lead time (L) = 2 weeks
Standard deviation of demand (sD) = 100 units
Customer service level (CSL) = 98%
Review cycle (T) = 4 weeks
On-hand balance = 2,250 units
Solution:
Demand during lead time and review cycle: 1,000 x (2 + 4) = 6,000 units
Target inventory: 6,000 + (503 x 100 x = 6,503 units
Reorder quantity: 6,503 – 22,50 = 2,403 units

41. Statistical Inventory Management
Chapter 8
Statistical Inventory Management
Order Quantity Techniques

42. Trial and Error Method a. Order cost:
(Annual inventory usage / order quantity) x ordering cost
(24,000 units / 2,000 units) x US$20 = US$240
b. Carrying cost:
b. Carrying cost:
Order quantity / 2 x carrying cost % x unit cost
(2,000 / 2) units x 24% x US$0.25 = US$60

43. EOQ Graph Total Cost Optimal Cost Carrying Cost Ordering Cost Costs
800
700
Total Cost
600
Optimal Cost
500
Carrying
400
Cost
300
200
Ordering Cost
100 50
Quantities
2000
4000
8000
12000
24000

44. EOQ Calcualtion 2 x Demand x Cost of ordering
Inventory carrying cost % x Unit cost
Annual demand = 20,000 units
Cost of ordering = US$125
Unit cost = US$34
Carrying cost = 21%
2 x 20,000 x US$125
= 837 units
21% x $34

45. EOQ Assumptions
The cost of the product does not depend on the replenishment quantity
There are no minimum or maximum restrictions on the replenishment quantity
Items are considered totally independent of each other
Lead time is zero
No shortages are permitted and the entire order quantity is delivered at the same time
The minimum purchase quantity from the supplier is not three or four times the calculated QOQ
Purchase order preparation and carrying costs are known and constant
Very high or very low item usage needs to be reviewed in relation to unit costs before applying the EOQ technique

46. Quantity Discounts – Example
Objective: Choose from two suppliers based on quantity discounts
Data:
Annual demand (D) = 30,000 units
Ordering cost (OC) = US$200
Item unit cost (UC) = US$15
Carrying cost (k) = 22%
Steps (base calculation):
Calculate EOQ = 1,907 (1,906.93)
Calculate number of orders per year = 30,000 / = 15.7
Calculate material cost = EOQ x orders per year x item unit cost = 1, x 15.7 x US$15 = US$450,000
Calculate ordering cost = order cost x orders per year = US$200 x = US$3,146.43

47. Quantity Discounts – Example (cont.)
Steps:
Carrying cost = (EOQ / 2) x unit cost x carrying cost = ( / 2) x US$15 x 22% = US$3,146.53
Total cost = material cost + ordering cost + carrying cost = US$456,292.85
Steps (supplier 1):
Data:
Discount price for minimum quantity of 5,000 units = US$14.55
Order per year = 6
Summaries:
Material cost = US$436,500
Ordering cost = US$1,200
Carrying cost = US$8,002.50
Total cost = US$445,702.50

48. Quantity Discounts – Example (cont.)
Steps (supplier 2):
Data:
Discount price for minimum quantity of 12,000 units = US$14.25
Order per year = 2.5
Summaries:
Material cost = US$427,500
Ordering cost = US$500
Carrying cost = US$18,810
Total cost = US$446,810
Decision: Suppler 1 has the lowest costs

49. Joint Replenishment – Example
Objective: Calculate joint replenishment for three items
Data:
Annual demand for item #3925 = 6,000 units
Annual demand for item #3819 = 3,575 units
Annual demand for item #3442 = 1,250 units
Ordering cost (OC) = US$200
Transportation cost (TC) = US$350
Item unit cost (UC) = US$45
Carrying cost (k) = 20%
Steps (base calculation):
Order cost = (Demand / EOQ) x (Order cost + Transportation cost)
Carrying cost = (EOQ / 2) x unit cost x carrying cost
Total cost = ordering cost + carrying cost

50. Joint Replenishment – Example (cont.)
The three items ordered independently
Summary:
The three items ordered jointly
Summary:

51. Joint Replenishment – Example (cont.)
The three items ordered jointly: selected family items
Steps:
Identify the most frequently order item (i)
Equation: Order frequency for item #3925
Calculate the frequency for items #3819 and #3442
Determine the order frequency for each item as a multiple of the order frequency of the most ordered item (mi).
For item #3819, 7.01 / 7.01 = 1.
For item #3442, 7.01 / 5.30 = 1.32
Recalcuate the order frequency of items
For item #3819, 20% x US$45 x 1 x 6,000 = US$54,000.

52. Joint Replenishment – Example (cont.)
The three items ordered jointly: selected family items
Steps:
Sum the values for step 8
US$54,000 + US$32,175 + $22,500 = US$108,675
Divide the standard order cost by the order frequency
For item #3925, 200/1 = US$200
Sum the values for step 11
US$200 + US$200 + US$100 + US$350 (TC) = US$500
New order frequency for item #3925 =
New order frequency for item #3819 = 8 / 1 (original rounded order frequency fi) = 8 orders.

53. Joint Replenishment – Example (cont.)
The three items ordered jointly: selected family items
Steps:
New order frequency for item #3442 = 8 / 2 (original rounded order frequency fi) = 4 orders
Calculate order costs by using steps for ordering jointly

54. Transportation EOQ
Objective: Calculate the EOQ with transportation cost
Data:
Annual demand (D) = 25,000 units
Ordering cost (OC) = US$100
Item unit cost (UC) = US$10
Carrying cost (k) = 22%
Rate for small shipments = US$1.25 per unit
Rate for large shipments = .75 per unit
Step 1: Base EOQ calculation:
Item
EOQ
Orders/ Year
Carrying cost
Ordering cost
Total cost
#3925
1,507.56 17
$1,658.31
$3,316.62

55. Transportation EOQ (cont.)
Step 2: Current EOQ freight cost:
Rate for EOQ of 1, = (Rate x order quantity) x number of orders per year = US$1.25 x 1, x 17 = $31,250
Freight added EOQ =
Ord qty
Orders/ Year
Carrying cost
Ordering cost
Shipment cost
Total cost
1,507.56 17
$1,658.31
$31,250
$34,566.62
Step 3: Large shipment rate requires OQ = 5,000 units
Ord qty
Orders/ Year
Carrying cost
Ordering cost
Shipment cost
Total cost
5,000 5
$5,500
$500
$18,750
$24,750

56. Replenishment by Item Class – Steps
Divide the inventory into classes based on volume usage, dollar value, or other parameters.
Link items to classes.
Assign an inventory turnover target for each class.
Determine the level below which only dead and obsolete products reside. Eliminate this class from the procedure.
Establish the replenishment quantity for each class by dividing the annual usage of each item by the turnover value.
Recalculate the inventory classification scheme for all items at least once a month, depending on the expected inventory turnover.

57. Replenishment by Item Class – Calculation
Objective: Replenishment using order class
Data:
ABC Class
# of Total Items
Expected Turns
Order Interval A
1,200 24
15 days B
10,500 12
1 month C
25,250 6
2 months D
8,000 3
4 months E
6,500 1
12 months
Calculation: Calculate a class A item order quantity with yearly demand of 24,000 units
24,000 units / 24 turns = 1,000 units

58. Investment Order Limit – Calculation
Objective: Determine investment limit for multiple items
Data:
Annual demand for item #3925 = 14,000 units
Annual demand for item #3819 = 9,500 units
Annual demand for item #3442 = 7,000 units
Unit cost #3925 (UC) = US$20.00
Unit cost #3819 (UC) = US$10.00
Unit cost #3442 (UC) = US$15.00
Ordering cost (OC) = US$100
Carrying cost (k) = 20%
Investment limit (IL) = US$16,000

59. Investment Order Limit – Calculation (cont.)
Step1: Calculate base EOQ for each item
Step2: Determine total inventory investment
Inventory investment = UC1(Q1/2) + UC2(Q2/2) + UC3(Q3/2)
= US$20(836.66/2) + US$10(974.68/2) + US$15(683.13/2)
= $18,363.47
Step3: Adjust original EOQ quantities
Since inventory investment of $18, exceeds the US$16,000 level, the original EOQs will need to be reduced by inflating (k) and determining an adjustment factor (a)

60. Investment Order Limit – Calculation (cont.)
Step3: Adjust original EOQ quantities
Since inventory investment of $18, exceeds the US$16,000 level, the original EOQs will need to be reduced. The formula is:
Step 4: Adjust original EOQ quantities with a factor

61. Investment Order Limit – Calculation (cont.)
Step 5: Combine new EOQ values and validate that they match the investment limit

62. Statistical Inventory Management
Chapter 8
Statistical Inventory Management
Lean Inventory Management

63. Defining Lean
A management and operations philosophy based on the planned minimization of all resources, the continuous improvement of productivity, and a relentless search to convert product and process waste into customer winning value both within the enterprise and outside in the supply chain.
APICS Dictionary, 13th edition

64. Lean Philosophy Operations Excellence Value-Added Processes
Dedication to continuous product and process improvement focused on total customer service
Operations Excellence
Value-Added Processes
Eliminate all business functions and activities that do not add value to the company or the customer
All aspects of business processes must be dedicated to incremental improvement in ways great and small
Continuous Improvement
Combination of lean techniques focused on productivity, total quality management (TQM), and people empowerment
Lean/TQM

65. Lean Tactics to Reduce Inventory
Focus on continuous inventory reduction
Implement an inventory pull system
Establish lean ordering and delivery with suppliers
Deliver inventory directly to the point of use
Map and streamline inventory flows
Reduce batch sizes and production queues
Reduce setup times

66. Inventory Flow Analogy
Clogged Inventory Channel
Inventory
Inventory
Inventory
Poor
Controls
Lack of
Training
Unclear
Responsibilities
Lack of
Disciplines
Open Inventory Channel
Inventory

67. Key Points of a Lean-Pull System
Produce products only to customer order
Create a level schedule so that production may proceed according to a desired flow rate
Schedule a mix of products in varying lot sizes so that the factory or the supplier produces and delivers inventory close to the same mix of products that will be sold that day
Link scheduling management to pull production through the use of visual demand signals
Maximize process flow-through by maximizing the flexibility of people and machinery

68. The Pull System – Basic Concepts
Operator #1 receives requirement and makes more inventory
Demand pull signal triggered and requirement sent to feeding workstation
Operator #2 removes material from buffer inventory to start work
Process 1
Buffer Inventory
Process 2
Operator #1
Operator #2
Workstation #1
Workstation #2 D
Replenishment quantity moved to Workstation #2 buffer inventory

69. Three Types of Kanban Production Move Supplier
Specifies the quantity of product that must be produced by upstream production work centers
Move
Specifies the quantity of product that will be moved from a reserve or remote buffer location to the requested buffer area
Supplier
Is used in place of a purchase order to replenish products from an outside supplier

70. Calculating Supplier Kanbans
Objective: Calculate the number of kanbans in a system
Data:
Daily demand (D) = 300 units
Transit delay pick up (Td) = 2 days
Transit delay delivery (Tp) = 2 days
Safety stock (SS) = 50%
Kanban container size (Q) = 50 units
Deliveries per day (R) = 1 delivery per day
Equation:
Solution:
((300 x (2 + 2)) x ( ) / (1 x 50) = 36 kanbans

71. Chapter 8 End of Session dp&c Chapter8
“Education in Pursuit of Supply Chain Leadership”
dp&c
Chapter8
Chapter 8
End of Session