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Supply Chain Analysis and
Design
Topic 1
Introduction to Modeling
Why this course?
• Accenture (2014) says that data analytics is one of the top priorities in supply
chain risk management.
• KPMG (2014) says that data analytics is the most critical in businesses.
• Deloitte (2015) says:
– Optimisation tools and demand forecasting are the most widely used today
in supply chain and will continue to be so; and
– Strategic thinking, problem solving, and analytics will become more
important in years to come.
• Basically, analytics is increasingly becoming critical!
Supply Chain Analysis and Design 2
Why this course? (cont)
• It will teach you how to make more money (e.g. revenue management), to
reduce operational cost (e.g. operations management), or to make an
informed decision while accounting for risks.
• It will open the doors to jobs such as Operations Research Analyst, Project
Manager, Logistics Planning Manager, Supply Chain Manager, and Supply
Chain Optimisation Analyst. These jobs require optimisation and analytical
skills.
• Knowledge and skills in this course are required in Supply Chain
Management Strategy (i.e. it is even harder!).
Supply Chain Analysis and Design 3
How this course relates to business?
• Business analytics, which has been widely available in enterprise resource
planning systems, is becoming more important. It consists of three types of
analytics:
– Descriptive analytics: descriptive statistics (business statistics)
– To answer: What happened?
– Predictive analytics: data mining, forecasting, simulation (operations
management and transport economics)
– To answer: What will happen?
– Prescriptive analytics: optimisations (this course is about this and a bit of
simulation)
– To answer: What is the best course of action?
Supply Chain Analysis and Design 4
Learning Outcomes
1. Use selected concepts, principles and procedures related to supply chain
management for effective decision making.
2. Investigate various methods to assess logistics and distribution practices.
3. Apply the tools and underlying principles of logistics to optimise operations
in network models.
4. Identify and evaluate the processes, tools and principles of logistics
practices in the manufacturing and service sectors.
5. Apply mathematical solutions to optimise supply chain networks and
logistics problems.
Supply Chain Analysis and Design 5
6
Lecture Topics
Week Topic Chapter
1 Introduction to modelling 1
2 Linear programming: Concepts and model formulation 2 & 5
3 Linear programming: Graphical and computer solutions 3
4 Sensitivity analysis 3
5 Network model 1: Transportation, transshipment, and
assignment problems6
6 Network model 2: Shortest-route, maximal flow, and
minimum spanning tree problems6 & 20
7 Integer programming 7
8 Project management 9
9 Waiting line models 11
10 Simulation 12
11 Decision theory 13
12 Course review --
Supply Chain Analysis and Design
Course Assessment
Supply Chain Analysis and Design 7
Tasks Weight
Case study (individual assignment) 20%
Business solution (individual assignment) 30%
Final exam 50%
Course Assessment Details
1. Case study, 20% of the total marks
– Work on a linear programming
– You must submit 2 files on myRMIT Studies:
– Word file to explain your mathematical models, to report your answers, and to
write recommendation for decision makers based on the solutions
– Excel file to demonstrate how you use Solver to identify the solutions. You must
use each sheet for each solution.
2. Business solution, 30% of the total marks
– You must collect real business data and ensure that the contact details of people
providing data are in the report. If there is any doubt, discuss it with your tutor.
– Use techniques in this course to propose a new solution.
– You must submit 2 files on myRMIT Studies:
– Word file that contains the report details with the length of 3,200–3,500 words.
– Excel file that shows how you come up with the solution.
Supply Chain Analysis and Design 8
Course Assessment Details
3. Final exam, 50% of the total marks
– During the University Exam Period.
– Covers the whole topics in this course including the listed chapters,
lecture notes, tutorial questions, and discussions.
– Details regarding the examination will be communicated during Lecture
12.
Supply Chain Analysis and Design 9
How to get good grade in this course?
• Practice
– This is an applied course, not a concept-based one. Get a textbook and
start solving problems at the end of the chapter. Reading slides and topic
notes are inadequate.
• Self-assess & reflect
– The answers provided in this course do not tell you how to solve problems.
They only tell you whether your answers are correct or incorrect. If your
answers are wrong, try to find out where it went wrong.
• Collaborate
– Team up with your peers to confirm whether you have solve problems
correctly.
– Do not copy each other in assignments otherwise you will do poorly in the
exam.
• Consult
– Make appointments with your tutors to understand where you get stuck.
Do not leave this until week 13!
Supply Chain Analysis and Design 10
Weak in mathematics?
• You should consider the following options:
– Contacting Study and Learning Centre
– Using Learning Lab
– Using Khan Academy
Supply Chain Analysis and Design 11
How to communicate with us?
• Be professional! You are
about to graduate from
RMIT! E-mail is a mean of
communication, not a chat.
• Use RMIT e-mails
• Add the course code (e.g.
OMGTxxxx) in the e-mail’
subject
• Try to solve issues with
your tutors before course
coordinator, unless you
have problems with tutors
themselves.
• Respond to CES survey!
Tell us good/bad about the
course and how to improve
it.Supply Chain Analysis and Design 12
CHAPTER 1
Supply Chain Analysis and Design 13
14
Overview
• Body of Knowledge
• Quantitative Analysis and Qualitative Analysis
• Quantitative Analysis Process
• Management Science Techniques
Supply Chain Analysis and Design
Body of Knowledge
• The body of knowledge involving quantitative approaches to decision making
is referred to as:
– Management Science
– Operations Research (OR)
– Decision Science
• It had its early roots in World War II and is flourishing in business and industry
due, in part, to:
– numerous methodological developments (e.g. simplex method for solving
linear programming problems)
– a virtual explosion in computing power
• Currently, OR is often discussed together with operations management (OM).
It has been widely used in business, military, health, and non-profit
organisations (e.g. disaster management).
Supply Chain Analysis and Design 15
7 Steps of Problem Solving
• (First 5 steps are the process of decision making)
1. Identify and define the problem.
2. Determine the set of alternative solutions.
3. Determine the criteria for evaluating alternatives.
4. Evaluate the alternatives.
5. Choose an alternative (make a decision).
6. Implement the selected alternative.
7. Evaluate the results.
Supply Chain Analysis and Design 16
Decision-Making Process
• Problems in which the objective is to find the best solution with respect to one
criterion are referred to as single-criterion decision problems.
• Problems that involve more than one criterion are referred to as multi-criteria
decision problems.
Supply Chain Analysis and Design 17
DefinetheProblem
IdentifytheAlternatives
DeterminetheCriteria
EvaluatetheAlternatives
ChooseanAlternative
Structuring the Problem Analyzing the Problem
Analysis Phase of Decision-Making Process
Qualitative analysis
• based largely on the manager’s
judgment and experience
• includes the manager’s intuitive
“feel” for the problem
• is more of an art than a science
Quantitative analysis
• analyst will concentrate on the
quantitative facts or data
associated with the problem
• analyst will develop
mathematical expressions that
describe the objectives,
constraints, and other
relationships that exist in the
problem
• analyst will use one or more
quantitative methods to make a
recommendation
Supply Chain Analysis and Design 18
Quantitative Analysis
• Potential Reasons for a Quantitative Analysis Approach to Decision Making
– The problem is complex.
– The problem is very important.
– The problem is new.
– The problem is repetitive.
• Quantitative Analysis Process:
1. Model Development
2. Data Preparation
3. Model Solution
4. Report Generation
Supply Chain Analysis and Design 19
20
Model Development
• Models are representations of real objects or situations
• Three forms of models are:
– Iconic models - physical replicas (scalar representations) of
real objects (e.g. a scale model of a house)
– Analog models - physical in form, but do not physically
resemble the object being modeled (e.g. thermometer)
– Mathematical models - represent real world problems through a
system of mathematical formulas and expressions based on
key assumptions, estimates, or statistical analyses
Supply Chain Analysis and Design
Advantages of Models
• Generally, experimenting with models (compared to experimenting with the
real situation):
– requires less time
– is less expensive
– involves less risk
• The more closely the model represents the real situation, the accurate the
conclusions and predictions will be.
• Nonetheless, frequently a less complicated (and perhaps less precise) model
is more appropriate than a more complex and accurate one due to cost and
ease of solution considerations.
Supply Chain Analysis and Design 21
22
Mathematical Models
• Objective Function – a mathematical expression that describes the
problem’s objective, such as maximizing profit or minimizing cost.
– Consider a simple production problem. Suppose x denotes the number of units produced and sold each week, and the firm’s objective is to maximize total weekly profit. With a profit of $10 per unit, the objective function is 10x.
• Constraints – a set of restrictions or limitations, such as production
capacities
– To continue our example, a production capacity constraint would be
necessary if, for instance, 5 hours are required to produce each unit and
only 40 hours are available per week. The production capacity constraint
is given by 5x =< 40. The value of 5x is the total time required to produce
x units; the symbol indicates that the production time required must be
less than or equal to the 40 hours available.
Supply Chain Analysis and Design
Mathematical Models
• Uncontrollable Inputs – environmental factors that are not under the control of
the decision maker
– In the preceding mathematical model, the profit per unit ($10), the
production time per unit (5 hours), and the production capacity (40 hours)
are environmental factors not under the control of the manager or decision
maker.
• Decision Variables – controllable inputs; decision alternatives specified by the
decision maker, such as the number of units of Product X to produce.
– In the preceding mathematical model, the production quantity x is the
controllable input to the model.
Supply Chain Analysis and Design 23
Mathematical Models
• A complete mathematical model for our simple production problem is:
• The second constraint reflects the fact that it is not possible to manufacture a
negative number of units.
Supply Chain Analysis and Design 24
Maximize 10x (objective function)
Subject to: 5x ≤ 40 (constraint)
x ≥ 0 (constraint)
Mathematical Models
• Deterministic Model – if all uncontrollable inputs to the model are known and
cannot vary
• Stochastic (or Probabilistic) Model – if any uncontrollable inputs are
uncertain and subject to variation
– Stochastic models are often more difficult to analyze.
– In previous production example, if the number of hours of production time
per unit could vary from 3 to 6 hours depending on the quality of the raw
material, the model would be stochastic.
Supply Chain Analysis and Design 25
26
Transforming Model Inputs into Output
Uncontrollable Inputs(Environmental Factors)
ControllableInputs
(DecisionVariables)
Output(Projected
Results)
MathematicalModel
Supply Chain Analysis and Design
27
Model Solution
• The analyst attempts to identify the alternative (the set of
decision variable values) that provides the “best” output for the
model.
• The “best” output is the optimal solution.
• If the alternative does not satisfy all of the model constraints, it is
rejected as being infeasible, regardless of the objective function
value.
• If the alternative satisfies all of the model constraints, it is feasible
and a candidate for the “best” solution.
Supply Chain Analysis and Design
Production Projected Total Hours Feasible
Quantity Profit of Production Solution
0 0 0 Yes
2 20 10 Yes
4 40 20 Yes
6 60 30 Yes
8 80 40 Yes
10 100 50 No
12 120 60 No
Model Solution
Trial-and-Error Solution for Production Problem
28Supply Chain Analysis and Design
29
Model Solution
• A variety of software packages are available for solving
mathematical models.
– Microsoft Excel
– OpenSolver
– LINGO
Supply Chain Analysis and Design
30
Model Testing and Validation
• Often, goodness/accuracy of a model cannot be assessed until
solutions are generated.
• Small test problems having known, or at least expected, solutions
can be used for model testing and validation.
• If the model generates expected solutions, use the model on the
full-scale problem.
• If inaccuracies or potential shortcomings inherent in the model
are identified, take corrective action such as:
– Collection of more-accurate input data
– Modification of the model
Supply Chain Analysis and Design
31
Report Generation
• A managerial report, based on the results of the model, should
be prepared.
• The report should be easily understood by the decision maker.
• The report should include:
– the recommended decision
– other pertinent information about the results (for example,
how sensitive the model solution is to the assumptions and
data used in the model)
Supply Chain Analysis and Design
32
Implementation and Follow-Up
• Successful implementation of model results is of critical
importance.
• Secure as much user involvement as possible throughout the
modeling process.
• Continue to monitor the contribution of the model.
• It might be necessary to refine or expand the model.
Supply Chain Analysis and Design
Models of Cost, Revenue, and Profit
Iron Works, Inc. manufactures two products made from steel and just
received this month's allocation of b kilograms of steel. It takes a1
kilograms of steel to make a unit of product 1 and a2 kilograms of steel
to make a unit of product 2.
Let x1 and x2 denote this month's production level of product 1 and
product 2, respectively.
Denote by p1 and p2 the unit profits for products 1 and 2, respectively.
Iron Works has a contract calling for at least m units of product 1 this
month. The firm's facilities are such that at most u units of product 2
may be produced monthly.
33Supply Chain Analysis and Design
Example: Iron Works, Inc.
• Mathematical Model
–The total monthly profit =
(profit per unit of product 1)
x (monthly production of product 1)
+ (profit per unit of product 2)
x (monthly production of product 2)
= p1x1 + p2x2
We want to maximize total monthly profit:
Max p1x1 + p2x2
34Supply Chain Analysis and Design
Example: Iron Works, Inc.
• Mathematical Model (continued)
–The total amount of steel used during monthly
production equals:
(steel required per unit of product 1)
x (monthly production of product 1)
+ (steel required per unit of product 2)
x (monthly production of product 2)
= a1x1 + a2x2
This quantity must be less than or equal to the
allocated b kilograms of steel:
a1x1 + a2x2 < b
35Supply Chain Analysis and Design
Example: Iron Works, Inc.
• Mathematical Model (continued)
–The monthly production level of product 1 must be
greater than or equal to m :
x1 > m
–The monthly production level of product 2 must be
less than or equal to u :
x2 < u
–However, the production level for product 2 cannot
be negative:
x2 > 0
36Supply Chain Analysis and Design
Example: Iron Works, Inc.
• Mathematical model summary:
Supply Chain Analysis and Design 37
Max p1x1 + p2x2
s.t. a1x1 + a2x2 ≤ b
x1 ≥ m
x2 ≤ u
x2 ≥ 0
Constraints
Objective Function
“Subject to”
Example: Iron Works, Inc.
• Question:
Suppose b = 2000, a1 = 2, a2 = 3, m = 60, u
= 720, p1 = 100, p2 = 200. Rewrite the model with
these specific values for the uncontrollable inputs.
38Supply Chain Analysis and Design
Example: Iron Works, Inc.
• Answer:
Supply Chain Analysis and Design 39
Max 100x1 + 200x2
s.t. 2x1 + 3x2 ≤ 2000
x1 ≥ 60
x2 ≤ 720
x2 ≥ 0
Constraints
Objective Function
“Subject to”
Example: Iron Works, Inc.
• Question:
The optimal solution to the current model is x1 =
60 and x2 = 6262
3. If the product were engines, explain
why this is not a true optimal solution for the "real-life"
problem.
• Answer:
One cannot produce and sell 2
3of an engine.
Thus the problem is further restricted by the fact that
both x1 and x2 must be integers. (They could remain
fractions if it is assumed these fractions are work in
progress to be completed the next month.)
40Supply Chain Analysis and Design
Example: Iron Works, Inc.
Uncontrollable Inputs
$100 profit per unit Prod. 1
$200 profit per unit Prod. 2
2 kg steel per unit Prod. 1
3 kg steel per unit Prod. 2
2000 kg steel allocated
60 units minimum Prod. 1
720 units maximum Prod. 2
0 units minimum Prod. 2
60 units Prod. 1
626.67 units Prod. 2
Controllable Inputs
Profit = $131,333.33
Steel Used = 2000
Output
Mathematical Model
Max 100(60) + 200(626.67)
s.t. 2(60) + 3(626.67) ≤ 2000
60 ≥ 60
626.67 ≤ 720
626.67 ≥ 0
41Supply Chain Analysis and Design
Example: Ponderosa Development Corp.
• Ponderosa Development Corporation (PDC) is a small real estate developer
that builds only one style house. The selling price of the house is $115,000.
• Land for each house costs $55,000 and lumber, supplies, and other materials
run another $28,000 per house. Total labour costs are approximately $20,000
per house.
• Ponderosa leases office space for $2,000 per month. The cost of supplies,
utilities, and leased equipment runs another $3,000 per month. The one
salesperson of PDC is paid a commission of $2,000 on the sale of each
house. PDC has seven permanent office employees whose monthly salaries
are given on the next slide.
Supply Chain Analysis and Design 42
Example: Ponderosa Development Corp.
Supply Chain Analysis and Design 43
Employee Monthly Salary
President $10,000
VP, Development $6,000
VP, Marketing $4,500
Project Manager $5,500
Controller $4,000
Office Manager $3,000
Receptionist $2,000
Example: Ponderosa Development Corp.
• Question:
– Identify all costs and denote the marginal cost and marginal revenue for
each house.
• Answer:
– The monthly salaries total $35,000 and monthly office lease and supply
costs total another $5,000. This $40,000 is a monthly fixed cost.
– The total cost of land, material, labour, and sales commission per house,
$105,000, is the marginal cost for a house.
– The selling price of $115,000 is the marginal revenue per house.
Supply Chain Analysis and Design 44
Example: Ponderosa Development Corp.
• Question:
– Write the monthly cost function c (x), revenue function r (x), and profit
function p (x).
• Answer:
– c (x) = variable cost + fixed cost = 105,000x + 40,000
– r (x) = 115,000x
– p (x) = r (x) - c (x) = 10,000x - 40,000
Supply Chain Analysis and Design 45
Example: Ponderosa Development Corp.
• Question:
– What is the breakeven point for monthly sales of the houses?
• Answer:
– r (x) = c (x)
– 115,000x = 105,000x + 40,000
– Solving, x = 4.
• Question:
– What is the monthly profit if 12 houses per month are built and sold?
• Answer:
– p (12) = 10,000(12) - 40,000 = $80,000 monthly profit
Supply Chain Analysis and Design 46
Example: Ponderosa Development Corp.
0
200
400
600
800
1000
1200
0 1 2 3 4 5 6 7 8 9 10
Number of Houses Sold (x)
Thousands o
f D
olla
rs
Break-Even Point = 4 Houses
Total Cost =
40,000 + 105,000x
Total Revenue =
115,000x
47Supply Chain Analysis and Design
Using Excel for Breakeven Analysis
• A spreadsheet software package such as Microsoft Excel can be used to
perform a quantitative analysis of Ponderosa Development Corporation.
• We will enter the problem data in the top portion of the spreadsheet.
• The bottom of the spreadsheet will be used for model development.
Supply Chain Analysis and Design 48
A B
1 PROBLEM DATA
2 Fixed Cost $40,000
3 Variable Cost Per Unit $105,000
4 Selling Price Per Unit $115,000
5 MODEL
6 Sales Volume
7 Total Revenue =B4*B6
8 Total Cost =B2+B3*B6
9 Total Profit (Loss) =B7-B8
Example: Ponderosa Development Corp.
• Question:
– What is the monthly profit if 12 houses are built and sold per month?
• Answer:
Supply Chain Analysis and Design 49
A B
1 PROBLEM DATA
2 Fixed Cost $40,000
3 Variable Cost Per Unit $105,000
4 Selling Price Per Unit $115,000
5 MODEL
6 Sales Volume 12
7 Total Revenue $1,380,000
8 Total Cost $1,300,000
9 Total Profit (Loss) $80,000
Example: Ponderosa Development Corp.
• Spreadsheet Solution: Goal Seek approach using Excel’s Goal Seek tool
1. Select Data on menu
2. Choose What-If Analysis in Data Tools submenu
3. Choose the Goal Seek option
4. When the Goal Seek dialog box appears:
– Enter B9 in the Set cell box
– Enter 0 in the To value box
– Enter B6 in the By changing cell box
– Click OK
Supply Chain Analysis and Design 50
Example: Ponderosa Development Corp.
Supply Chain Analysis and Design 51
A B
1 PROBLEM DATA
2 Fixed Cost $40,000
3 Variable Cost Per Unit $105,000
4 Selling Price Per Unit $115,000
5 MODEL
6 Sales Volume 4
7 Total Revenue $460,000
8 Total Cost $460,000
9 Total Profit (Loss) $0
Example: Ponderosa Development Corp.
• Question:
– What is the breakeven point for monthly sales of the houses?
• Spreadsheet Solution:
– One way to determine the break-even point using a spreadsheet is to use
the Goal Seek tool.
– Microsoft Excel’s Goal Seek tool allows the user to determine the value for
an input cell that will cause the output cell to equal some specified value.
– In our case, the goal is to set Total Profit to zero by seeking an appropriate
value for Sales Volume.
Supply Chain Analysis and Design 52
53
Example: Austin Auto Auction
An auctioneer has developed a simple mathematical model
for deciding the starting bid he will require when auctioning a
used automobile.
Essentially, he sets the starting bid at seventy percent of
what he predicts the final winning bid will (or should) be. He
predicts the winning bid by starting with the car's original selling
price and making two deductions, one based on the car's age
and the other based on the car's mileage.
The age deduction is $800 per year and the mileage
deduction is $.025 per mile.
Supply Chain Analysis and Design
54
Example: Austin Auto Auction
Question:
The model is based on what assumptions?
Answer:
The model assumes that the only factors
influencing the value of a used car are the original
price, age, and mileage (not condition, rarity, or other
factors).
Also, it is assumed that age and mileage devalue
a car in a linear manner and without limit. (the starting
bid for a very old car might be negative!)
Supply Chain Analysis and Design
55
Example: Austin Auto Auction
• Question:
Develop the mathematical model that will give the starting bid
(B) for a car in terms of the car's original price (P), current age (A)
and mileage (M).
• Answer:
The expected winning bid can be expressed as:
P - 800(A) - .025(M)
The entire model is:
B = .7(expected winning bid)
B = .7(P - 800(A) - .025(M))
B = .7(P) - 560(A) - .0175(M)
Supply Chain Analysis and Design
56
Example: Austin Auto Auction
Question:
Suppose a four-year old car with 60,000 miles on the odometer
is being auctioned. If its original price was $12,500, what starting
bid should the auctioneer require?
Answer:
B = .7(12,500) - 560(4) - .0175(60,000) = $5,460
Supply Chain Analysis and Design
Q&A
57Supply Chain Analysis and Design
References
• Accenture (2014). Accenture global operations megatrends study.
• Deloitte (2015). Supply chain talent of the future: Findings from the third
annual supply chain survey.
• KPMG (2014). Transforming for growth: Consumer business in the digital
age.
Supply Chain Analysis and Design 58
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