SCAD 1 slides(1).pdf

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!).


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?


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.


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


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.


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.


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!


Weak in mathematics?

• You should consider the following options:

– Contacting Study and Learning Centre

– Using Learning Lab

– Using Khan Academy


http://www.rmit.edu.au/browse;ID=xc6hgzn4q7ce

http://emedia.rmit.edu.au/learninglab/content/maths

https://www.khanacademy.org/

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


14

Overview

• Body of Knowledge

• Quantitative Analysis and Qualitative Analysis

• Quantitative Analysis Process

• Management Science Techniques


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).


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.


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.


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


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


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


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.


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.


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.


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.


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.


26

Transforming Model Inputs into Output

Uncontrollable Inputs(Environmental Factors)

ControllableInputs

(DecisionVariables)

Output(Projected

Results)

MathematicalModel


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.


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


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


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)


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.


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.


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)


= p1x1 + p2x2

We want to maximize total monthly profit:

Max p1x1 + p2x2



• Mathematical Model (continued)

–The total amount of steel used during monthly

production equals:

(steel required per unit of product 1)


+ (steel required per unit of product 2)


= a1x1 + a2x2

This quantity must be less than or equal to the

allocated b kilograms of steel:

a1x1 + a2x2 < b



• 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



• Mathematical model summary:


Max p1x1 + p2x2

s.t. a1x1 + a2x2 ≤ b

x1 ≥ m

x2 ≤ u

x2 ≥ 0

Constraints

Objective Function

“Subject to”


• 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.



• Answer:


Max 100x1 + 200x2

s.t. 2x1 + 3x2 ≤ 2000

x1 ≥ 60

x2 ≤ 720

x2 ≥ 0

Constraints

Objective Function

“Subject to”


• 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.)



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


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.




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


• 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.



• 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



• 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



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


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.


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


• Question:

– What is the monthly profit if 12 houses are built and sold per month?

• Answer:


A B

1 PROBLEM DATA




5 MODEL

6 Sales Volume 12

7 Total Revenue $1,380,000

8 Total Cost $1,300,000

9 Total Profit (Loss) $80,000


• 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




A B

1 PROBLEM DATA




5 MODEL

6 Sales Volume 4

7 Total Revenue $460,000

8 Total Cost $460,000

9 Total Profit (Loss) $0


• 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.


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.


54


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!)


55


• 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)


56


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


Q&A


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.


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