04_Decision_Analysis_Part2-2.pdf

8/17/2019 04_Decision_Analysis_Part2-2.pdf

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DECISION ANALYSIS – PART 2

Topics Outline

• Developing a Decision Model

• Using the Precision Tree Add-In

Developing a Decision Model

SciTools Bidding

SciTools Incorporated, a company that specializes in scientific instruments, has been invited to

make a bid on a government contract. The contract calls for a specific number of these

instruments to be delivered during the coming year. The bids must be sealed, so that no company

knows what the others are bidding, and the low bid wins the contract.

SciTools estimates that it will cost $5000 to prepare a bid and $95,000 to supply the instruments

if it wins the contract. On the basis of past contracts of this type, SciTools believes that the

possible low bids from the competition, if there is any competition, and the associated

probabilities are those shown in following table.

Low Bid Probability

Less than $115,000 0.2

Between $115,000 and $120,000 0.4

Between $120,000 and $125,000 0.3

Greater than $125,000 0.1

In addition, SciTools believes there is a 30% chance that there will be no competing bids.

Objective: To develop a decision model that finds the EMV for various bidding strategies and

indicates the best bidding strategy.

Solution:

1. Describe the decisions available to SciTools.

SciTools has two basic strategies: submit a bid or do not submit a bid. If SciTools submits a bid,

then it must decide how much to bid. Based on the cost to SciTools to prepare the bid and supplythe instruments, there is clearly no point in bidding less than $100,000 – SciTools wouldn’t make

a profit even if it won the bid. (Actually, this isn’t totally true. Looking ahead to future contracts,

SciTools might make a low bid just to “get in the game” and gain experience. However, we

won’t consider such a possibility here.) Although any bid amount over $100,000 might be

considered, the data in the table above suggest that SciTools might limit its choices to $115,000,

$120,000, and $125,000.


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2. Describe the possible outcomes and the probabilities of these outcomes.

The only source of uncertainty is the behavior of the competitors – will they bid, and if so, how

much? We assume that SciTools has been involved in similar bidding contests in the past and

can reasonably predict competitor behavior from past competitor behavior. The result of such

prediction is the assessed probability distribution in the table and the 30% estimate of theprobability of no competing bids.

3. Build a value model that transforms decisions and outcomes into monetary values.

If SciTools decides not to bid, its monetary value is $0 – no gain, no loss.

If it makes a bid and is underbid by a competitor, it loses $5000, the cost of preparing the bid.

If it bids B dollars and wins the contract, it makes a profit of B minus $100,000 (that is, B dollars

for winning the bid, minus $5000 for preparing the bid and $95,000 for supplying the instruments).

For example, if it bids $115,000 and the lowest competing bid, if any, is greater than $115,000,

then SciTools wins the bid and makes a profit of $15,000.

Here is the corresponding payoff table.

SciTools’ Bid($1000s)

Monetary Value Probability thatSciTools Wins

Probability thatSciTools LosesSciTools Wins SciTools Loses

No Bid NA 0 0.00 1.00115 15K –5 0.86 0.14120 20K –5 0.58 0.42125 25K –5 0.37 0.63

The rightmost columns show the probabilities that SciTools wins or loses the bid for each possible

decision. For example, if SciTools bids $120,000, then it wins the bid if there are no competing bids

(probability 0.3) or if there are competing bids (probability 0.7) and the lowest of these is greater

than $120,000 (probability 0.3 + 0.1). Therefore, the total probability that SciTools wins the bid is

0.3 + 0.7(0.3 + 0.1) = 0.58

Then, the probability that SciTools loses the bid is 1 – 0.58 = 0.42.

4. Develop a risk profile for SciTools’s decision to bid $120,000.

If SciTools bids $120,000, there are two monetary values possible, a profit of $20,000 and a loss

of $5000, and their probabilities are 0.58 and 0.42, respectively. The corresponding risk profile is

a spike chart with two spikes, one above –$5000 with height 0.42 and one above $20,000 with

height 0.58.


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5. What is the risk profile for SciTools’s decision not to bid?

If SciTools decides not to bid, there is a sure monetary value of $0 – no profit, no loss.

Therefore, the risk profile for the “no bid” decision has a single spike above $0 with height 1.

6. Calculate the EMV for each decision.

Each EMV (other than the EMV of $0 for not bidding) is a sum of products of monetary

outcomes and probabilities:

SciTools’ Bid EMV Calculation EMV

No bid 0(1) $0

$115,000 15,000(0.86) + (−5,000)(0.14) $12,200

$120,000 20,000(0.58) + (−5,000)(0.42) $9,500

$125,000 25,000(0.37) + (−5,000)(0.63) $6,100

7. How much should SciTools bid according to the EMV criterion?

If SciTools uses the EMV criterion for making its decision, it should bid $115,000.

The EMV from this bid, $12,200, is the largest of the EMVs.

8. Interpret the meaning of the EMV for this bid.

If SciTools bids $115,000, its EMV is $12,200. However, SciTools will definitely not earn a

profit of $12,200. It will earn $15,000 or it will lose $5000. The EMV of $12,200 represents only

a weighted average of these two possible values.


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9. Develop the corresponding decision tree.

The company first makes a bidding decision, then observes what the competition bids, if anything,and finally receives a payoff. The folding-back process is equivalent to the calculations of EMVs in (6).

There are often equivalent ways to structure a decision tree. One alternative for this example isshown below.

The company first decides whether to bid at all.

If the company does not make a bid, the profit is a sure $0.


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Otherwise, the company then decides how much to bid. Note that if the company decides to bid,it incurs a sure cost of $5000, so this cost is placed under the Bid branch.

Once the company decides how much to bid, it then observes whether there is any competition.If there isn't any, the company wins the bid for sure and makes a corresponding profit.

Otherwise, if there is competition, the company eventually discovers whether it wins or loses thebid, with the corresponding probabilities and payoffs.

Note that these payoffs are placed below the branches where they occur in time. Also, thecumulative payoffs are placed at the ends of the branches. Each cumulative payoff is the sum of allpayoffs on branches that lead to that end node.

The folding-back procedure is somewhat more complex than it was for the smaller tree.To illustrate, the EMVs above a selected few of these nodes are calculated as follows:

Node 7: EMV = 20000(0.40) + (−5000)(0.60) = $5000 (uses monetary values from end nodes)

Node 4: EMV = 20000(0.30) + (5000)(0.70) = $9500 (uses monetary value from an end nodeand the EMV from node 7)

Node 2: EMV = max(12200, 9500, 6100) = $12,200 (uses EMVs from nodes 3, 4, and 5)

Node 1: EMV = max(0, 12200) = $12,200 (uses monetary value from an end node and EMVfrom node 2)

The results are the same, regardless of whether you use the table of EMVs developed in (6), thesmaller decision tree, or the larger one, because they all calculate the same EMVs in equivalent ways.

10. Does the decision made with the EMV criterion guarantee a good outcome for the company?

Acoording to the EMV criterion, the company should bid $115,000, with a resulting EMV of$12,200. This decision is not guaranteed to produce a good outcome for the company.For example, the competition could bid less than $115,000, in which case SciTools would lose $5000.

Alternatively, the competition could bid more than $120,000, in which case SciTools would bekicking itself for not bidding $120,000 and gaining an extra $5000 in profit.

Unfortunately, in problems with uncertainty, there is virtually never a guarantee that the optimaldecision will produce the best result. The only guarantee is that the EMV-maximizing decision isthe most rational decision, given the information known when the decision must be made.


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11. Use the following spreadsheet model to describe how the optimal EMV changes as theprobability of no competing bid changes. (See SciTools_Bidding_Spreadsheet_Model.xlsx.)

In the data table for sensitivity analysis, the probability of no competing bid is allowed to vary

from 0.2 to 0.7. The data table shows that the optimal EMV increases over this range from

$12,200 to $16,900.

The third column of the data table shows that the $115,000 bid is optimal for small values of the

input, but that a $125,000 bid becomes optimal for larger values.


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Using the Precision Tree Add-In

The PrecisionTree, developed by Palisade Corporation, is an Excel add-in which can be used to

draw and label a decision tree, perform the folding-back procedure and sensitivity analysis on

key input parameters.

1. Run the PrecisionTree Add-In

With Palisade DecisionTools suite already installed, there are two options to run the PrecisionTree:

1. If Excel is not currently running, you can launch Excel and PrecisionTree by clicking on the

Windows Start button and selecting the PrecisionTree item from the Palisade Decision Tools

group in the list of Programs.

2. If Excel is currently running, the first procedure will launch PrecisionTree on top of Excel.

You will know that PrecisionTree is ready for use when you see its tab and the associated ribbon:

If you want to unload PrecisionTree without closing Excel, you can do so from its Utilitiesdropdown list in the Tools group.

2. Build the Decision Tree

Use the file SciTools_Bidding.xlsx to build your tree.Use the file SciTools_Bidding_Finished.xlsx as a reference.

Click on the Decision Tree button on the PrecisionTree ribbon, and then select cell A14 belowthe input section to start a new tree. In the dialog box, enter a name for the tree, e.g. SciToolsBidding, and click on OK. The beginnings of a tree appears:

To obtain decision nodes and branches, select the (only) triangle end node to open the dialog box.Click on the green square to indicate that you want a decision node, and fill in the dialog box asshown below.


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Then click on the Branches (2) tab and supply labels for the branches under Name(No for Branch #1 and Yes for Branch #2).

Click OK. The tree expands. Under the “Yes” branch, enter the following link to the bid cost cell:= – B4 (Note: It is negative to reflect a cost .)

The top branch is completed; if SciTools does not bid, there is nothing left to do.So click on the bottom end node (the triangle), following SciTools's decision to bid, and proceedas in the previous step to add and label the decision node and three decision branches for theamount to bid. (By default, you get two branches. Click on Add to get additional branches.)The tree to this point should appear as follows.


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Note that there are no monetary values below these decision branches because no immediate payoffs or costs are associated with the bid amount decision.

Using the same procedure (and keeping in mind the finished tree you eventually want),

create probability (chance) nodes extending from the “bid $115,000” decision.You should have the skeleton shown below.

Right-click on the leftmost probability node and click on Copy SubTree.Then right-click on either end node below it and click on Paste SubTree.Do this again with the other end node.

You should now have a tree that is structurally the same as the completed tree, but theprobabilities and monetary values on the probability branches are incorrect.

Each probability branch has a value above and below the branch.The value above is the probability (the default values make the branches equally likely),and the value below is the monetary value (the default values are 0).You can enter any values or formulas in these cells (the cells with black font only!), exactly asyou do in typical Excel worksheets.

It is a good practice to enter cell references, not numbers, whenever possible.In addition, range names can be used instead of cell addresses.


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3. Find the optimal decision strategy

A comparison of the decision tree that was created manually and the tree from PrecisionTreeindicates virtually identical results. The best decision strategy is now indicated by the TRUE andFALSE labels above the decision branches (rather than the notches we entered by hand).

Each TRUE corresponds to the optimal decision out of a decision node, whereas each FALSEcorresponds to a suboptimal decision.

Therefore, to find the optimal decision strategy in any PrecisionTree tree, follow the TRUE labels.In this case, the company should bid, and its bid amount should be $115,000.

You can also build a subtree for the optimal decision by choosing Policy Suggestion from theDecision Analysis dropdown list and filling in the resulting dialog box as shown below.

The Policy Suggestion shows only the subtree corresponding to the optimal decision strategy:


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4. Obtain a risk profile

To obtain a graphical risk profile of the optimal decision select Risk Profile from the DecisionAnalysis dropdown list and fill in the resulting dialog box as shown below.

As the risk profile indicates, there are only two possible monetary outcomes if SciTools bids$115,000. It either wins $15,000 or loses $5000, and the former is much more likely.(The associated probabilities are 0.86 and 0.14, respectively.)


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5. Perform Sensitivity AnalysisClick on PrecisionTree's Sensitivity Analysis button. This brings up the following dialog box.

It has a lot of options and it takes some practice and experimenting to get used to them.Here are the main options and how to use them.

– The Analysis Type dropdown list allows you to vary one input (One-Way Sensitivity)or two inputs (Two-Way Sensitivity) simultaneously.

– The Starting Node dropdown list lets you choose any node in the tree, and the sensitivityanalysis is then performed for the EMV from that node to the right. In other words, it assumesyou have gotten to that node and are now interested in what will happen from then on.

– You add inputs to vary in the Inputs section. When you add an input to this section, you canspecify the range over which you want it to vary. For example, you can vary it by plus or minus 10%in 10 steps from a selected base value, as we did for the production cost in cell B5, or you can

vary it from 0 to 0.6 in 12 steps, as we did for the probability of no competing bids in cell B7.

– The Include Results checkboxes allow you to select up to four types of charts, depending on thetype of sensitivity analysis. (The bottom two options are disabled for a two-way sensitivity analysis.)

– By default, the results are presented in a new workbook. If you would rather have them in thesame workbook as the model, click on the PrecisionTree Utilities dropdown arrow, selectApplication Settings, and select Active Workbook from the Place Reports In option.(This is a global setting. It will take effect for all future PrecisionTree analyses.)


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6. Interpretion of a Strategy Region Chart

In strategy region charts for one-way sensitivity analysis, the primary interest is in where(or whether) lines cross. This is where decisions change. Here are two examples.

The following one-way sensitivity chart shows how the EMV varies with the production cost forboth of the original decisions (bid or don't bid). This type of chart is useful for seeing whether theoptimal decision changes over the range of the input variable. It does so only if the two lines cross.In this particular graph it is clear that the “Bid” decision dominates the “No bid” decision over theselected production cost range.

The following chart was constructed by choosing cell C29 as the cell to analyze. This is the optimalEMV for the problem, given that the company has decided to place a bid. The sensitivity chartindicates how the EMV varies with the probability of no competing bid for each of the three bidamount decisions. The $115,000 bid is best for most of the range, but when the probability of nocompeting bid is sufficiently large (about 0.55), the $120,000 bid becomes best (by a small margin.)


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A one-way sensitivity analysis varies only one input at a time.A two-way sensitivity shows how the selected EMV varies as each pair of inputs varies simultaneously.Here is the result from analyzing the EMV in cell C29 with this option, using the same inputs asbefore.

For each of the possible values of production cost and the probability of no competitor bid,this chart indicates which bid amount is optimal.(By choosing cell C29, we are assuming SciTools will bid; the only question is how much.)

As you can see, the optimal bid amount remains $115,000 unless the production cost and theprobability of no competing bid are both large.

Then it becomes optimal to bid $120,000 or $125,000. This makes sense intuitively.

As the probability of no competing bid increases and a larger production cost must be recovered,it seems reasonable that SciTools should increase its bid.


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7. Interpretion of a Tornado Chart

A tornado chart shows how sensitive the EMV of the optimal decision is to each of the selectedinputs over the specified ranges. The length of each bar shows the change in the EMV in eitherdirection, so inputs with longer bars have a greater effect on the selected EMV.(If you checked the next-to-bottom checkbox in Sensitivity Analysis dialog box, the lengths of

the bars would indicate percentage changes from the base value.)The bars are always arranged from longest on top to shortest on the bottom – hence the nametornado chart. Here it is apparent that production cost has the largest effect on EMV, and bid costhas the smallest effect.

8. Interpretion of a Spider Chart

Finally, a spider chart shows how much the optimal EMV varies in magnitude for variouspercentage changes in the input variables. The steeper the slope of the line, the more the EMV is

affected by a particular input.

It is again apparent that the production cost has a relatively large effect, whereas the other twoinputs have relatively small effects.


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Notes:

1. Allowable Entries

You should enter your own probabilities and monetary values only in the cells with black font.

2. Sum of probabilities

PrecisionTree does not enforce the rule that probabilities on branches leading out of a node mustsum to 1. You must enforce this rule with appropriate formulas.

3. Entering monetary values and probabilities

A good practice is to calculate all of the monetary values and probabilities that will be needed inthe decision tree in some other area of the spreadsheet. Then the values needed next to the treebranches can be created with simple linking formulas.

4. Folding-back procedure

Note that you do not have to perform the folding-back procedure manually. In addition, if youchange any of the inputs, the tree reacts automatically. For example, try changing the bid cost incell B4 from $5000 to some large value such as $20,000. You will see that the tree calculationsupdate automatically, and the best decision is then not to bid, with an associated EMV of $0.

5. Values at end nodes

There are two values following each triangle end node.The bottom value is the sum of all monetary values on branches leading to this end node.The top value is the probability of getting to this end node when the optimal strategy is used.This explains why many of these probabilities are 0; the optimal strategy will never lead to theseend nodes.

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