McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 200316.1

Table of ContentsChapter 16 (Computer Simulation with Crystal Ball)

A Case Study: Freddie the Newsboy’s Problem (Section 16.1) 16.2–16.24Bidding for a Construction Project (Section 16.2) 16.25–16.31Project Management: Reliable Construction Co. (Section 16.3) 16.32–16.43Cash Flow Management: Everglade Golden Years Co. (Section 16.4) 16.44–16.49Financial Risk Analysis: Think-Big Development Co. (Section 16.5) 16.50–16.55Revenue Management in the Travel Industry (Section 16.6) 16.56–16.61Choosing the Right Distribution (Section 16.7) 16.62–16.83Decision Making with Decision Tables (Section 16.8) 16.84–16.99Optimizing with OptQuest (Section 16.9) 16.100–16.118

Monte-Carlo Simulation with Crystal Ball (UW Lecture) 16.119–16.137These slides are based upon a lecture from the MBA core course in Management Science at the University of Washington (as taught by one of the authors).

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Freddie the Newsboy

• Freddie runs a newsstand in a prominent downtown location of a major city.

• Freddie sells a variety of newspapers and magazines. The most expensive of the newspapers is the Financial Journal.

• Cost data for the Financial Journal:– Freddie pays $1.50 per copy delivered.– Freddie charges $2.50 per copy.– Freddie’s refund is $0.50 per unsold copy.

• Sales data for the Financial Journal:– Freddie sells anywhere between 40 and 70 copies a day.– The frequency of the numbers between 40 and 70 are roughly equal.

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Spreadsheet Model for Applying Simulation

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Freddie the Newsboy

DataUnit Sale Price $2.50

Unit Purchase Cost $1.50Unit Salvage Value $0.50

Decision VariableOrder Quantity 60

Simulation Minimum MaximumSimulated Demand 55 Uniform 40 70Demand (rounded) 55

Sales Revenue $137.50Purchasing Cost $90.00

Salvage Value $2.50

Profit $50.00

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Application of Crystal Ball

• Four steps must be taken to use Crystal Ball on a spreadsheet model:

1. Define the random input cells.

2. Define the output cells to forecast.

3. Set the run preferences.

4. Run the simulation.

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Step 1: Define the Random Input Cells

• A random input cell is an input cell that has a random value.

• An assumed probability distribution must be entered into the cell rather than a single number.

• Crystal Ball refers to each such random input cell as an assumption cell.

• Procedure to define an assumption cell:1. Select the cell by clicking on it.

2. If the cell does not already contain a value, enter any number into the cell.

3. Click on the Define Assumption button (first button in Crystal Ball toolbar).

4. Select a probability distribution from the Distribution Gallery.

5. Click OK to bring up the dialogue box for the selected distribution.

6. Use the dialogue box to enter parameters for the distribution (preferably referring to cells on the spreadsheet that contain these parameters).

7. Click on OK.

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The Crystal Ball Toolbar

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Crystal Ball Distribution Gallery

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Crystal Ball Uniform Distribution Dialogue Box

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Static versus Dynamic Option

• When cell references are used to enter parameters for a distribution, the Distribution Dialogue Box gives a choice between the “Static” option and the “Dynamic” option.

• The static option means that each cell reference is only evaluated once, at the beginning of the simulation run, and then each parameter value (e.g., Min and Max) is used for all trials of the simulation.

• The dynamic option means that each cell reference is evaluated for each separate trial. This would be needed if the parameter value might change from trial to trial because it depends on another assumption cell.

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Step 2: Define the Output Cells to Forecast

• Crystal Ball refers to the output of a computer simulation as a forecast, since it is forecasting the underlying probability distribution when it is in operation.

• Each output cell that is being used to forecast a measure of performance is referred to as a forecast cell.

• Procedure for defining a forecast cell:1. Select the cell.

2. Click on the Define Forecast button (3rd button) in the Crystal Ball toolbar, which brings up the Define Forecast dialogue box.

3. This dialogue box can be used to define a name and (optionally) units for the forecast cell.

4. Click on OK.

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Crystal Ball Define Forecast Dialogue Box

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Step 3: Set the Run Preferences

• Setting run preferences refers to such things as choosing the number of trials to run and deciding on other options regarding how to perform the simulation.

• This step begins by clicking on the Run Preferences button on the Crystal Ball toolbar.

• The Run Preferences dialogue box has six tabs to set various types of options.

• The Trials tab allows you to specify the maximum number of trials to run for the computer simulation.

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The Crystal Ball Run Preferences Dialogue Box

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Step #4: Run the Simulation

• To begin running the simulation, click on the Start Simulation button.

• Once started, a forecast window displays the results of the computer simulation as it runs.

• The following can be obtained by choosing the corresponding option under the View menu in the forecast window display:– Frequency chart– Statistics table– Percentiles table– Cumulative chart– Reverse cumulative chart

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The Frequency Chart for Freddie’s Profit

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The Statistics Table for Freddie’s Profit

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The Percentiles Table for Freddie’s Profit

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The Cumulative Chart for Freddie’s Profit

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The Reverse Cumulative Chart for Freddie’s Profit

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Certainty that Profit ≥ $40

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How Accurate Are the Simulation Results?

• An important number provided by the simulation is the mean profit of $46.67.

• This sample average provides an estimate of the true mean of the distribution. The true mean might be somewhat different than $46.67.

• The mean standard error (on the Statistics Chart) of $0.60 gives some indication of how accurate the estimate might be. The true mean will typically (approximately 68% of the time) be within the mean standard error of the estimated value.– It is about 68% likely that the true mean profit is between $46.07 and $47.27.

• The mean standard error can be reduced by increasing the number of trials. However, cutting the mean standard error in half typically requires approximately ƒour times as many trials.

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Precision Control: Expanded Define Forecast Dialogue Box

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Results with Precision Control

750 trials were required to get the 95% confidence interval around the mean within $1.

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Results with Precision Control

This table shows the precision obtained for the various percentiles of profit after 750 trials.

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Bidding for a Project: Reliable Construction Co.

• Reliable Construction Co. is bidding to construct a new plant for a major manufacturer.

• Reliable estimates the cost of the project to be $4.55 million, There also is an additional cost of approximately $50,000 for preparing the bid.

• Three other construction companies also were invited to submit bids for the project.– Competitor 1 is known to use a 30 percent profit margin, but are unpredictable

bidders because of an inability to accurately estimate the true cost of the project. Previous bids have ranged from 5% below the expected cost to 60% above.

– Competitor 2 uses a 25% profit margin, but is more accurate at predicting the true cost. In the past, they have missed this profit margin by up to 15% in either direction.

– Competitor 3 is unusually accurate in estimating project cost. It is equally likely to set its profit margin anywhere between 20% and 30%.

Question: How much should Reliable bid for this project?

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Spreadsheet Model for Applying Computer Simulation

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A B C D E

Reliable Construction Co. Contract Bidding

DataOur Project Cost ($million) 4.550

Our Bid Cost ($million) 0.050

Competitor Bids Competitor 1 Competitor 2 Competitor 3Bid ($million) 5.839 5.688 5.688

Distribution Triangular Triangular Uniform

Competitor Distribution Parameters (Proportion of Our Project Cost)Minimum 95% 110% 120%

Most Likely 130% 125%Maximum 160% 140% 130%

Competitor Distribution Parameters ($millions)Minimum 4.323 5.005 5.460

Most Likely 5.915 5.688Maximum 7.280 6.370 5.915

Minimum CompetitorBid ($million) 5.688

Our Bid ($million) 5.400

Win Bid? 1 (1=yes, 0=no)

Profit ($million) 0.800

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Triangular Distribution for Competitor 2

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Frequency Chart for Reliable’s Bidding Problem

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Statistics Table for Reliable’s Bidding Problem

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Percentiles Table for Reliable’s Bidding Problem

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Cumulative Chart for Reliable’s Bidding Problem

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Project Management: Reliable Construction Co.

• Reliable Construction Co. has won the bid to construct a new plant for a major manufacturer.

• The contract includes a large penalty if construction is not completed by the deadline 47 weeks from now.

• There are 14 tasks that need to be completed to finish the project.– (a) excavate, (b) foundation, (c) rough wall, (d) roof, (e) exterior plumbing,

(f) interior plumbing, (g) exterior siding, (h) exterior painting, (i) electrical work, (j) wallboard, (k) flooring, (l) interior painting, (m) exterior fixtures, (n) interior fixtures.

– For each task, three estimates of their completion time have been made—a most-likely, an optimistic, and a pessimistic estimate

Question: What is the probability that the project will complete by the deadline?

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 200316.33

Project Network for Reliable Construction Co.

A

START

G

H

M

F

J

FINISH

K L

N

D IE

C

B

Activity Code

A. Excavate

B. Foundation

C. Rough wall

D. Roof

E. Exterior plumbing

F. Interior plumbing

G. Exterior siding

H. Exterior painting

I. Electrical work

J. Wallboard

K. Flooring

L. Interior painting

M. Exterior fixtures

N. Interior fixtures

2

4

10

746

7

9

5

8

4 5

6

2

0

0

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The Triangular Distribution for an Activity Duration

Elapsed time

0 o m p

Triangular distribution

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Spreadsheet Model for Applying Computer Simulation

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Simulation of Reliable Construction Co. Project

ActivityImmediate Time Estimates Start Time Finish

Activity Predecessor o m p Time (triangular ) TimeA Ğ 1 2 3 0 2 2B A 2 3.5 8 2 4.5 6.5C B 6 9 18 6.5 11 17.5

D C 4 5.5 10 17.5 6.5 24E C 1 4.5 5 17.5 3.5 21F E 4 4 10 21 6 27G D 5 6.5 11 24 7.5 31.5H E, G 5 8 17 31.5 10 41.5I C 3 7.5 9 17.5 6.5 24J F, I 3 9 9 27 7 34K J 4 4 4 34 4 38L J 1 5.5 7 34 4.5 38.5M H 1 2 3 41.5 2 43.5N K, L 5 5.5 9 38.5 6.5 45

Project Completion 45

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The Triangular Distribution Dialogue Box

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The Frequency Chart for Reliable’s Project Duration

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The Statistics Table for Reliable’s Project Duration

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The Percentiles Table for Reliable’s Project Duration

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Probability of Meeting the Project Deadline

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Probability of Meeting the Project Deadline

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Calculate Sensitivity Option

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The Sensitivity Chart for Reliable’s Project

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Cash Flow Management: Everglade Golden Years Co.

• Because of a temporary decline in business and some current or future construction costs, the company is facing some negative cash flows in the next few years.

• A long-term (10-year) loan can be taken now at a 7% annual interest rate.

• A series of short-term (1-year) loans can be taken as needed at 10% interest.

• The cash flows over the next 10 years are not certain. For each year, an estimate of the minimum, most-likely, and maximum cash flow has been made.

Question: How large of a long-term loan should Everglade take out now?

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Projected Net Cash Flows

YearProjected Net Cash Flow

(millions of dollars)

2003 –8

2004 –2

2005 –4

2006 3

2007 6

2008 3

2009 –4

2010 7

2011 –2

2012 10

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Linear Programming Spreadsheet Model

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Everglade Cash Flow Management Problem

LT Rate 7%ST Rate 10%

Start Balance 1 (all cash figures in millions of dollars)Minimum Cash 0.5

Cash LT ST LT ST LT ST Ending MinimumYear Flow Loan Loan Interest Interest Payback Payback Balance Balance2003 -8 6.649 0.851 0.500 >= 0.52004 -2 3.401 -0.465 -0.085 -0.851 0.500 >= 0.52005 -4 8.207 -0.465 -0.340 -3.401 0.500 >= 0.52006 3 6.493 -0.465 -0.821 -8.207 0.500 >= 0.52007 6 1.607 -0.465 -0.649 -6.493 0.500 >= 0.52008 3 0.000 -0.465 -0.161 -1.607 1.266 >= 0.52009 -4 3.699 -0.465 0.000 0.000 0.500 >= 0.52010 7 0.000 -0.465 -0.370 -3.699 2.965 >= 0.52011 -2 0.000 -0.465 0.000 0.000 0.500 >= 0.52012 10 0.000 -0.465 0.000 0.000 10.035 >= 0.52013 -0.465 0.000 -6.649 0.000 2.920 >= 0.5

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Spreadsheet Model for Applying Computer Simulation

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Everglade Cash Flow Management Problem When Applying Simulation

LT Rate 7%ST Rate 10%

Start Balance 1 (all cash figures in millions of dollars)Minimum Cash 0.5

Cash Flow (Triangular Distribution) Simulated BalanceMost Cash LT LT ST LT ST Before ST Ending Minimum

Year Minimum Likely Maximum Flow Loan Interest Interest Payback Payback ST Loan Loan Balance Balance2003 -9 -8 -7 -8.00 6.65 -0.35 0.85 0.50 >= 0.502004 -4 -2 1 -1.67 -0.47 -0.09 -0.85 -2.57 3.07 0.50 >= 0.502005 -7 -4 0 -3.67 -0.47 -0.31 -3.07 -7.01 7.51 0.50 >= 0.502006 0 3 7 3.33 -0.47 -0.75 -7.51 -4.89 5.39 0.50 >= 0.502007 3 6 9 6.00 -0.47 -0.54 -5.39 0.11 0.39 0.50 >= 0.502008 1 3 5 3.00 -0.47 -0.04 -0.39 2.60 0.00 2.60 >= 0.502009 -6 -4 -2 -4.00 -0.47 0 0 -1.86 2.36 0.50 >= 0.502010 4 7 12 7.67 -0.47 -0.24 -2.36 5.10 0.00 5.10 >= 0.502011 -5 -2 4 -1.00 -0.47 0 0 3.64 0.00 3.64 >= 0.502012 5 10 18 11.00 -0.47 0 0 14.17 0.00 14.17 >= 0.502013 -0.47 0 -6.65 0 7.05 7.05 >= 0.50

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Frequency Chart for Everglade’s Ending Balance

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Cumulative Chart for Everglade’s Ending Balance

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Financial Risk Analysis: Think-Big Development Co.

• The Think-Big Development Co. is a major investor in commercial real estate development projects.

• It has been considering taking a share in three large construction projects—a high-rise office building, a hotel, and a shopping center.

• In each case, three years will be spent in construction, they will retain ownership for another three years while establishing the property, and then sell the property in the seventh year.

• Proposal: Don’t take any share in the high-rise, take a 16.5% share of the hotel, and take a 13.11% share of the shopping center.

• Management wants risk analysis to be performed (with computer simulation) to obtain a risk profile (frequency distribution) of what the total NPV might turn out to be for this proposal.

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Estimated Cash Flows for 100 Percent Share

Hotel Project Shopping Center Project

Year Cash Flow ($1,000,000s) Year Cash Flow ($1,000,000s)

0 –80 0 –90

1 Normal (–80, 5) 1 Normal (–50, 5)

2 Normal (–80, 10) 2 Normal (–20, 5)

3 Normal (–70, 15) 3 Normal (–60, 10)

4 Normal (+30, 20) 4 Normal (+15, 15)

5 Normal (+40, 20) 5 Normal (+25, 15)

6 Normal (+50, 20) 6 Normal (+40, 15)

7 Uniform (200, 844) 7 Uniform (160, 600)

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Spreadsheet Model for Applying Computer Simulation

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A B C D E F G HProject Simulated

Cash FlowHotel Project: ($millions)

Construction Costs: Year 0 -80Year 1 -80 Normal -80 5 (mean, st. dev.)Year 2 -80 Normal -80 10 (mean, st. dev.)Year 3 -70 Normal -70 15 (mean, st. dev.)

Revenue per Share Year 4 30 Normal 30 20 (mean, st. dev.)Year 5 40 Normal 40 20 (mean, st. dev.)Year 6 50 Normal 50 20 (mean, st. dev.)

Selling Price per Share Year 7 522 Uniform 200 844 (min, max)

Shopping Center ProjectConstruction Costs: Year 0 -90

Year 1 -50 Normal -50 5 (mean, st. dev.)Year 2 -20 Normal -20 5 (mean, st. dev.)Year 3 -60 Normal -60 10 (mean, st. dev.)

Revenue per Share Year 4 15 Normal 15 15 (mean, st. dev.)Year 5 25 Normal 25 15 (mean, st. dev.)Year 6 40 Normal 40 15 (mean, st. dev.)

Selling Price per Share Year 7 387.5 Uniform 160 615 (min, max)

Think Big'sSimulated Cash Flow

($millions) ShareYear 0 -24.999 Hotel 16.50%Year 1 -19.755 Shopping Center 13.11%Year 2 -15.822Year 3 -19.416 Cost of Capital 10%Year 4 6.917Year 5 9.878Year 6 13.494Year 7 136.931

Net Present Value ($millions) 18.120

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The Normal Distribution Dialogue Box

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Risk Profile (Frequency Chart) for Think-Big

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Percentiles Chart for Think-Big

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Transcontinental Airlines Overbooking Problem

• Transcontinental has a daily flight (excluding weekends) from San Francisco to Chicago that is mainly used by business travelers.

• There are 150 seats available in a single cabin.• The average fare per seat is $300. This is a nonrefundable fare, so no-shows

forfeit the entire fare.• The fixed cost of operating the flight is $30,000.• The average number of reservation requests for this flight has been 195, with a

standard deviation of 30.• Only 80% of passengers with a reservation actually show up to take the flight,

so it makes sense to take more than 150 reservations (overbooking).• If more passengers arrive to take the flight than there are seats, some

passengers must be “bumped”. The total cost (including rebooking, travel vouchers, and lost goodwill) is estimated to be $450.

Question: How many reservations should Transcontinental accept for this flight?

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Spreadsheet Model for Applying Computer Simulation

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Transcontinental Airlines Overbooking

DataAvailable Seats 150

Fixed Cost $30,000Avg. Fare / Seat $300Cost of Bumping $450

Mean Standard Dev.Ticket Demand 195 Normal 195 30

Demand (rounded) 195

Reservations to Accept 190

Tickets ProbabilityPurchased to Show up

Number that Show 152 Binomial 190 80%

Number of Filled Seats 150 Ticket Revenue $45,000Number Denied Boarding 2 Bumping Cost $900

Fixed Cost $30,000Profit $14,100

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Binomial Distribution with Dynamic Option forNumber that Show

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Frequency Chart for Profit

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Frequency Chart for Number of Filled Seats

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Frequency Chart for Number Denied Boarding

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Choosing the Right Distribution

• A continuous distribution is used if any values are possible, including both integer and fractional numbers, over the entire range of possible values.

• A discrete distribution is used if only certain specific values (e.g., only some integer values) are possible.

• However, if the only possible values are integer numbers over a relatively broad range, a continuous distribution may be used as an approximation by rounding any fractional value to the nearest integer.

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A Popular Central-Tendency Distribution: Normal

• Some value most likely (the mean)• Values close to mean more likely• Symmetric (as likely above as below mean)• Extreme values possible, but rare

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A Popular Central-Tendency Distribution: Triangular

• Some value most likely• Values close to most likely value more common• Can be asymmetric• Fixed upper and lower bound

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A Popular Central-Tendency Distribution: Lognormal

• Some value most likely• Positively skewed (below mean more likely)• Values cannot fall below zero• Extreme values (high end only) possible, but rare

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The Uniform Distribution

• Fixed minimum and maximum value• All values equally likely

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A Three-Parameter Distribution: Weibull

• Random value above some number (location)• Shape > 0 (usually ≤ 10)• Shape < 3 becomes more positively-skewed (below mean more likely) until it

resembles exponential distribution (equivalent at Shape = 1)• Symmetrical at Shape = 3.25, becomes negatively skewed above that• Scale defines width

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A Three-Parameter Distribution: Beta

• Random value between 0 and some positive number (Scale)• Shape specified using two positive values (alpha, beta)• Alpha < beta: positively skewed (below mean more likely)• Beta < alpha: negatively skewed

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A Distribution for Random Events: Exponential

• Widely used to describe time between random events (e.g., time between arrivals)• Events are independent• Rate = average number of events per unit time (e.g., arrivals per hour)

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A Distribution for Random Events: Poisson

• Describes the number of times an event occurs during a given period of time or space• Occurrences are independent• Any number of events is possible• Rate = average number of events per unit of time, assumed constant over time

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Distribution for Number of Times an Event Occurs: Binomial

• Describes number of times an event occurs in a fixed number of trials (e.g., number of heads in 10 flips of a coin)

• For each trial, only two outcomes are possible• Trials independent• Probability remains the same for each trial

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Distribution for Number of Trials Until Event Occurs: Geometric

• Describes number of trials until an event occurs (e.g., number of times to spin roulette wheel until you win)

• Probability same for each trial• Continue until succeed• Number of trials unlimited

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Distribution for Number of Trials Until n Events Occur: Negative Binomial

• Describes number of trials until an event occurs n times• Same as geometric when Shape = n = 1• Probability same for each trial• Continue until nth success• Number of trials unlimited

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The Custom Distribution (Set of Discrete Values)

• Enter set of values with varying probabilities• For each discrete value, enter “Value” and “Prob.” (leave other boxes blank)• Clicking Enter clears boxes for entering next discrete value

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The Custom Distribution (Range of Discrete Values)

• Enter range of discrete values, each equally likely• Enter lower and upper end of range in “Value” and “Value2”• Enter the total probability for the whole set in “Prob.”• Enter the distance between discrete values in “Step”

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The Custom Distribution (Continuous Distribution)

• Enter the lower and upper end of range in “Value” and “Value2”• Enter the total probability for the range in “Prob.”• Leave “Step” blank for a continuous distribution• Drag the corners of the distribution graph up or down to change relative probabilities• Dragging corners may affect total probability. Click on “Rescale” to reset total probability.

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The Custom Distribution (Combination)

• Any combination of discrete values, ranges of discrete values, or continuous distributions can be entered

• Input each element, click on Enter, input next element, etc.• If cumulative probabilities do not add to 1, click on “Rescale”

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Historical Demand Data for the Financial Times

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Freddie the Newsboy HistoricalDemand

Data Day DataUnit Sale Price $2.50 1 62

Unit Purchase Cost $1.50 2 45Unit Salvage Value $0.50 3 59

4 65Decision Variable 5 50

Order Quantity 60 6 647 56

Simulation 8 51Simulated Demand 55 9 55Demand (rounded) 55 10 61

11 40Sales Revenue $137.50 12 47

Purchasing Cost $90.00 13 63Salvage Value $2.50 14 68

15 67Profit $50.00 16 67

17 6855 4156 4257 6458 4559 5960 70

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Procedure for Fitting the Best Distribution to Data

1. Gather the data needed to identify the best distribution to enter into an assumption cell.

2. Enter the data into the spreadsheet containing your simulation model.

3. Select the cell that you want to define as an assumption cell that contains the distribution that best fits the data.

4. Choose Define Assumption from the Crystal Ball toolbar, which brings up the Distribution Gallery dialogue box.

5. Click the Fit button on the dialogue box, which brings up the Fit Distribution dialogue box.

6. Use the Range box in this dialogue box to enter the range of the historical data in your worksheet.

7. Click the Next button in the dialogue box, which brings up the Second Fit Distribution Dialogue box.

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Procedure for Fitting the Best Distribution to Data

8. Use this dialogue box to specify which continuous distributions are being considered for fitting. (Discrete distributions are not considered by this procedure.)

9. Also use this dialogue box to select which ranking method should be used to evaluate how well a distribution fits the data. (The default is the chi-square test.)

10. Click OK, which brings up the comparison chart that identifies the distribution (including its parameter values) that best fits the data.

11. If desired, the Next Distribution button can be clicked repeatedly for identifying the other types of distributions that are next in line for fitting the data well.

12. After choosing the distribution that you want to use, click the Accept button while that distribution is showing. This will enter the appropriate parameters into the dialogue box for this distribution. Clicking OK then enters this distribution into the assumption cell.

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The First Fit Distribution Dialogue Box

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The Second Fit Distribution Dialogue Box

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Comparison Chart Showing Best Fit

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Decision Making with Decision Tables

• Many simulation models include at least one decision variable– Examples: Order quantity, Bid, Number of reservations to accept

• Crystal Ball can be used to evaluate a particular value of the decision variable by providing a wealth of output for the forecast cells.

• However, this approach does not identify an optimal solution for the decision variable(s).

• Trial and error can be used to try different values of the decision variable(s).– Run a simulation for each, and see which one provides the best estimate of the

chosen measure of performance.

• The Decision Table tool in Crystal Ball does this approach in a systematic way.

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Procedure for Defining a Decision Variable

1. Select the cell containing the decision variable.

2. If the cell does not already contain a value, enter any number into the cell.

3. Click on the Define Decision button in the Crystal Ball toolbar, which brings up the Define Decision Variable dialogue box.

4. Enter the lower and upper limit of the range of values to be simulated for the decision variable.

5. Click on either Continuous or Discrete to define the type of variable.

6. If Discrete is selected in Step 5, use the Step box to specify the difference between the successive possible values (not just those to be simulated).

7. Click on OK.

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Define Decision Variable Dialogue Box

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Decision Table: Specify Target Cell

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Decision Table: Specify Decision Variable(s) to Vary

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Decision Table: Specify Options

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The Decision Table for Freddie’s Order Quantity

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Overlay Chart Comparing Order Quantities of 55 and 60

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Trend Chart for Freddie’s Order Quantity

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Decision Variable for Reliable’s Bidding Problem

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Decision Table: Specify Target Cell

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Decision Table: Specify Decision Variable

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Decision Table: Specify Options

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Decision Table for Reliable’s Bid

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Decision Table for Transcontinental’sReservations to Accept

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Trend Chart for Transcontinental’sReservations to Accept

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Optimizing with OptQuest

• Crystal Ball includes a module called OptQuest that automatically searches for an optimal solution for a simulation model with any number of decision variables.

• The search is conducted by executing a series of simulation runs of leading candidates to be the actual optimal solution.

• The results of each run are used to determine the most promising remaining candidate to try next.

• A powerful search engine (based on genetic algorithms) conducts an intelligent and efficient search.

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Recommended Crystal Ball Run Preferences

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Recommended Crystal Ball Run Preferences

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Recommended Crystal Ball Run Preferences

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Procedure for Applying OptQuest

1. Formulate your simulation model on a spreadsheet.

2. Use Crystal Ball to complete your formulation by defining your assumption cells, forecast cells, and decision variables, as well as setting your run preferences.

3. Choose OptQuest from the Crystal Ball Tools menu and select New under the File menu.

4. Use the Decision Variable Selection dialogue box to select your decision variables.

5. Use the Constraints dialogue box to specify your constraints (if any).

6. Use the Forecast Selection dialogue box to specify the running time.

7. Use the Options dialogue box to specify the running time.

8. Select Start from the Run menu to run the optimization.

9. Choose Copy to Excel from the Edit menu to copy your results to your spreadsheet model.

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OptQuest for Freddie’s Problem:Selecting Variables and Specifying Constraints

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OptQuest for Freddie’s Problem:Specifying Objective and Running Time

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OptQuest Results for Freddie’s Problem

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Project Selection: Tazer Corp.

• Tazer Corp., a pharmaceutical manufacturing company, is beginning the search for a breakthrough drug.

• The following five potential R&D projects have been identified:– Project Up: Develop a more effective antidepressant that does not cause serious

mood swings.– Project Stable: Develop a drug that addresses manic depression.– Project Choice: Develop a less intrusive birth control method for women.– Project Hope: Develop a vaccine to prevent HIV infection.– Project Release: Develop a more effective drug to lower blood pressure.

• $1.2 billion is available (enough for only two or three projects).

Question: Which projects should Tazer Corp. undertake?

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Data for Tazer Corp. Project Selection

Revenue ($millions) if Successful

ProjectR&D Investment

($millions)Success

Rate MeanStandardDeviation

Up $400 50% $1,400 $400

Stable 300 35 1,200 400

Choice 600 35 2,200 600

Hope 500 20 3,000 900

Release 200 45 600 200

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Spreadsheet Model for Applying Computer Simulation

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Budget-Constrained Project Selection

R&DInvestment Success Revenue ($millions)

Project ($millions) Rate Mean St. Dev. Success? (if Successful) Profit DecisionsUp 400 50% 1,400 400 0.5 1,400 0.00 0

Stable 300 35% 1,200 400 0.35 1,200 0.00 0Choice 600 35% 2,200 600 0.35 2,200 0.00 0Hope 500 20% 3,000 900 0.2 3,000 0.00 0

Release 200 45% 600 200 0.45 600 0.00 0

Invested 0 Total profit ($millions) 0.00<=

Budget 1,200

$millions if Successful(Normal Distribution)

Estimated Revenue

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Binary Decision Variables

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OptQuest for Tazer’s Project Selection:Selecting Variables and Specifying Constraints

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OptQuest for Freddie’s Problem:Specifying Objective and Running Time

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OptQuest Results for Tazer’s Project Selection

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Frequency Chart for Tazer’s Total Profit

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Maximizing Probability (Profit ≥ $100 million)

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Maximizing Probability (Profit ≥ $100 million)

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Frequency Chart for Tazer’s Project Selection

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Monte-Carlo Simulation with Crystal Ball

1. Setup SpreadsheetBuild a spreadsheet that will calculate the performance measure (e.g., profit) in terms of the inputs (random or not). For random inputs, just enter any number.

2. Define Assumptions (Random Variables)Define which cells are random and what distributions they should follow.

3. Define Forecast (Output or Performance Measure)Define which cell(s) you are interested in forecasting (typically the performance measure, e.g., profit).

4. Choose Number of TrialsSelect the number of trials. If you would later like to generate the Sensitivity Analysis chart, choose “Sensitivity Analysis” under Options in Run Preferences.

5. Run SimulationRun the simulation. If you would like to change parameters and re-run the simulation, you should “reset” the simulation (click on the “Reset Simulation button on the toolbar or in the Run menu) first.

6. View ResultsThe forecast window showing the results of the simulation appears automatically after (or during) the simulation. Many different results are available (frequency chart, cumulative chart, statistics, percentiles, sensitivity analysis, and trend chart). The results can be copied into the worksheet.

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The Crystal Ball Toolbar

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Freddie the Newsboy

• Freddie runs a newsstand in a prominent downtown location of a major city.

• Freddie sells a variety of newspapers and magazines. The most expensive of the newspapers is the Financial Journal.

• Cost data for the Financial Journal:– Freddie pays $1.50 per copy delivered.– Freddie charges $2.50 per copy.– Freddie’s refund is $0.50 per unsold copy.

• Sales data for the Financial Journal:– Freddie sells anywhere between 40 and 70 copies a day.– The frequency of the numbers between 40 and 70 are roughly equal.

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Step #1 (Setup Spreadsheet)

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Freddie the Newsboy

DataUnit Sale Price $2.50

Unit Purchase Cost $1.50Unit Salvage Value $0.50

Decision VariableOrder Quantity 60

Simulation Minimum MaximumSimulated Demand 55 Uniform 40 70Demand (rounded) 55

Sales Revenue $137.50Purchasing Cost $90.00

Salvage Value $2.50

Profit $50.00

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Step #2 (Define Assumptions)

• Select a cell that contains a random variable.

• Click on the “Define Assumptions” button in the toolbar (or in Cell menu):

• Select the type of distribution.

• Provide the parameters of the distribution.

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Step #2 (Define Assumptions)

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Step #2 (Define Assumptions)

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Step #3 (Define Forecast)

• Select the cell that contains the output variable to forecast.

• Click on the “Define Forecast” button in the toolbar (or in the Cell menu):

Fill in the Define Forecast dialogue box:

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Step #4 (Choose Number of Trials)

• Click on the “Run Preferences” button in the toolbar (or in the Run menu):

• Select the number of trials to run:

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Step #5 (Run Simulation)

Click on the “Start Simulation” button in the toolbar (or Run in the Run menu):

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Step #6 (View Results)

The results of the simulation can be viewed in a variety of different ways (frequency chart, cumulative chart, statistics, and percentiles). Choose different options under the View menu in the forecast window.

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Step #6 (View Results)

The results can be copied into a worksheet or Word document (choose Copy under the Edit menu in the simulation output window).

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Step #6 (View Results)

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Step #6 (View Results)

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Certainty that Profit ≥ $40

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Fitting a Distribution

• Crystal Ball can be used to “fit” a distribution to data.

• The following data has been collected for the previous 100 phone calls to a mail-order house:

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Phone Data

Arrival Interarrival Length of Call Interarrival Length of CallCustomer # (minutes) Time (minutes) Time (minutes)

1 8.22 8.22 3.77 Averages 2.004 4.512 12.25 4.03 4.533 12.27 0.02 4.044 16.26 3.98 3.70 Simulation 2 45 18.06 1.81 5.386 18.87 0.81 4.367 23.46 4.58 4.418 23.53 0.08 5.149 28.73 5.20 4.76

10 30.56 1.83 4.6895 194.02 0.28 4.2696 195.48 1.46 3.3797 195.87 0.38 4.4598 196.84 0.98 5.0699 197.81 0.97 5.20

100 200.43 2.61 4.25

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Using Crystal Ball to Fit Data to a Distribution

1. Select a spreadsheet cell for which you want to fit a distribution.

2. Choose Define Assumption.

3. Click the Fit button, then select the source of the fitted data.

4. Click the Next button, then select the distributions to try to fit.

5. Click OK.

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Best Fit for the Interarrival Time

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Best Fit for the Service Time