Sensitivity Analysis - Human Decision Making - Lecture Slides, Slides of Human-Computer Interaction Design

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Sensitivity Analysis

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Introduction

 Before Implementing a Decision, We Should

 Verify that numbers were entered correctly and calculations were performed

properly

 Identify the specific assumptions behind the analysis

 What is Sensitivity Analysis?

 A systematic study of how the solution to a decision model changes as the

assumptions are varied

 Varying one, two, or all the parameters simultaneously

 Also known as “what-if” analysis

 “what would happen if …”

 Importance of Sensitivity Analysis

 Helps to obtain a fuller understanding of the dynamics of the decision problem

 Whether the best decision strategy is robust

 Helps to identify the important elements in the decision problem

 To construct a requisite decision model

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Eagle Airlines Case

Dick Carothers, the president of Eagle Airlines, wants to expand his operation. Eagle airlines owns 3 aircrafts and provides 50% charter flights and 50% scheduled commuter service (only 90 min. of flying time on average). He has a news that a small airline in the Midwest is selling an airplane (Piper Senecca).

 The owner of Senecca has offered: 1) sell the airplane outright at price $95K (Carothers could probably buy it for $85K ~ $90K) or 2) sell an option to purchase the airplane within a year at a specified price (the cost of the option is $2.5k ~ $4k).  The properties of the airplane: 1) new engines, FAA maintained; 2) contains all the needed equipment; 3) 5 seats; 4) operating cost: $245/hour; 5) fixed cost: $20k yearly insurance + finance charges  Finance charges: borrow 30-50% of the price at 2% above the prime rate (currently 9.5%, but subject to change)  Revenue: 1) charter flights at $300 - $350 per hour; 2) scheduled flights at around $100 per person per hour (planes are 50% full on average); 3) expect to fly the plane 800 ~1000 hours per year (50% charter flights)  Carothers can always invest his cash in the money market at 8% yearly interest rate  Variables in control: 1) the price he is willing to pay; 2) the amount financed  Variables not in control: 1) insurance cost; 2) operation cost

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 Objectives

Maximize profits

Revenue from charters = (charter flight ratio)(hours flown)(charter price) Revenue from scheduled flights = (1-charter flight ratio)(hours flown)(ticket price)(#seats)(capacity of scheduled flights)

Profits = Revenue – Cost Revenue:

Fixed cost = insurance+Finance=insurance+(purchase price)(% financed) (interest rate) Variable cost = (hours flown)*(operating cost/hour)

Cost:

Decision Elements

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 Uncertain Events (Relevant to the Decisions)

 Charter flight ratio  Hours flown  Capacity of scheduled flights  Insurance  Purchase price  Interest rate  Operating cost/hour

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Total Cost

Revenue

Operating cost

Hours flown

Capacity on scheduled flights

Charter flight ratio

Charter Price

Ticket Price

Finance Cost

Purchase Seneca

Proportion financed

Interest rate

Insurance

Purchase Price

Profit

Variable Cost Fixed Cost

Charter Revenue

Scheduled flight revenue

Influence Diagram

Profit

Total Cost

Revenue

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One-Way Sensitivity Analysis

 Examine whether a variable really makes a difference in the decision

by varying its value while keeping other variables at their base values

(best guesses)

One-Way Sensitive Analysis of Hours Flown

Question: Under what condition is this procedure adequate? Profit

Hours Flown

Hours flown = 664 h

Purchase Seneca Money Market

Profit=$4,

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Tornado Diagram

 A bar (or line) is used to represent the range of payoffs due to the

variation of an input variable

 Allows us to compare one-way sensitive analyses for many input

variables at once

Capacity of scheduled flight Operating cost Hours flown Charter price

Money Market

Interest rate Purchase price

Tornado Diagram of Eagle Airlines Decision

Profits

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Two-way Sensitive Analysis of Eagle Airlines Decision

(indifference line)

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Sensitivity to Probabilities

 Study the impact of uncertainties of events

Decision Tree of Research-and-Development Decision

Demands High

Development Decision (^) Stop Development

Continue Development Development Result

Patent Awarded

No Patent

License Technology

-$2M

Develop Production and Marketing to Sell Product

$23M

Demands Med. Demands Low

(0.7) (p=?) (q=?) (1-p-q)

$43M

$21M

$3M

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Two-way Sensitive Analysis of Probabilities for Research-and-Development Decision

EMV(C) and EMV(B) are always greater than EMV(A), so only EMV(B) and EMV(C) need to be compared to find the best strategy

EMV(C) = EMV(B)  28p + 12.6q = 14 (indifference line)

p

q

p=0.

p=0.

EMV(C) = EMV(B)

EMV(C) > EMV(B)

EMV(C) < EMV(B)

Impossible Region

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The town of Bedford is planning a celebration of honor its gold-metal-winning Olympic Cross-country skier. The celebration is set to be held in the town’s center for the day she returns. Unfortunately, the weather report predicts that the temperature might not be conducive to an outdoor event on that day. As a backup plan, they are thinking about reserving indoor space. However, that reservation would cost additional taxpayer’s money. Therefore, Julie Bauer, the town manager, needs to decide whether to reserve the indoor space.

Exercise

1. Draw the decision tree of this decision
2. Suppose that the probability of a cold weather is estimated to be 40% and that holding the event is twice as important as saving taxpayer’s money, what would you suggest to Julie Bauer from the analyses of both the expected values and risk profiles?
3. Julie Bauer is also wondering how her decision would be affected by the probability of the cold weather and the tradeoff between the two objectives, so what would you tell her by performing a two-way sensitive analysis for the two parameters? (Hint: set the ratio of the weight of “holding event” to the weight of “saving money”, say k , as the parameter for tradeoff)

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Let wh and ws denote the weight of holding the event and the weight of saving money, respectively. Because wh = 2ws and wh + ws = 1, solving the equations, we can get wh = 2/3, and ws = 1/3.

Converting both attributes to 0 -100 scale, we can set “holding event” to 100, “canceling event” to 0, “saving money” to 100, and “costing money” to 0.

Overall Score =1002/3+0 1/3=200/

Reserve

Don’t Reserve

Cold

Cold

Event Held

Save Money

100

100

Not Cold

Not Cold

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Reserve: EV(Reserve) = 0.4 • 200/3 + 0.6 • 200/3 = 200/ Overall score: 200/3(100%)

Don’t Reserve: EV(Don’t Reserve) = 0.4 • 100/3 + 0.6 • 100 = 220/ Overall score: 100/3(40%), 100(60%)

Cumulative Risk Profile

No strategy dominates the other

Compared to the strategy of “reserving the indoor space”, the strategy of “not reserving the indoor space” has a slightly higher expected value of the overall score but is riskier as well.

(Draw the risk profiles on your own)