“Education in Pursuit of
Supply Chain Leadership”
dp&c Chapter8
Chapter 8
Statistical Inventory
Management
8-1
dp&c Chapter8
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
8-2
dp&c Chapter8
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
8-3
dp&c Chapter8
Chapter 8
Statistical Inventory Management
Inventory
Statistical
Inventory
Management
Basics
Replenishment
Concepts
8-4
dp&c Chapter8
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
8-5
dp&c Chapter8
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.
8-6
dp&c Chapter8
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
8-7
dp&c Chapter8
BOM Structure Example
Independent Demand
Independent
Demand
(Service Part)
A
Dependent
B
Demand
C
Dependent
Demand
D
E
Dependent
Demand
Dependent
Demand
8-8
dp&c Chapter8
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.
8-9
dp&c Chapter8
“Saw-Tooth Chart”
Quantity
Replenishment
Order
A
Trigger
Point
B
Inventory
C
Lead
Time
Safety Stock
Time
8-10
dp&c Chapter8
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
8-11
dp&c Chapter8
Continuous and Periodic Review Systems
Issue
Continuous
Periodic
Lower maintenance expense
X
Ordering by item family
X
Lower inventory investment
X
Replenishment predictability
X
Overall control
X
Fast-moving items
X
Low cost bulk items
X
Higher customer service levels
X
Use of computer required
X
Lower purchase order costs
X
8-12
dp&c Chapter8
Basic Replenishment Technique Terms
Demand
Determines the rate at which an item’s
inventory is consumed
Cycle Stock
Determines the average amount of
inventory on hand for a product sufficient
to satisfy demand during the lead time
Safety Stock
Determines the extra inventory a company
decides to hold in addition to cycle stock
Replenishment
Trigger
On-Hand
Balance
Determines the available inventory onhand balance at which a replenishment
order is triggered
Determines the current available quantity
of an item
8-13
dp&c Chapter8
Basic Replenishment Technique Terms (cont.)
Review Interval
Determines the point in time inventory
balance records should be reviewed for
possible replenishment
Lead Time
Determines the span of time from the
moment the need for resupply is identified
until it has been received
Reorder
Quantity
Determines the replenishment quantity to
restore inventory above the trigger point
Lot Size
Determines the standard quantity in which
items are either manufactured or
purchased
8-14
dp&c Chapter8
Chapter 8
Statistical Inventory Management
Inventory
Inventory
Replenishment
Management
Basics
Techniques
8-15
dp&c Chapter8
Replenishment Ordering Techniques
Visual Review
Two-Bin
Replenishment determined by physically
reviewing the inventory on-hand balance
Fix order system using two containers: one
for picking and one for reserve
A fixed review cycle is established and
Periodic Review 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 noncomputer tools, such as a kanban card
8-16
dp&c Chapter8
Chapter 8
Statistical Inventory Management
Inventory
Reorder
Point
Management Basics
Systems
8-17
dp&c Chapter8
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
8-18
dp&c Chapter8
Order Point – Basic Model
Demand
Quantity
Inventory
Stockout point
Time
8-19
dp&c Chapter8
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 2 + 50 = 250 units
8-20
dp&c Chapter8
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 = 174.46
Prior period’s trend = 0.58
Lead time = 2 weeks
Solution:
1. New smoothed average demand = a(Dt) + (1 – a) (Dt-1) =
0.1 x 205 + .9 x 174.46 = 177.51
2. The difference is Dt1 – Dt = 177.51 – 174.46 = 3.05
3. The trend is Trendt-1(1 – a) + a x Differencet = 0.82
8-21
dp&c Chapter8
Reorder Point Using Trend – Exercise (cont.)
Solution:
4. New expected period demand is ((Trendt(1 – a) / a) +
Smoothed averaget = 0.82 x 0.9/0.10 + 177.5 = 184.93
5. New forecast of reorder point demand is expected period
demand x LT = 184.93 x 2 = 370 units
Smoothing constant (a)
Date
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Demand
170
176
181
189
196
205
Simple
Average
168.00
338.00
345.00
353.50
365.75
378.88
394.44
0.1
(1-a)
Smoothed
Average
Difference
168.00
168.20
168.98
170.18
172.06
174.46
177.51
0.9 Lead Time
Trend
0.20
0.78
1.20
1.88
2.39
3.05
0.00
0.02
0.10
0.21
0.37
0.58
0.82
8-22
Expected
Demand
168.38
169.84
172.04
175.43
179.64
184.93
2
Forecast
337
340
344
351
359
370
Actual
Demand
315
348
394
329
352
432
Average
Variance
22
-8
-50
22
7
-62
-69
dp&c Chapter8
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 = 119.7 (calculated by using the
surrounding quarter demand from the previous year.)
Solution:
1. New demand ratio = current demand / current base series =
145 / 119.7 = 1.211.
2. New average ratio = (1-a) x Previous average ratio + (a x
Current demand ratio) = (.9 x 1.098) + (.1 x 112.11) = 1.109.
8-23
dp&c Chapter8
Cyclical Order Point Using Trend (cont.)
Solution:
3. The difference is Current demand ratio – Current average
ratio
= 1.211
– 1.1090.1= .011.
Smoothing
constant
(a)
(1-a)
(1-a) / a
0.9
9
4. New
trend Base
is (1-a)
x Previous
difference)
Demand
Average trend + (a x Current
Expected
Expected
Month
Demand
Difference
Trend
Series
Ratio
Ratio
Ratio
Demand
=
(.9
x
.0034)
+
(.1
x
.011)
=
.0042.
Jan-12
115
1.050
0
1.050
Feb-13
126
120.70ratio1.044
1.049 period
-0.001 average
-0.0001 ratio
1.049
126.60
5. New expected
is Current
+ (1-a)
/
Mar-13
141
126.30
1.116
1.056
0.007
0.0006
1.062
134.08
a
+
Current
trend
=
1.109
+
9
+
.0042
=
1.148.
Apr-13
135
127.30
1.060
1.057
0.000
0.0006
1.062
135.18
May-13
125
128.30
0.974
1.048
-0.008
-0.0003
1.046
134.17
6.
New
expected
demand
is
Current
expected
ratio
x
current
Jun-13
149
134.70
1.106
1.054
0.006
0.0003
1.057
142.38
base series
= 1.1481.183
x 119.7
= 137.36
Jul-13
170
143.70
1.067
0.013
0.0016
1.081
155.37
Aug-13
Sep-13
Oct-13
Nov-13
Dec-13
Jan-14
170
158
133
114
140
145
144
134.3
119.7
113.7
112.3
119.7
1.181
1.176
1.111
1.003
1.247
1.211
1.078
1.088
1.090
1.082
1.098
1.109
8-24
0.011
0.010
0.002
-0.009
0.016
0.011
0.0026
0.0033
0.0032
0.0020
0.0034
0.0042
1.101
1.118
1.119
1.100
1.129
1.148
158.60
150.11
133.96
125.02
126.80
137.36
dp&c Chapter8
Defining Lead Time
Oder Review
Order Prep
The time it takes for review and selection of
items for replenishment order action
Time to generate the order and review for
quantity discounts
Order
Transmission
Time to print, verify, and transmit order to the
supply source
Supplier
Processing
Time for supplier order processing, pick and
pack, and shipment to the ordering source
Receiving
Time spent receiving, checking, quality
control, and staging the order
Item
Restocking
Time spent in item movement, put-away, and
any final information recording
8-25
dp&c Chapter8
Defining Safety Inventory
Inventory
Expected demand
Q
A quantity of stock planned to be in
inventory to protect against
Q/2
fluctuations
in demand or supply
Cycle
S
Inventory
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
8-26
dp&c Chapter8
Normal Distribution - Diagram
1,000
1,285
715
1σ = 285 units
1,350
600
1,570
430
1,855
145
+/-1σ
68.27%
+/ - 2σ
95.45%
+/ - 3σ
99.73%
8-27
dp&c Chapter8
Calculating the Safety Stock – Part 1
Week
1
2
3
4
5
6
7
8
9
10
Sales Forecast
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
Actual Sales
Absolute Deviation
550
450
1,350
350
1,175
175
1,125
125
750
250
1,425
425
675
325
876
124
1,300
300
875
125
Deviation²
202,500
122,500
30,625
15,625
62,500
180,625
105,625
15,376
90,000
15,625
Sum Absolute Deviation
Sum Squared Deviation
2,649
841,001
8-28
dp&c Chapter8
Calculating the Standard Deviation – Part 2
Two methods possible:
1. Squared Deviation:
Formula:
SD =
 (Actual Demand – Forecast) 2
number of periods-1
a.) Squared deviation = 841,001 / 9 = 93444.6
b.) Standard Deviation (1s) = 93,444.44 = 305.69 units
2. MAD Method
a.) Mean Absolute Deviation (MAD) = 2649 / 10 = 264.9
b.) Standard Deviation (1s) = 264.9 x 1.25 = 331.13 units
8-29
dp&c Chapter8
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) = 305.69
Unit cost = US$235.00
Solution:
1. Demand during lead time = 1,000 x 2 weeks = 2,000 units
2. Safety stock (SS) = CSL x (s) = NORMSINV (.98) x 305.69 =
627.81 units
3. ROP = 2,000 units + 627.81 units = 2,627.81 units
4. SS cost = US$235 x 627.81 = US$147,535 (rounded)
8-30
dp&c Chapter8
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
2,000
2,100
2,200
2,300
2,400
Probability
24%
15%
8%
2%
1%
8-31
dp&c Chapter8
Safety Stock Using Probability (cont.)
Safety
Stock
Solution:
Carrying Cost
+ Stock out Cost =
Total
Cost
1. Calculate safety (100
stock
* .15 * carrying
US$100 * 26) +cost by multiplying the
(200 *the
.08 * US$100
* 26)stock
+
carrying
cost times
safety
2,000
0
US$106,600
(300 * .02 * US$100 * 26) +
2. Calculate stock out cost: the sum of the units stocked out x
(400 * .01 * US$100 * 26) = US$106,600
the probability x the unit cost x the number of orders per year
2,100
2,200
2,300
2,400
100 * US$30 =
US$3,000
(100 * .08 * US$100 * 26) +
(200 * .02 * US$100 * 26) +
(300 * .01 * US$100 * 26) = US$39,000
200 * US$30 =
(100 * .02 * US$100 * 26) +
US$6,000
(200 * .01 * US$100 * 26) = US$10,400
300 * US$30 =
US$9,000
400 * US$30 =
US$12,000
US$42,000
US$16,400
(100 * .01 * US$100 * 26) = US$2,600
US$11,600
0
US$12,000
8-32
dp&c Chapter8
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:
8-33
dp&c Chapter8
Supply Uncertainty and Safety Stock (cont.)
Solution:
1. Solve for standard deviation of demand during the lead time:
sL =
= 1,275.74
2. Solve for safety stock (SS):
SS = sL x CSL = 1275.74 x 1.65 = 2,105 (rounded)
3. New order point calculation:
250 (D) x 9 (LT) + 2,105 (SS) = 4,355 units
8-34
dp&c Chapter8
Min/Max Order System
Definition:
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)
8-35
dp&c Chapter8
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:
Max = (D x LT) + (CSL x s x 𝐿𝑇) = (50 x 4) + (2.05 x 20 x 4) =
200 + 82 = 282
8-36
dp&c Chapter8
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:
1. Used when it is difficult to record withdrawals and
additions of stock on a continuous basis
2. Used when items are ordered in families
3. Used for items with a limited shelf life
4. Significant economies can be gained by ordering in bulk
8-37
dp&c Chapter8
Periodic Review System Technique
Review Cycle
1
Target
Inventory
A
2
3
Order
Quantity
Demand
Review
Point
Quantity
Replenishment
Receipt
Lead
Time
Safety Stock
8-38
dp&c Chapter8
Periodic Review Calculation
Equations:
a. Order review cycle = dividing an item’s units sold annually
by the standard lot quantity
b. Target inventory level (TI) =
TI = (D(L + T)) + (SSsD L T )
where
D = the demand rate
L = item lead time
T = the review period
SS = item safety stock
8-39
dp&c Chapter8
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:
1. Demand during lead time and review cycle: 1,000 x (2 + 4) = 6,000
units
2. Target inventory: 6,000 + (503 x 100 x 2  4) = 6,503 units
3. Reorder quantity: 6,503 – 22,50 = 2,403 units
8-40
dp&c Chapter8
Chapter 8
Statistical Inventory Management
Inventory
Order
Quantity
Management Basics
Techniques
8-41
dp&c Chapter8
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.
cost:
b. Carrying
Carrying
cost:
Order quantity / 2 x carrying cost % x unit cost
(2,000 / 2) units x 24% x US$0.25 = US$60
Order Quantity Order Per Year Carrying Cost
Order Cost
Total Cost
2,000
12
$60
$240
$300
4,000
6
$120
$120
$240
8,000
3
$240
$60
$300
12,000
2
$360
$40
$400
24,000
1
$720
$20
$740
8-42
dp&c Chapter8
EOQ Graph
Costs
800
700
Total Cost
600
500
Optimal Cost
Carrying
Cost
400
300
200
Ordering Cost
100
50
Quantities
2000
4000
8000
8-43
12000
24000
dp&c Chapter8
EOQ Calcualtion
2 x Demand x Cost of ordering
Inventory carrying cost % x Unit cost
Annual demand
Cost of ordering
Unit cost
Carrying cost
=
=
=
=
20,000 units
US$125
US$34
21%
2 x 20,000 x US$125
= 837 units
21% x $34
8-44
dp&c Chapter8
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
8-45
dp&c Chapter8
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):
1. Calculate EOQ = 1,907 (1,906.93)
2. Calculate number of orders per year = 30,000 / 1906.93 = 15.7
3. Calculate material cost = EOQ x orders per year x item unit cost =
1,906.93 x 15.7 x US$15 = US$450,000
4. Calculate ordering cost = order cost x orders per year = US$200 x
15.7 = US$3,146.43
8-46
dp&c Chapter8
Quantity Discounts – Example (cont.)
Steps:
5. Carrying cost = (EOQ / 2) x unit cost x carrying cost = (1906.93 / 2)
x US$15 x 22% = US$3,146.53
6. 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:
1.
2.
3.
4.
Material cost = US$436,500
Ordering cost = US$1,200
Carrying cost = US$8,002.50
Total cost = US$445,702.50
8-47
dp&c Chapter8
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:
1.
2.
3.
4.
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
8-48
dp&c Chapter8
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):
1. Order cost = (Demand / EOQ) x (Order cost + Transportation cost)
2. Carrying cost = (EOQ / 2) x unit cost x carrying cost
3. Total cost = ordering cost + carrying cost
8-49
dp&c Chapter8
Joint Replenishment – Example (cont.)
I. The three items ordered independently
Summary:
Ordered Independently
Product
#3925
#3819
#3442
EOQ
856
661
391
# Orders / year
7.0
5.4
3.2
Carrying Cost
$
3,853.57
$
2,974.58
$
1,758.91
Ordering Cost
$
3,853.57
$
2,974.58
$
1,758.91
Total Cost
$
$
$
$
Total Cost
7,707.14
5,949.16
3,517.81
17,174.11
$
$
$
$
Total Cost
7,708.97
3,678.77
2,217.68
13,605.42
II. The three items ordered jointly
Summary:
Ordered Jointly
Product
#3925
#3819
#3442
# Orders / year
7.16
7.16
7.16
Order Lot Size
837.9
499.2
174.6
Carrying Cost
$
3,770.56
$
2,246.62
$
785.53
8-50
Ordering Cost
$
3,938.41
$
1,432.15
$
1,432.15
Total Cost
dp&c Chapter8
Joint Replenishment – Example (cont.)
III. The three items ordered jointly: selected family items
Steps:
1. Identify the most frequently order item (i)
2. Equation: Order frequency for item #3925
3. Calculate the frequency for items #3819 and #3442
4. Determine the order frequency for each item as a multiple of
the order frequency of the most ordered item (mi).
5. For item #3819, 7.01 / 7.01 = 1.
6. For item #3442, 7.01 / 5.30 = 1.32
7. Recalcuate the order frequency of items
8. For item #3819, 20% x US$45 x 1 x 6,000 = US$54,000.
8-51
dp&c Chapter8
Joint Replenishment – Example (cont.)
III. The three items ordered jointly: selected family items
Steps:
9. Sum the values for step 8
10. US$54,000 + US$32,175 + $22,500 = US$108,675
11. Divide the standard order cost by the order frequency
12. For item #3925, 200/1 = US$200
13. Sum the values for step 11
14. US$200 + US$200 + US$100 + US$350 (TC) = US$500
15. New order frequency for item #3925 =
16. New order frequency for item #3819 = 8 / 1 (original rounded
order frequency fi) = 8 orders.
8-52
dp&c Chapter8
Joint Replenishment – Example (cont.)
III. The three items ordered jointly: selected family items
Steps:
17. New order frequency for item #3442 = 8 / 2 (original rounded
order frequency fi) = 4 orders
18. Calculate order costs by using steps for ordering jointly
Ordered Selectively
Product
#3925
#3819
#3442
Product
#3925
#3819
#3442
Order Frequency
7.01
8.97
5.30
#Orders / year
8.00
8.00
4.00
Freq to most
ordered (f )
Round Order
Frequency (fi )
$
54,000.00
$
32,175.00
$
22,500.00
SUM $
108,675.00
SUM
TC+ S R/f i
Order Lot Size
Carrying Cost
Ordering Cost
750.4
$
3,376.94 $
4,397.47
447.1
$
2,012.09 $
1,599.08
312.7
$
1,407.06 $
799.54
SUM $
6,796.09
Total Cost
1.00
0.78
1.32
1.00
1.00
2.00
Cost (kUCf i D i )
8-53
Order Cost / f i
$
$
$
$
$
$
$
$
$
200
200
100
500
850
Total Cost
7,774.41
3,611.17
2,206.60
13,592.19
dp&c Chapter8
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
#3925 1,507.56
Orders/
Year
Carrying cost
Ordering cost
Total cost
17
$1,658.31
$1,658.31
$3,316.62
8-54
dp&c Chapter8
Transportation EOQ (cont.)
Step 2: Current EOQ freight cost:
1. Rate for EOQ of 1,507.56 = (Rate x order quantity) x number of
orders per year = US$1.25 x 1,507.56 x 17 = $31,250
2. Freight added EOQ =
Ord qty
Orders/
Year
Carrying
cost
Ordering cost
Shipment
cost
Total cost
1,507.56
17
$1,658.31
$1,658.31
$31,250
$34,566.62
Step 3: Large shipment rate requires OQ = 5,000 units
Ord
qty
5,000
Orders/ Carrying
Year
cost
5
$5,500
Ordering
cost
Shipment cost
Total cost
$500
$18,750
$24,750
8-55
dp&c Chapter8
Replenishment by Item Class – Steps
1. Divide the inventory into classes based on volume usage,
dollar value, or other parameters.
2. Link items to classes.
3. Assign an inventory turnover target for each class.
4. Determine the level below which only dead and obsolete
products reside. Eliminate this class from the procedure.
5. Establish the replenishment quantity for each class by
dividing the annual usage of each item by the turnover
value.
6. Recalculate the inventory classification scheme for all
items at least once a month, depending on the expected
inventory turnover.
8-56
dp&c Chapter8
Replenishment by Item Class – Calculation
Objective: Replenishment using order class
Data:
ABC Class
A
B
C
D
E
# of Total Items
1,200
10,500
25,250
8,000
6,500
Expected Turns
24
12
6
3
1
Order Interval
15 days
1 month
2 months
4 months
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
8-57
dp&c Chapter8
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
8-58
dp&c Chapter8
Investment Order Limit – Calculation (cont.)
Step1: Calculate base EOQ for each item
EOQ
Product
#3925
#3819
#3442
# Orders / year
16.73
9.75
10.25
EOQ
836.66
974.68
683.13
Carrying Cost
$
1,673.32
$
974.68
$
1,024.70
Ordering Cost
$
1,673.32
$
974.68
$
1,024.70
Total Cost
$ 3,346.64
$ 1,949.36
$ 2,049.39
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 $18,363.47 exceeds the
US$16,000 level, the original EOQs will need to be reduced by
inflating (k) and determining an adjustment factor (a)
8-59
dp&c Chapter8
Investment Order Limit – Calculation (cont.)
Step3: Adjust original EOQ quantities
Since inventory investment of $18,363.47 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
8-60
dp&c Chapter8
Investment Order Limit – Calculation (cont.)
Step 5: Combine new EOQ values and validate that they
match the investment limit
Min Investment EOQ
Product
#3925
#3819
#3442
# Orders / year
19.20
11.19
11.76
New EOQ
728.98
849.23
595.21
Carrying Cost
$
1,457.96
$
849.23
$
892.81
Ordering Cost
$
1,920.50
$
1,118.66
$
1,176.06
Totals
8-61
Total Cost
$ 3,378.45
$ 1,967.89
$ 2,068.87
$ 7,415.21
Investment Cost
$
7,289.78
$
4,246.17
$
4,464.06
$
16,000.00
dp&c Chapter8
Chapter 8
Statistical Inventory Management
Inventory
Lean
Inventory
Management Basics
Management
8-62
dp&c Chapter8
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
8-63
dp&c Chapter8
Lean Philosophy
Operations
Excellence
Dedication to continuous product and
process improvement focused on total
customer service
Value-Added
Processes
Eliminate all business functions and
activities that do not add value to the
company or the customer
Continuous
Improvement
All aspects of business processes must be
dedicated to incremental improvement in
ways great and small
Lean/TQM
Combination of lean techniques focused on
productivity, total quality management
(TQM), and people empowerment
8-64
dp&c Chapter8
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
8-65
dp&c Chapter8
Inventory Flow Analogy
Clogged Inventory Channel
Poor
Controls
Inventory
Inventory
Inventory
Lack of
Training
Unclear
Responsibilities
Lack of
Disciplines
Open Inventory Channel
Inventory
8-66
dp&c Chapter8
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
8-67
dp&c Chapter8
The Pull System – Basic Concepts
C
B
Operator #1
receives
requirement and
makes more
inventory
Demand pull
signal triggered
and requirement
sent to feeding
workstation
Buffer
Inventory
Process 1
Operator #1
Operator #2
removes
material from
buffer inventory
to start work
Process 2
Operator #2
Workstation #1
D
A
Workstation #2
Replenishment
quantity moved to
Workstation #2
buffer inventory
8-68
dp&c Chapter8
Three Types of Kanban
Production
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
8-69
dp&c Chapter8
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:
𝐷 𝑇𝑑 + 𝑇𝑝 (1 + 𝑆𝑆)
# 𝑘𝑎𝑛𝑏𝑎𝑛 =
𝑄𝑅
Solution:
((300 x (2 + 2)) x (1 + .50) / (1 x 50) = 36 kanbans
8-70
dp&c Chapter8
“Education in Pursuit of
Supply Chain Leadership”
dp&c Chapter8
Chapter 8
End of Session
8-71
dp&c Chapter8