Introduction to Modeling & Problem Solving

Introduction to Modeling & Problem Solving

Introduction

• We face numerous decisions in life & business.

• We can use computers to analyze the potential outcomes of decision alternatives.

• Spreadsheets are the tool of choice for today’s managers.

• Motorola– Procurement of goods and services account for

50% of its costs– Developed an Internet-based auction system for

negotiations with suppliers – The system optimized multi-product, multi-

vendor contract awards– Benefits:

$600 million in savings

• Waste Management– Leading waste collection company in North America– 26,000 vehicles service 20 million residential & 2

million commercial customers– Developed vehicle routing optimization system– Benefits:

Eliminated 1,000 routesAnnual savings of $44 million

• Hong Kong International Terminals– Busiest container terminal in the world– 122 yard cranes serve 125 ships per week– Thousands of trucks move containers in & out of storage yard– Used DSS to optimize operational decisions involving trucks,

cranes & storage locations– Benefits:

• 35% reduction in container handling costs• 50% increase in throughput• 30% improvement in vessel turnaround time

• John Deere Company– 2500 dealers sell lawn equipment & tractors with support of

5 warehouses– Each dealer stocks 100 products, creating 250,000 product-

stocking locations – Demand is highly seasonal and erratic– Developed inventory system to optimize stocking levels over

a 26-week horizon– Benefits:

• $1 billion in reduced inventory• Improved customer-service levels

What is a “Computer Model”?

• A set of mathematical relationships and logical assumptions implemented in a computer as an abstract representation of a real-world object of phenomenon.

• Spreadsheets provide the most convenient way for business people to build computer models.

The Modeling Approach to Decision Making

• Everyone uses models to make decisions.• Types of models:

– Mental (arranging furniture)– Visual (blueprints, road maps)– Physical/Scale (aerodynamics, buildings)– Mathematical (what we’ll be studying)

Characteristics of Models

• Models are usually simplified versions of the things they represent

• A valid model accurately represents the relevant characteristics of the object or decision being studied

Benefits of Modeling• Economy - It is often less costly to analyze

decision problems using models.• Timeliness - Models often deliver needed

information more quickly than their real-world counterparts.

• Feasibility - Models can be used to do things that would be impossible.

• Models give us insight & understanding that improves decision making.

Example of a Mathematical Model

Profit = Revenue - Expensesor

Profit = f(Revenue, Expenses)or

Y = f(X1, X2)

A Generic Mathematical Model

Y = f(X1, X2, …, Xn)

Y = dependent variable (aka bottom-line performance measure)

Xi = independent variables (inputs having an impact on Y)

f(.) = function defining the relationship between the Xi & Y

Where:

Mathematical Models & Spreadsheets

• Most spreadsheet models are very similar to our generic mathematical model:

Y = f(X1, X2, …, Xn)

Most spreadsheets have input cells (representing Xi) to which mathematical functions ( f(.)) are applied to compute a bottom-line performance measure (or Y).

Categories of Mathematical Models

Prescriptive known, known or under LP, Networks, IP,well-defined decision maker’s CPM, EOQ, NLP,

control GP, MOLP

Predictive unknown, known or under Regression Analysis, ill-defined decision maker’s Time Series Analysis, control Discriminant Analysis

Descriptive known, unknown or Simulation, PERT,well-defined uncertain Queueing,

Inventory Models

Model Independent OR/MSCategory Form of f(.) Variables Techniques

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Decision Analysis• Effective decision-making requires that we

understand:– The nature of the decision that must be made– The values, goals, and objectives that are

relevant to the decision problem– The areas of uncertainty that affect the decision– The consequences of each possible decision

The Problem Solving Process

Identify Problem

Formulate & Implement

ModelAnalyze Model

Test Results

Implement Solution

unsatisfactoryresults

Most important

The Psychology of Decision Making

• Models can be used for structurable aspects of decision problems.

• Other aspects cannot be structured easily, requiring intuition and judgment.

• Caution: Human judgment and intuition is not always rational!

Anchoring and Framing

• Errors in judgment arise due to what psychologists term anchoring and framing

Anchoring• Arise when trivial factors influence initial

thinking about a problem.• Decision-makers usually under-adjust from

their initial “anchor”.• 2 groups are asked to estimate the value of:

1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 or 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1

Anchoring• Median estimate of first series was 512• Median estimate of 2nd series was 2,250• The order of the numbers is, of course,

meaningless and the answer is 40,320

Framing (Example)• Refers to how decision-makers view a problem from a

win-loss perspective.• The way a problem is framed often influences choices in

irrational ways…• Suppose you’ve been given $1000 and must choose

between:– A. Receive $500 more immediately– B. Flip a coin and receive $1000 more if heads occurs or $0

more if tails occurs

• A) is a sure win and the choice most people prefer

Framing Effects (Example)

• Now suppose you’ve been given $2000 and must choose between:

– A. Give back $500 immediately– B. Flip a coin and give back $0 if heads occurs or

give back $1000 if tails occurs

• When framed this way, alternative A) is a “sure loss” and many people who previously preferred alternative A) now opt for alternative B) (because it holds a chance of avoiding a loss)

Framing (Example)

• However it is clear that that in both cases the A) alternative guarantees a total payoff of $1,500, whereas B) offers a 50% chance of a $2,000 total payoff and a 50% chance of $1,000 total payoff.

• A rational decision maker should focus on the consequences of his/her choices and consistently select the same alternative, regardless of how the problem is framed

A Decision Tree for Both Examples

Initial state

$1,500

Heads (50%)

Tails (50%)

$2,000

$1,000

Alternative A

Alternative B(Flip coin)

Payoffs

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A Framing Example“Careful analysis at a major U.S. steel company showed it could save hundreds of thousands of dollars per year by replacing its hot-metal mixing technology, which required that metal be heated twice, with direct-pouring technology, in which the metal was only heated once. But the move was approved only after considerable delay because senior engineers complained that the analysis did not include the cost of the hot metal mixers that had been purchased for $3 million just a few years previously.”

How would you critique this decision?

Adapted from Winning Decisions, by Russo and Shoemaker

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A Framing Example“Careful analysis at a major U.S. steel company showed it could save hundreds of thousands of dollars per year by replacing its hot-metal mixing technology, which required that metal be heated twice, with direct-pouring technology, in which the metal was only heated once. But the move was approved only after considerable delay because senior engineers complained that the analysis did not include the cost of the hot metal mixers that had been purchased for $3 million just a few years previously.”

How would you critique this decision?

Adapted from Winning Decisions, by Russo and Shoemaker

Good Decisions vs. Good Outcomes

• Good decisions do not always lead to good outcomes...

A structured, modeling approach to decision making helps us make good decisions, but can’t guarantee good outcomes.