Vietnam
Japan
Mexico
Ohio
Poduction Yield
90%
100%
90%
95%
Salvage Revenue
$2.40
$2.40
$2.40
$2.40
$32.00
$32.00
$32.00
$32.00
3000
3000
3000
3000
37.5%
30.0%
22.5%
12.5%
Lead Time (Weeks)
40
35
25
15
Gross Product Cost
$12.00
$14.00
$14.00
$17.00
Net Product Cost
$13.33
$14.00
$15.56
$17.89
Sales Revenue
Demand Forecast
Forecast CV
AD680 Global Supply Chains
Problem Set #3: Optimization
You have been hired by a vendor who is preparing for an upcoming K-Pop (Korean pop music) concert
featuring the singer IU (Lee Ji-eun) in Cincinnati. The concert organizer is allowing vendors to sell IU
paraphernalia. You determine that certain one-size-fits-all winter hats featuring IU’s image will be sold.
You have four choices for OEM suppliers of the hats. Due to their locations, their lead times differ, along
with your costs. Based on past concerts, the product sales forecast is for 3000 hats, but this estimate is
uncertain depending on the concert attendance. Each hat will sell for $32. Once the concert ends, products
not sold will be bought by a discounter at a heavily reduced price of $2.40 per hat. Sales forecasts will be
more accurate as the concert approaches (forecast CV’s are available based on past forecasting
performance). Production quality varies according to location, which is expressed as an expected
production yield. Production costs are adjusted to account for these yields(and shown below as net
product cost). Because the products all require careful handling, there will be an inventory holding cost
that will apply as soon as the order is placed. However, the annual holding percentage is unknown at this
time. The table below summarizes the important information regarding the locations under consideration.
Vietnam
Japan
Mexico
Ohio
Poduction Yield
90%
100%
90%
95%
Salvage Revenue
$2.40
$2.40
$2.40
$2.40
$32.00
$32.00
$32.00
$32.00
3000
3000
3000
3000
37.5%
30.0%
22.5%
12.5%
Lead Time (Weeks)
40
35
25
15
Gross Product Cost
$12.00
$14.00
$14.00
$17.00
Net Product Cost
$13.33
$14.00
$15.56
$17.89
Sales Revenue
Demand Forecast
Forecast CV
Create a spreadsheet that determines, for each manufacturing location, the expected profits and how many
units the vendor should order from each manufacturer. Assume that demand variation is normally
distributed. Vary the annual holding cost percentage and show how the expected profits and order
quantities for a range of holding rates from 10% to 40%. Show these results in tabular and graphical form.
Clearly organize and label the spreadsheet to show inputs and results (i.e., a user may wish to modify
inputs later as more information becomes available). The assessment of this work will be based on the
accuracy and clarity of your spreadsheet.
Attach one Excel file, using a file name Lastname_PS3.
Boston University
Metropolitan College
AD680: Global Supply Chains
Live Session
Module 5/Week 5
David L. Rainey, Ph.D.
Spring 2020
Module 5 Agenda
● Discussion Board Review
● Preview of Lecture 9 (Supply Chain Optimization)
● Review Problem Set 2
● Preview of Lecture 10 (Business Function Integration)
● Preview of Assignments/Assessments
● Questions and Answers
2
Module 5: Highlights
Topics & Readings:
Lecture 9: Supply Chain Optimization
• Importance of Assumptions to Ensure Model Accuracy
• News-Vendor Model with Holding Costs
• Simulation Modeling in Supply Chains
• Integration of Optimization Models and Decision Making
Lecture 10: Business Function Integration
• Concept of Linked Activities
• Incentive System Integration
• Supply Chain Management Software
• Comprehensive Examples
Module 3 Study Guide
February 4 - 10
Discussion:
Group Discussion #5: Rapid-Fire Fulfillment (Article).
Postings end Monday, February 24 at 11:59 PM ET
Assignment:
Problem Set #3: Using an optimization model to choose supplier
and determine order quantity.
Due Monday, February 24, at 11:59 PM ET
Assessment:
Quiz #5: Available from 9:00 AM ET Saturday, February 22, through
11:59 PM ET Monday, February 24
3
Boston University
Metropolitan College
AD680: Global Supply Chains
Lecture 9
Supply Chain Optimization
David L. Rainey, Ph.D.
Spring 2020
Lecture 9 Agenda
● Preview of Lecture 9 Supply Chain Optimization
● Review of Problem Set 3
● Questions and Answers
5
Lecture 9 Agenda
Lecture 9: Learning Outcomes
As a result of completing this lecture, students will be able to:
1. Communicate the various types of models used in the analysis
of supply chains.
2. Calculate optimal order quantities for newsvendor problems
with or without the inclusion of holding costs.
3. Calculate expected profits under optimal conditions with or
without the inclusion of holding costs in newsvendor models.
4. Compare alterative profit expectations for various lead time.
5. Choose between optimization models and simulation models in
supply chain analyses.
6. Describe simulation models in terms of their inputs and outputs
(See video on Blackboard).
7. Develop a basic Monte Carlo simulation using Excel
(Blackboard).
6
Overview
This lecture concerns two important uses of models in a supply
chain related to optimization.
The first use of a supply chain model will be for mathematical
optimization. That is, the model will be used to find the best
solution under an assumed set of conditions.
“Optimization models" are more complex. The calculations can be
done manually, but Excel is a great tool.
The second use of a supply chain model will be for exploring how
the supply chain system will respond to various decisions, which
can indirectly lead to optimizing of performance.
7
Applications
Just about everyone uses a model (albeit often a simple
heuristic model) to support decision making
– for example, you may want to estimate the cost of a car trip
(e.g., 500 miles) by dividing the number of miles by an
assumed miles per gallon (mpg) of gasoline (e.g., 25 mpg) and
then multiplying the result by the expected price per gallon of
gasoline (e.g., $2.00/gallon).
– Cost =(500 miles ÷25mpg) x $2.00 = $40
8
Limitations
● Although models can be useful, they have certain limitations
that must be understood prior to their use.
– for the car cost model, what happens if snow causes you to
drive a lot slower and the car’s mpg is lower than assumed?
● Every model has an underlying set of “assumptions” that are
required to create a manageable model.
– buffering models often assume that the demand distribution is
normal
– EOQ assumes that holding costs and ordering costs are the
primary cost considerations
● Models that include uncertainty are called “stochastic”
models while those that do not include uncertainty are called
9
“deterministic models.”
Deterministic & Stochastic Models
● Deterministic models (e.g., linear programming, EOQ) tend
to provide solutions to problems that may be complex but
do not consider uncertainties.
– running the model with “what if” scenarios allows for limited
analysis of uncertainty. (example, what if the rate changes?)
● Stochastic models (e.g., inventory safety stock (ss) or
capacity buffering) tend to provide solutions to problems
that consider uncertainty but tend to be very simple.
– in supply chains, stochastic models tend to be focused
specifically on one stage of supply, usually for one product,
without capacity or other constraints.
10
Newsvendor Model
● The “newsvendor model” is a stochastic model that is used
to determine the optimal inventory level when there is a
single order placed just prior to a selling period, and no
other orders may be placed to satisfy demand.
– originally referred to as the “newsboy” model, the assumed
scenario would represent the daily decision making of a
person selling newspapers.
● Other applications include:
– perishable food items on a cruise ship, clothing or other
items associated with a special event, seasonal items that
cannot be stored for next season, …..
11
Notation
c = production cost or seller’s purchase price per unit
p = retail price or seller’s revenue per unit
s = salvage price per unit (applies to all overstocked units)
Q = Order quantity (Q* is the optimal order quantity)
D = Actual demand
CU = p – c: Understock cost per unit
CO = c – s: Overstock cost per unit
CSL = Cycle Service Level (CSL* is optimal CSL)
12
Example
The Sunday newspaper retails for $2.50/newspaper, costs the
seller $1.00/newspaper, and unsold newspapers can be sold to a
recycler at $0.25/newspaper.
c = $1
p = $2.5
s = $0.25
CO = 1 – 0.25 = 0.75 ($0.75/newspaper)
CU = 2.5 – 1 = 1.50 ($1.50/newspaper)
CO = 0.5 Cu
13
Cost Function
For a given value of demand (D), the cost function is:
For the newsvendor, if 40 newspapers are obtained by the seller
(i.e., Q=40):
Cost = (0.75) max(0,40 − D) + (1.50) max(0, D − 40)
14
For the newsvendor, if 40 newspaper are bought and actual
demand is 65 newspapers, the cost to the seller is $37.50:
Cost = (0.75) max(0,40 − 65) + (1.50) max(0,65 − 40)
Cost = (0.75)(0) + (1.50)(25) = 37.5
if 40 newspaper are obtained by the seller and actual demand is 15
newspapers, the cost to the seller is $18.75:
Cost = (0.75) max(0,40 − 15) + (1.50) max(0,15 − 40)
Cost = (0.75)(25) + (1.50)(0) = 18.75
15
Example
● Consider a single season scenario (with newsvendor assumptions)
where the following costs are incurred, and the demand forecast is
1000 units with a CV of 40%:
c = $45, p = $60, s = $35, CO = $10; CU = $15
● Note, if the seller orders 1000 units (i.e., the forecast), we have:
– If actual demand is 200 less than forecast (D = 800), the resulting
cost is $2000
Cost = ($10) max (0,1000-800) + ($15) max (0,800-1000) = $2000
– If actual demand is 200 more than forecast (D = 1200), the
resulting cost is $3000
Cost = ($10) max (0,1000-1200) + ($15) max (0,1200-1000) = $3000
16
Optimal Cycle Service Level
By balancing expected overstock and understock costs, the optimal
service cycle level is obtained:
Cu
CSL* =
Cu + C o
c = production cost or seller’s purchase price per unit
p = retail price or seller’s revenue per unit
s = salvage price per unit (applies to all overstocked
Q = Order quantity (Q* is the optimal order quantity)
D = Actual demand
CU = p – c: Understock cost per unit
CO = c – s: Overstock cost per unit
CSL = Cycle Service Level (CSL* is optimal CSL)
Note that:
When Co = Cu, CSL* = 0.5 (order same as forecast)
When Co > Cu, CSL* < 0.5 (order less than forecast)
When Co < Cu, CSL* > 0.5 (order more than forecast)
17
Optimal Order Quantity (Normal)
Q* = NORMINV(CSL*,m,s)
m = the forecast (i.e., mean)
s = the forecast standard deviation
CSL*
Q*
18
A daily newspaper retails for $2.50/newspaper, costs the seller
$1.00/newspaper, and unsold newspapers can be sold to a
recycler at $0.25/newspaper. As previously described, we have:
c = 1, p = 2.5, s = 0.25, CO =c-s= 0.75, CU = p-c =1.50
If the demand is forecasted to be normally distributed with a
mean of 50 units and a standard deviation of 10, the optimal
order quantity will be 54 newspapers:
Cu
1.5
CSL* =
=
= 0.667
Cu + Co 1.5 + 0.75
Q* = NORMINV(0.667,50,10) = 50 + (10 x 0.44) = 54
NORMINV- Also use Excel: Formulas; More Functions, Statistical.
19
Z=norminv(CSL,0,1)
CSL
Z
CSL
Z
CSL
Z
CSL
Z
CSL
Z
50%
0.000
60%
0.253
70%
0.524
80%
0.842
90%
1.282
51%
0.025
61%
0.279
71%
0.553
81%
0.878
91%
1.341
52%
0.050
62%
0.305
72%
0.583
82%
0.915
92%
1.405
53%
0.075
63%
0.332
73%
0.613
83%
0.954
93%
1.476
54%
0.100
64%
0.358
74%
0.643
84%
0.994
94%
1.555
55%
0.126
65%
0.385
75%
0.674
85%
1.036
95%
1.645
56%
0.151
66%
0.412
76%
0.706
86%
1.080
96%
1.751
57%
0.176
67%
0.440
77%
0.739
87%
1.126
97%
1.881
58%
0.202
68%
0.468
78%
0.772
88%
1.175
98%
2.054
59%
0.228
69%
0.496
79%
0.806
89%
1.227
99%
2.326
20
Q* = NORMINV(0.667,50,10) = 54
Q* = 50+z x std dev= 50+0.44 x 10 = 50 + 4.4 = 54
50 54
21
Consider a single season scenario (with newsvendor assumptions)
where the following costs are incurred, and the demand forecast is
1000 units with a CV of 40%:
c = $45, p = $60, s = $35, CO = c-s = $10; CU = p-c = $15
The optimal order quantity will be 1101 products:
Cu
15
CSL* =
=
= 0.6
Cu + Co 15 + 10
Q* = NORMINV(0.6,1000,400) = 1101
Q* = 1000+z x std dev= 1000+ (0.253 x 400) = 1000 + 101 = 1101
22
Z=norminv(CSL,0,1)
CSL
Z
CSL
Z
CSL
Z
CSL
Z
CSL
Z
50%
0.000
60%
0.253
70%
0.524
80%
0.842
90%
1.282
51%
0.025
61%
0.279
71%
0.553
81%
0.878
91%
1.341
52%
0.050
62%
0.305
72%
0.583
82%
0.915
92%
1.405
53%
0.075
63%
0.332
73%
0.613
83%
0.954
93%
1.476
54%
0.100
64%
0.358
74%
0.643
84%
0.994
94%
1.555
55%
0.126
65%
0.385
75%
0.674
85%
1.036
95%
1.645
56%
0.151
66%
0.412
76%
0.706
86%
1.080
96%
1.751
57%
0.176
67%
0.440
77%
0.739
87%
1.126
97%
1.881
58%
0.202
68%
0.468
78%
0.772
88%
1.175
98%
2.054
59%
0.228
69%
0.496
79%
0.806
89%
1.227
99%
2.326
23
Expected Profit (Normal Case)
When the order quantity is Q and demand is normally distributed,
the expected profit in the newsvendor case is shown below. Be
careful to distinguish between the order quantity (Q) and the
number zero (0).
Expected Profit =EP=
(p-s)*m*NORMDIST((Q-m)/s,0,1,1)–
(p-s)*s*NORMDIST((Q-m)/s,0,1,0)–
Q*(c-s)*NORMDIST(Q,m,s,1)+
Q*(p-c)*(1-NORMDIST(Q,m,s,1))
NORMDIST - Use Excel: Formulas. More Functions, Statistical
24
Expected Profit (Normal Case)
A daily newspaper retails for $2.50/newspaper, costs the seller
$1.00/newspaper, and unsold newspapers can be sold to a
recycler at $0.25/newspaper. As previously described, we have:
c = 1, p = 2.5, s = 0.25, CO = 0.75, CU = 1.50
If the demand is forecasted to be normally distributed with a
mean of 50 units and a standard deviation of 10, the optimal
order quantity will be 54 newspapers (shown earlier) and the
expected profit is $668.19.
2.25
50
2.25*50*NORMDIST(0.4,0,1,1)–
2.25
10
54
0.75
2.25*10*NORMDIST(0.4,0,1,0)–
54
1.5
54*0.75*NORMDIST(54,50,10,1)+
54*1.5*(1-NORMDIST(54,50,10,1))=668.19
0.6554217
0.3682701
0.6554217
0.3445783
-
737.3
82.9
265.4
279.1
668.2
25
Consider a single season scenario (with newsvendor assumptions)
where the following costs are incurred, and the demand forecast is
1000 units with a CV of 40%:
c = $45, p = $60, s = $35, CO = $10; CU = $15
With an optimal order quantity of 1101 units (shown earlier) the
expected profit would be $11,137:
25
25
1101
1101
1000
400
10
15
25*1000*NORMDIST(0.2525,0,1,1)–
25*400*NORMDIST(0.2525,0,1,0)–
1101*10*NORMDIST(1101,1000,400,1)+
1101*15*(1-NORMDIST(1101,1000,400,1))=11136.57
0.5996727
0.3864253
0.5996727
1-0.5996727
14991.82
- 3864.25
- 6602.40
6611.40
11136.57
Expected Profit =EP=
(p-s)*m*NORMDIST((Q-m)/s,0,1,1)–
(p-s)*s*NORMDIST((Q-m)/s,0,1,0)–
Q*(c-s)*NORMDIST(Q,m,s,1)+
Q*(p-c)*(1-NORMDIST(Q,m,s,1))
26
Modified Newsvendor Model
● An inventory model can be modified to represent certain
conditions, for example:
– quantity discounts
– continuously stocked items
– backorders
● The addition of holding costs is easy to accomplish,
representing a scenario where there is one order placed well
ahead of the selling season; this would cause additional costs
that are not accounted for the traditional newsvendor model:
– security, warehousing, taxes, storage, etc.
27
Modified Newsvendor Model
Note that a new cost is added:
CH = Unit cost for holding product ordered (must be
consistent with length of the time period prior to
demand realization).
The optimal CSL is:
Cu − C H
CSL* =
Cu + Co
The optimal order quantity is determined in the same way (as the
classical model) and expected profit is modified by adding the
product of CH and the order quantity.
28
Modified Newsvendor Model
Consider a product with a cost of $25 that incurs an annual
holding rate of 20%. For an analysis of production 6 months
ahead of the selling season, the value of CH be $2.50:
C H = (0.2)(25)(0.5) = 2.5
20% annual
holding cost
percentage
Product cost
per unit
Portion of
year products
are held
29
Consider a single season scenario (with newsvendor assumptions
plus holding costs) where the demand forecast is 1000 units with
a CV of 40%, the product has an annual holding rate of 20%, the
order must be placed 3 months in advance of sales, and the
following costs are incurred:
c = $45, p = $60, s = $35, CO = $10; CU = $15
Note that the holding cost (CH is $2.25/unit).
C H = (0.2)(45)(0.25) = 2.25
The optimal order quantity will be 1010 products:
Cu − C H 15 − 2.25
CSL* =
=
= 0.51
Cu + Co
15 + 10
O* = NORMINV(0.51,1000,400) = 1010
See Excel – Formulas; More Functions, Statistical.
30
Z=norminv(CSL,0,1)
CSL
Z
CSL
Z
CSL
Z
CSL
Z
CSL
Z
50%
0.000
60%
0.253
70%
0.524
80%
0.842
90%
1.282
51%
0.025
61%
0.279
71%
0.553
81%
0.878
91%
1.341
52%
0.050
62%
0.305
72%
0.583
82%
0.915
92%
1.405
53%
0.075
63%
0.332
73%
0.613
83%
0.954
93%
1.476
54%
0.100
64%
0.358
74%
0.643
84%
0.994
94%
1.555
55%
0.126
65%
0.385
75%
0.674
85%
1.036
95%
1.645
56%
0.151
66%
0.412
76%
0.706
86%
1.080
96%
1.751
57%
0.176
67%
0.440
77%
0.739
87%
1.126
97%
1.881
58%
0.202
68%
0.468
78%
0.772
88%
1.175
98%
2.054
59%
0.228
69%
0.496
79%
0.806
89%
1.227
99%
2.326
31
Optimal CSL w/Holding Cost
With the addition of holding costs, the expected profit when
ordering O units is:
The expected profit with holding costs (normally distributed demand) is:
E(P)=
(p−s) × μ × NORMDIST(Q−μ/σ,0,1,1)
−(p−s) × σ × NORMDIST(Q−μ/σ,0,1,0)
−Q × (c−s) × NORMDIST(Q,μ,σ,1)
+Q × (p−c) × (1−NORMDIST(Q,μ,σ,1))
−CH x Q
32
Optimal CSL w/Holding Cost
Note that, as expected, the optimal order quantity decreases with
the inclusion of holding costs.
With an optimal order quantity of 1010 units, the expected profit
with holding cost would be $8,762 (a reduction from $11,137
without holding costs):
25*1000*NORMDIST(0.025,0,1,1)–
25*400*NORMDIST(0.025,0,1,0)–
1010*10*NORMDIST(1010,1000,400,1)+
1010*15*(1-NORMDIST(1010,1000,400,1)) –
2.25*1010=8761.83
33
Simulation Modeling
● When problems become too complex for a stochastic
model, a “simulation” model can be employed.
– simulation models are also useful when an analyst does not
know the existence of a more sophisticated model.
● Simulation models mimic the problem under study;
monte carlo simulation is a simulation that uses random
numbers to mimic uncertainty.
– the key to this development is the ability to generate
random numbers that are consistent with an assumed
statistical distribution, and to “run” the simulation a large
number of “iterations.”
(See video on Blackboard)
34
Problem Set 3 Assignment
Optimization
You have been hired by a vendor who is preparing for an upcoming
K-Pop (Korean pop music) concert featuring the singer IU (Lee Ji-eun)
in Cincinnati. The concert organizer is allowing vendors to sell IU
paraphernalia. You determine that certain one-size-fits-all winter
hats featuring IU’s image will be sold. You have four choices for OEM
suppliers of the hats. Due to their locations, their lead times differ,
along with your costs. Based on past concerts, the product sales
forecast is for 3000 hats, but this estimate is uncertain depending on
the concert attendance. Each hat will sell for $32. Once the concert
ends, products not sold will be bought by a discounter at a heavily
reduced price of $2.40 per hat. Sales forecasts will be more accurate
as the concert approaches(forecast CV’s are available based on past
forecasting performance). Production quality varies according to
location, which is expressed as an expected production yield.
35
Problem Set 3 Assignment
Optimization
Production quality varies according to location, which is expressed as
an expected production yield. Production costs are adjusted to
account for these yields (and shown below as net product cost).
Because the products all require careful handling, there will be an
inventory holding cost that will apply as soon as the order is placed.
However, the annual holding percentage is unknown at this time.
The table below summarizes the important information regarding the
locations under consideration.
36
Problem Set 3 Assignment
Optimization
Vietnam
Japan
Mexico
Ohio
Production Yield
90%
100%
90%
95%
Salvage Revenue
$2.40
$2.40
$2.40
$2.40
$32.00
$32.00
$32.00
$32.00
3000
3000
3000
3000
37.5%
30.0%
22.5%
12.5%
Lead Time (Weeks)
40
35
25
15
Gross Product Cost
$12.00
$14.00
$14.00
$17.00
Net Product Cost
$13.33
$14.00
$15.56
$17.89
Sales Revenue
Demand Forecast
Forecast CV
37
Problem Set 3 Assignment
Optimization
Create a spreadsheet that determines, for each manufacturing
location, the expected profits and how many units the vendor should
order from each manufacturer. Assume that demand variation is
normally distributed. Vary the annual holding cost percentage and
show how the expected profits and order quantities for a range of
holding rates from 10% to 40%. Show these results in tabular and
graphical form. Clearly organize and label the spreadsheet to show
inputs and results (i.e., a user may wish to modify inputs later as
more information becomes available). The assessment of this work
will be based on the accuracy and clarity of your spreadsheet. Attach
one Excel file, using a file name Lastname_PS3.
38
Boston University
Metropolitan College
AD680: Global Supply Chains
Lecture 10
Business Function Integration
David L. Rainey, Ph.D.
Spring 2020
Lecture 10 Agenda
● Preview of Lecture 9 Business Function Integration
● Preview of Article #3
● Questions and Answers
40
Lecture 10 Agenda
Lecture 10: Learning Outcomes
As a result of completing this lecture, students will be able to:
• Appreciate the impact that linked activities have on business
effectiveness.
• Project the impact that activates in any business process has on
supply chain effectiveness.
• Design incentive systems that promote better performance of
the whole, with little chance of gaming.
• Choose a supply chain management (SCM) software system
that meets the needs of the global supply chain.
• Provide specific examples of effective business process
integration and why this integration is critical.
• Develop and deploy business function integration across the
41
supply chains.
Overview
Business Integration
Integration in a global supply chain necessitates that every business
activity within the firm is aligned with the strategic focus of the
firm’s supply chain.
“Linked" activities would take place in operations-related functions.
A full integrated supply chain would also integrate all administrative,
support, and other business functions.
Full integration also requires that all internal systems and processes
are aligned and consistent with the supply chain focus.
42
Overview
Connectedness
The global economy is a complex structure that engenders both
opportunities and challenges. It is the linking of economies,
markets, and customers through the expansion of trade and the
liberalization of market restrictions.
Global supply chains and the management thereof require
innovative strategies for managing the complex array of forces
that impinge on supply chain management (SCM) decisionmaking.
Markets and customers expect customized, sophisticated, high
quality products and services with exceptional value.
Markets and stakeholder expectations often cross industry lines43
Business Function Integration
Connectedness
Many factors can complicate successful business process
integration in supply chains.
First, many corporate leaders can lack enough understanding
of the complex supply chain system (like in the Honda case).
Thus, they may consider the supply chain to be a selfcontained function that operates independently of the firm’s
other business functions.
Second, there are facets of supply chain performance that
are directly affected by decisions made in seemingly
unrelated business functions.
44
Business Function Integration
Connectedness
Function
Executive
Other Names or Purposes
Leadership, Management
Operations Production, Manufacturing
Planning
IT
Finance
Scheduling, Forecasting
Information Services, Computing
Accounting, Investing, Payroll, Accounts
Procurement Purchasing, Supplier Management
Sales
Customer Relationship Management
Marketing
Demand Management, Promotions
Quality
Logistics
Design
HR
Legal
Performance, Accreditation, Certification
Warehousing, Transportation
Engineering, Innovation Management
Personnel, Talent Management
Law, Contract Management
45
Incentive System Integration
One of the main features of a fully integrated supply chain is
the alignment of incentives.
Challenges exist, however, due to the diversity of supply
chain members. Often, "hidden" information and actions
exist that some members choose not to disclose for
proprietary or competitive reasons.
Poorly designed incentive systems are those that are geared
towards "local" optimization, those that are shortsighted,
and those that promote "gaming."
Ideally, by using effective metrics, a strong sense of
cooperation (rather than competition) will permeate the
supply chain.
46
Incentive System Examples
Types of Incentives
Merit pay impacted by quantity of
cost savings in Six Sigma projects.
Salesforce incentive system that
pays percentage of revenue.
“Piecework” pay for each unit
made by production workers.
Bonus to service employee based
on satisfaction survey results.
Although some
practitioners tend to
like and others dislike
individualized
incentives, both would
agree that if used,
they should align with
system goals and be
resistant to “gaming.”
47
Better Alignment
Incentive
Merit pay impacted by quantity of
cost savings in Six Sigma projects.
Salesforce incentive system that
pays percentage of revenue.
“Piecework” pay for each unit
made by production workers.
Bonus to service employee based
on satisfaction survey results.
When projects deal
with easily
quantifiable problems.
For innovative
products in a
responsive system.
When quality goals are
is easy to meet and
inventory is buffered.
When sample sizes are
large & server has sole
control over service.
48
Worse Alignment
Incentive
Merit pay impacted by quantity of
cost savings in Six Sigma projects.
Salesforce incentive system that
pays percentage of revenue.
“Piecework” pay for each unit
made by production workers.
Bonus to service employee based
on satisfaction survey results.
When project effects
are difficult to quantify
precisely.
For products whose
production is based on
level loading.
When it is important
for operators to pay
attention to quality.
When sample sizes are
small or server is a just
a “cog in the wheel.”
49
SCM Integration
Linking Business Functions
As the number of entities (especially in supply chains) increases,
integration becomes even more critical. For example,
fragmented linkages often characterized the traditional supply
chains. Each entity in a given process may have fulfilled its
responsibilities without much input or considerations from the
other participants in the system.
Networking with suppliers, distributors, partners, allies,
customers, and stakeholders requires sharing information,
knowledge, and experiences about products, materials, parts,
components and waste streams, and the requisite interfaces
between the entities. The intent of business function integration,
with respect to external entities, is to facilitate cooperation,
collaboration, and communications among entities.
SCM Integration
Connecting with Supply Networks
Connecting with suppliers allows the producers and service
providers to acquire a more complete understanding the flows
of goods, services and information that go into the products
and the implications and impacts of choices and decisions.
Despite the sophistication of modern SCM, most global
corporations have only limited information about the
processes and activities of their suppliers, especially of
suppliers of suppliers and beyond.
While it is seemingly impossible to keep track of all external
entities, the whole business enterprise can function more
effectively if it is properly linked and there is a common ground
of understanding among the entities and participants.
SCM Integration
Connecting with Supply Networks
Steps
Identifying and
Defining
Identifying
reality and
determining the
driving forces in
the business
environment.
Elements
-Identifying the driving forces in the business environment.
-Identifying the regulatory mandates that pertain to suppliers and the business
enterprise.
-Defining environment, health and safety concerns
-Determining key stakeholders involved in the flow of goods and information
-Determining their objectives, needs, and expectations.
-Identifying the information requirements.
-Identifying trade associations and industry groups that can provide
information and support.
-Obtaining related research from academic communities.
Analyzing
-Assessing the key issues, concerns and mandates.
Assessing driving -Benchmarking important peers and competitors.
forces and
-Determining the needs and requirements related to supply chain aspects.
supply chain
-Assessing the main strategic suppliers and distributors.
capabilities,
-Determining supply chain uncertainties, risks, vulnerabilities and potential
resources and
disruptions.
performance
-Developing alternative sources of supply, especially considering potential
disruptions.
SCM Integration
Connecting with Supply Networks
Steps
Elements
Goal Setting
Defining the
short-term and
long-term goals,
including the
actions required
for improving
the processes.
-Determining and prioritizing the opportunities for improvements.
-Reviewing media reports and the literature to determine the most critical
needs & expectations.
-Listing specific targets for improvements.
-Identifying the most relevant social, economic and environmental objectives.
-Identifying ways for improving compliance and eliminating the need for it.
-Defining targets for reducing uncertainties and risks.
-Setting the goals and objectives.
-Developing appropriate metrics.
-Establishing protocols and information sharing systems to link the
participants.
-Linking supply chains to the business enterprise.
-Creating short-term success outcomes to build momentum.
-Educating supply chains.
-Changing attitudes about the expectations.
-Building a spirit of cooperation, collaboration, and commitment across the
enterprise.
-Preparing actions plans and long-term initiatives
Articulating
Action Plans
Establishing the
initiatives to
improve
outcomes,
reduce impacts,
and obtain
success.
SCM Integration
Connecting with Supply Networks
Steps
Implementing and
Sustaining
Implementing initiatives
and programs to achieve
balanced solutions;
building awareness,
acceptance and
confidence in the
making improvements
and ongoing progress.
Elements
-Changing mindsets about the value proposition.
-Establishing new criteria for materials, parts, components, and goods
including requirements for minimizing resources utilization,
degradation, disruptions, and impacts and improving end-of-life
considerations by facilitating recycling.
-Communicating the program to suppliers, distributors, customers,
stakeholders and communities.
-Auditing progress over time and taking corrective actions.
-Evaluating ongoing results and making improvements
-Reporting on the progress and ongoing challenges.
-Celebrating and rewarding outstanding achievements.
-Continuing the process.
SCM Integration
Connecting with Supply Networks
Suggested Goal Setting Items
Types of Business Function
Integration
Determining a Model for Business Function Integration
The multidimensional perspectives involve sophisticated
management systems, proactive strategies, cutting-edge product
development, and innovative methods that are developed and
deployed to enhance the positive aspects and eliminate the negative
aspects of the social, political, economic, technological,
environmental, and ethical forces.
Business function integration requires advanced information and
communications technologies; cost-effective means and mechanisms
for designing, producing and transporting goods; sophisticated
business models; and new-to-the-world solutions. It is based on the
realization that success depends on all the entities and participants
engaged in the business transactions.
Reflections
Successful and sustainable global supply chain integration requires
leaders and professionals who are knowledgeable, confident, and
technical astute. They take a long-term, holistic perspective while
navigating the day-to-day functions, issues and challenges. They also
have to be decision makers who play a role in strategic planning,
operational development, and leadership.
Although the professionals who are assigned to these positions are
generally skilled in one or more technical competencies, they are
often not prepared to fully appreciate the myriad functional
requirements, issues and navigate the various challenges.
Discussion Article #3
Article: Rapid Fire Fulfillment by Ferdows, Lewis,
and Machuca
For this group discussion, read the article listed above and that
illustrates the integration of business functions and other decisions
in a responsive supply chain. The article states that, although Zara’s
supply chain practices seem crazy when considered individually,
their overall supply chain system is very effective. That is, as stated
in the article, Zara’s supply chain approach can be said to be “penny
foolish, and pound wise.”
Consider any or all business functions including planning,
production, procurement, quality, logistics, sales, marketing,
finance, HR, accounting, engineering, design, and IT.
58
Processing math: 100%
Module 5
This is a single, concatenated file, suitable for printing or saving as a PDF for offline
viewing. Please note that some animations or images may not work.
Module 5 Study Guide
February 18 - 24
Topics &
Lecture 9: Supply Chain Optimization
Readings:
•
Importance of Assumptions to Ensure Model Accuracy
•
News-Vendor Model with Holding Costs
•
Simulation Modeling in Supply Chains
•
Integration of Optimization Models and Decision Making
Lecture 10: Business Function Integration
Discussions:
•
Concept of Linked Activities
•
Incentive System Integration
•
Supply Chain Management Software
•
Comprehensive Examples
Group Discussion #5: Rapid-Fire Fulfillment (Article).
Postings end Monday, February 24, at 11:59 PM ET
Assignments:
Problem Set #3: Using an optimization model to choose supplier and
determine order quantity.
Due Monday, February 24, at 11:59 PM ET
Assessments:
Quiz #5 - available from 9:00 AM ET Saturday, February 22 through
11:59 PM ET Monday, February 24
Live
Tuesday, February 18, at 7:00 PM ET
Classrooms:
(will be recorded)
Lecture 9: Supply Chain Optimization
Lecture 9: Supply Chain Optimization
Sections:
1. Learning Objectives
2. Traditional Newsvendor Model
3. Modified Newsvendor Model
4. Simulation Modeling
5. References
Learning Objectives
As a result of completing this lecture, students will be able to:
1. Communicate the various types of models used in the analysis of supply chains.
2. Calculate optimal order quantities for newsvendor problems with or without the
inclusion of holding costs.
3. Calculate expected profits under optimal conditions with or without the inclusion
of holding costs in newsvendor models.
4. Compare alterative profit expectations for various lead-time supply chains.
5. Choose between optimization models and simulation models in supply chain
analyses.
6. Describe simulation models in terms of their inputs and outputs.
7. Develop a basic Monte Carlo simulation using Excel.
Background
This course has highlighted the use of analytical approaches to support supply chain
decision making. These approaches have included forecasting, performance metric
analysis, inventory aggregation, and buffer size determination. More complex approaches
have been developed that consider a broader perspective. These approaches require that a
supply chain "model" is specified that represents the operation of a supply chain. The
models include both complex versions of the forecasting and buffering models contained
in this course (e.g., buffering in a multistage inventory system) and models that
"optimize" supply chain operations.
It is important to clarify that the term optimization always applies to a model. This
model should adequately represent the real-world system under study but will not be a
perfectly accurate representation. That is, a model is only as good as the assumptions that
underlie its use. For example, many models covered in this course assume that
uncertainty can accurately be modeled by the normal distribution. Although this is often
a valid assumption in many cases, the normality assumption can also be violated in many
real-world supply chains.
Any user of a model must be cognizant of its underlying assumptions, and must also
ensure that the assumptions are consistent with the real world. This is not to say that
models must always be a perfect representation of reality. By use of "what if" or
"sensitivity analysis," an analyst can explore how the supply chain would function under
a range of assumptions rather than relying on a single assumption that is subject to
uncertainty.
This lecture concerns two important uses of models in a supply chain related to
optimization. The first use of a supply chain model will be for mathematical
optimization. That is, the model will be used to find the best solution under an assumed
set of conditions. We have already done some of this earlier, such as the calculation of
optimize buffer sizes. Here, these "optimization models" will be more complex. The
second use of a supply chain model will be for exploring how the supply chain system
will respond to various decisions, which can indirectly lead to optimizing of
performance. These "simulation models" are usually used for even more complex
scenarios and for those that do not have mathematically optimal results.
Other phrases used in supply chain modeling include deterministic modeling (usually
optimization modeling with uncertainty not accounted for in the model); stochastic
modeling (usually optimization modeling with uncertainty accounted for in the model);
and heuristic modeling (the use of rules of thumb or simplified solutions that have been
shown to work well in some situations).
Traditional Newsvendor Model
The newsvendor model (formerly known as the newsboy model) is a stochastic model
that is used to determine the optional order quantity when there is a single order placed
just prior to a single selling period; no other orders may be placed to satisfy demand
during the period. The phrase is derived from the problem faced by a traditional
newspaper vendor. This vendor sells newspapers that are bought from a publisher and
sold to consumers. The seller must discard unsold newspapers at the end of the day (or
sell them to a recycler). The preferred order quantity needs to strike a balance between
the cost of underestimating demand (lost sales opportunities) and the cost of
overestimating demand (leftover newspapers).
The newsvendor model has many real-world applications. They include sellers of highly
perishable food (e.g., a sushi restaurant, food on a cruise ship); high-fashion clothing (i.e.,
one selling season and an offshore vendor with a long lead time, precluding more than
one order); souvenirs and other targeted products at a special event (e.g., Expo, World’s
Fair, concert tour); or any products sold in short seasons with long production or
procurement lead times.
In addition, minor variations of the newsvendor model’s assumptions can be
incorporated. For example, in this module, we will incorporate an assumption of holding
cost (which applies when the products need to be ordered ahead of time and held in
storage until the selling season commences). It should be noted, however, that each
expanded application brings more complexity and often the necessity of simplifying
certain assumptions.
Table 1 provides notation that will be used in the newsvendor model. For example, if a
daily newspaper retails for $2.50 and costs the seller $1.00 per newspaper and unsold
newspapers are sold to a recycler for $0.25 per newspaper, we
have: c=1, p=2.5, s=0.25, Co=0.75 and Cu=1.5. Note that Cu=p−c is the per unit lost
opportunity to make a profit and Co=c−s is the difference between the procurement cost
and the salvage value.
Table 1: Newsvendor Model Notation
Notation
c
Description
Procurement or production cost (seller’s purchase price per
unit)
p
Retail price or seller’s revenue per unit
s
Salvage price per unit (applies to all overstocks)
Q
Order quantity (Q∗ denotes the optimal value of Q)
D
Actual demand (units)
Cu=p−c
Understock cost per unit
Co=c−s
Overstock cost per unit
CSL
Cycle service level (CSL∗ denotes the optimal value of CSL)
The revenue to the newsvendor is simply the product of the number of newspapers sold
and the selling price. As shown in Equation 1, the quantity sold is either D (the actual
demand) or Q (the amount ordered), depending on whether the order quantity exceeds
the actual demand. For example, if 450 products are ordered and demand is 500, the
revenue will be $1,125 --- the product of the selling price (p=2.5) and the order
quantity (Q=450). If, on the other hand, 450 products are ordered and demand is 400, the
revenue will be $1000 --- the product of the selling price (p=2.5) and the actual
demand (D=400).
Revenue =p×min(Q,D)[1]
The cost to the newsvendor depends on whether or not there are overstocks or
understocks at the end of the day. This cost function is shown as Equation 2. For example,
if 450 newspapers are ordered and demand is 500, the cost will be $75 –-- the product of
the understock cost (1.5) and the understock quantity (D−Q=50). If, on the other hand,
450 newspapers are ordered and demand is 400, the cost will be $37.5 –-- the product of
the overstock cost (0.75) and the overstock quantity (Q−D=50).
Cost =Comax(0,Q−D)+Cumax(0,D−Q)[2]
The calculation for the order quantity that minimizes Equation 2 (called the optimal
order quantity) is provided as Equation 3, where CSL is called the cycle service level.
Note that, when CO equals CU, there is indifference between understocks and
overstocks. In this case, the optimal CSL is 0.5 –-- and therefore the optimal order
quantity will be the median demand. When CO< CU, the optimal CSL will be higher than
0.5, and therefore the optimal order quantity would be higher than the demand forecast.
Correspondingly, the optimal order quantity will be lower than the forecast when CO>
CU.
CSL∗=CuCu+Co[3]
When demand is normally distributed, the optimal order quantity (Q*) is easily
derived. In Excel, the function shown as Equation 4 is used to obtain the optimal order
quantity. When demand follows other distributions, the optimal order quantity is found
in a similar manner (using the Excel function for that distribution).
NORMINV(CSL∗,μ,σ)[4]
The optimal order quantity (Q*) for a normally distributed demand scenario is shown in
Figure 1. Specifically, the area to the left of the optimal order quantity would be equal to
the optimal CSL (CSL∗).
Figure 1: Optimal Order Quantity (Normal Demand)s
Example 1
For the example stated earlier: A daily newspaper retails for $2.50 and costs the seller
$1.00 per newspaper and unsold newspapers are sold to a recycler for $0.25 per
newspaper. As shown earlier: c=1, p=2.5, s=0.25, CO=0.75 and CU=1.5. Demand is
assumed to be normal with a forecast (i.e., mean) of 500 newspapers and a standard
deviation FOP 100 newspapers. The value of CSL∗ is 0.667 (Equation 3) and the optimal
order quantity (Q*) is 543 units (Equation 4). The result is illustrated in Figure 2. Note
that the order quantity is always an integer (i.e., it is rounded from the Excel function
result).
Figure 2: Optimal Order Quantity (Example 1)
Example 2
Consider a single-season scenario (with newsvendor assumptions) in which the revenue
per product is $60, the procurement cost is $45 and the salvage value is $35 per unit.
Demand is forecasted to follow a normal distribution with a mean of 1000 units and a
coefficient of variation (CV) of 40%. We have: c=45, p=60, s=35, CO=10, CU=15, μ=1000,
and σ=400.
Prior to doing the optimization calculations, it is always a good idea to predict the correct
answer. This will prevent mistakes (i.e., incorrect calculations) and can help to
understand the methodology (when the estimate is incorrect, but the calculations are
correct). In this case, because the understock cost is higher that the overstock cost, we
expected that the optimal order quantity would be greater than the forecast (to avoid
understocks).
In any case, for this problem the value of CSL∗ is 0.600 (Equation 3) and the optimal
order quantity (Q∗) is 1101 units (Equation 4). The result is illustrated in Figure 3.
Figure 3: Optimal Order Quantity (Example 2)
For an order quantity, the mathematical expectation for the profit, E(P), can be calculated
when demand is normally distributed. The Excel version of this equation is shown in
Equation 5.
Equation 5
E(P)=(p-s)*μ*NORMDIST((Q-μ)/σ,0,1,1)-(p-s)*σ*NORMDIST((Q-μ)/σ,0,1,0)Q*(c-s)*NORMDIST(Q,μ,σ,1)+Q*(p-c)*(1-NORMDIST(Q,μ,σ,1))
Example 1 (Revisited)
For the first example stated earlier: A daily newspaper retails for $2.50 and costs the seller
$1.00 per newspaper and unsold newspapers are sold to a recycler for $0.25 per
newspaper. Demand is assumed to be normal with a forecast of 500 newspapers and a
standard deviation of 100 newspapers. The value of CSL∗ is 0.667 and the optimal order
quantity (Q∗) is 543 units. The expected profit is $66.82, obtained using Equation 5.
Example 2 (Revisited)
For the second example stated earlier: A single-season scenario (with newsvendor
assumptions) in which the revenue per product is $60, the procurement cost is $45 and
the salvage value is $35 per unit. Demand forecasted to follow a normal distribution with
a mean of 1000 units and a coefficient of variation (CV) of 40%. The value of CSL∗ is
0.600 and the optimal order quantity (Q∗) is 1101 units. The expected profit is $11,137,
obtained using Equation 5.
Test Yourself
The traditional newsvendor model requires the following inputs:
a. Variation of the demand forecast.
b. Fixed ordering costs.
c. Cycle service level (CSL).
d. All of the above.
Show Answer
Modified Newsvendor Model
A supply chain optimization model can sometimes be modified to represent unique
conditions. Some examples of modifications would include quantity discounts,
continuously stocked items, backorders, non-normal demand, and multi-stage storage. At
times, the resulting model can be solved mathematically. Although mathematical
expertise is required, this approach is generally fast and can be applied relatively
quickly. At other times, the problem can be solved only by using a simulation approach,
discussed later in this module.
The inclusion of holding costs in an otherwise traditional newsvendor model is relatively
easy to accomplish (Maleyeff, 2014). The resulting model can be solved
mathematically. In this scenario, one order is placed well ahead of the selling season. The
long lead time would cause additional costs that are not accounted for in the traditional
newsvendor model. These costs, called holding costs or carrying costs, would include
security, warehousing, taxes, and storage, as well as the cost of capital (i.e., money that
could have been earned by putting the same funds to productive use).
The model that includes holding costs will be used to assist in decision making regarding
the production or procurement of goods for a single selling season. It will help a supply
chain planner compare more efficient long lead time ordering with responsive short lead
time ordering. The main reason for long lead time ordering is to minimize manufacturing
costs by smoothing production or reducing procurement costs by offshoring. However,
ordering goods in this way will would typically result in higher holding costs and the
need to accommodate higher forecast uncertainty. But more responsive later ordering
would often require a more expensive supply chain.
The newsvendor model with holding costs would use a modified cost function as shown
in Equation 6.
Cost=CHQ+COmax(0,Q−D)+CUmax(0,D−Q)[6]
The value of CH (holding cost) must be consistent with the length of time that the item
will be held in storage prior to being sold. Its calculation is shown as Equation 7,
where h is the annual holding cost rate, c remains as defined earlier, and t is the relevant
length of time (expressed as a fraction of a year).
CH=h×c×t[7]
For example, consider a product with a cost of $25 that incurs an annual holding rate of
20%. For an analysis of production six months ahead of the selling season, the value of
CH be $2.50 -p the product of 0.2 (h), 25 (c), and 0.5 (t).
When holding cost is included, the optimal order quantity is derived using Equation
8. Notice that, as expected, when the holding cost increases, the optimal order quantity
will decrease.
CSL∗=CU−CHCU+CO[8]
The expected profit with holding costs (normally distributed demand) is shown as
Equation 9.
E(P)=
(p−s)×μ×NORMDIST
(
Q−μσ,0,1,1 [9]−(p−s)×σ×NORMDIST
)
(
NORMDIST(Q,μ,σ,1)+Q×(p−c)×(1−NORMDIST(Q,μ,σ,1))−CHQ
Example 2 (Revisited)
Q−μσ,0,1,0
)
−Q×(c−s)×
For the second example stated earlier: A single-season scenario (with newsvendor
assumptions) in which the revenue per product is $60, the procurement cost is $45 and
the salvage value is $35 per unit. Demand forecasted to follow a normal distribution with
a mean of 1000 units and a coefficient of variation (CV) of 40%. Assuming that the
product has an annual holding rate of 20%, the product must be ordered three months in
advance of sales and held in storage for that time frame.
The following costs are incurred: c=45, p=60, s=35, CO=10 and CU=15. In addition, μ=1000,
σ=400, and the value of CH is 2.25 --- the product of 0.2 (h), 45 (c), and 0.25 (t), using
Equation 7. The value of CSL* is 0.510 using Equation 8 (this value is reduced from 0.600
--- its value without holding costs). The value of Q* is 1010 units using Equation 4 (this
value is reduced from 1101 units --- its value without holding costs). Finally, the expected
profit is $8,762, obtained using Equation 9 (this value is reduced from $11137 --- its value
without holding costs).
The incorporation of holding cost has had a profound effect on the results of the
optimization. This is the type of analysis used by Maleyeff (2014) in evaluating the
advantages of moving from an efficient supply chain to a responsive supply chain when a
manufacturer changes from selling commodity (i.e., functional) products to fashion (i.e.,
innovative) products.
Comprehensive Exercise
A manufacturer is attempting to determine the benefits of postponing production of new
wood products. Forecasters can do a better job of forecasting if they have more time to
study consumer preferences by organizing focus groups, surveying potential customers, or
doing other forms of market research. Specifically, the forecast CV is expected to be 40%
when products are produced nine months ahead of sales, 25% when products are ordered
six months ahead of sales, and 15% when products are ordered three months ahead of
sales. For the sake of comparison, the analysis will assume a forecast of 100,000 units,
with revenue averaging $125 per unit sold.
Three options are available: (1) offshoring (a nine-month lead time), with a production
cost of $37.50; (2) outsourcing domestically (a six-month lead time), with a production
cost of $44; and (3) in-house production (a three-month lead time), with a production
cost of $50. The annual holding rate is estimated at 35% (it is high due to climate controls
required during storage of wood products). Overstocked items will be sold at a heavy
discount (to a reseller such as overstock.com) estimated to be $12.50 per unsold unit.
The results of applying the model are shown in Table 2 (readers should confirm all
calculations). Based on this analysis, the best solution would be to produce the product
in-house, because it has the highest expected profit.
Table 2: Inputs and Results (Comprehensive Exercise)
(1) Offshoring
(2) Outsourcing
(3) In-House
Lead Time
9
6
3
t
0.75
0.5
0.25
c
37.5
44
50
p
125
125
125
s
12.5
12.5
12.5
h
0.35
0.35
0.35
CU
87.5
81
75
CO
25
31.5
37.5
CH
9.844
7.700
4.375
CSL*
0.6903
0.6516
0.6278
CV
0.400
0.250
0.150
μ
100,000
100,000
100,000
σ
40,000
25,000
15,000
Q*
119,868
109,741
104,890
E(P)
$6,178,668
$6,289,948
$6,424,119
Often an analysis is based on estimates that may not all be highly reliable. In these
instances, the analyst can do a sensitivity analysis based on one or more key uncertain
factors. The effect of these factors can be evaluated as they are changed across a range of
potential values. For this scenario, it is likely that the main uncertain factors may include
the forecast, the CV of the forecast, and the holding rate.
As an example, we can adjust the value for the holding rate while keeping all other
variables consistent with their assumed values. The results of this analysis are shown in
Figure 4. It is clear that, as the holding rate changes, the preferred production location
(and associated lead time) changes. It appears that outsourcing domestically is never the
optimal option. The offshoring option is preferred when the holding rate is about 22%23% or below; otherwise the in-house option is preferred. The analyst should confirm
the most accurate value of holding rate (even if a study needs to be undertaken) before
presenting a firm recommendation.
Figure 4: Sensitivity Analysis (Comprehensive Example)
Simulation Modeling
When problems become too complex for an optimization model, a simulation model can
be employed. Simulation models are also useful when an analyst does not know of the
existence of a more sophisticated model. Simulation models mimic the problem under
study, Monte Carlo simulation is a simulation that uses random numbers to mimic
uncertainty. Simulations generally contain random input variables, the logic that
represents the system under study, and the tabulation of results. The simulation is "run"
for a large number of "iterations" (i.e., the simulation can mimic the actual system
thousands or even millions of times). Like all models, the key to their effectiveness is the
accuracy between the model and the real system being analyzed.
AD 680 Lecture 9 Video 1 shows a supply chain facility that would be well suited for
simulation. It includes a multistage system, many random input variables, and other
uncertainties across the many variables that influence performance. (Source: Tour of
Fulfillment by Amazon (FBA))
msm_ad680_17_su1_jmaleyeff_mod9_v1 video cannot be displayed here
Random Number Generation
Simulations include the generation of random numbers that mimic real distributions of
uncertainty, for example customer demand, production or service times, and product
quality (rejects, rework). The generation of random numbers that fit any random
probability distribution is not difficult. The main requirement is the capability to
generation random data for a continuous uniform distribution between 0 and 1, called the
U(0,1) random function. In Excel, for example, the U(0,1) random function is generated
as follows (F9 generates new sets of random data).
A simple example of simulation logic would be the generation of defect data in a
manufacturing simulation (or, similarly, mistake data in a service simulation). For
example, if a defect or mistake occurs 10% of the time, the user would input the
following expression into an Excel cell:
=if(rand()
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