ARUNABHA SAHA Final Exam: Large Instrument Manufacturer, Inc

ARUNABHA SAHA

Final Exam: Large Instrument Manufacturer,

Inc.

Recommendations

Our intial recommendation to LIM at this point is to pursue the alternative that involves training UDC to handle Beta failures.

We further recommend a subsequent analysis taking into account much of the information from the first round and assessing the uncertainties.

Outline

Decision Tools UsedFraming

Decision Hierarchy Decision Diagram

Deterministic Analysis NPV of Alternatives Deterministic Sensitivity

Probabilistic Analysis Decision Tree Probabilistic Dominance

Appraisal Sensitivity Analysis Value of Information and

Control Recommendations for future

analysis

Decision Hierarchy

• Policy is to be Risk-Neutral in this Range.• Making a profit is the end goal of this exercise.

Selling a product but not making a profit is not a desirable option.

• ROE-II will be sold only for a period of 5 years hence any strategy should be optimized for the next 5 year period.Policy

Strategy

Tactics

To sell ROE-II to UDC or not ?

Eliminate or mitigate the risk associated with servicing that caused the bad experience with ROE-II

Determine the uncertainties early and how they affect the eventual outcome.

Concentrate on evaluating the important uncertainties before making the decision

Attempt to control the important uncertainties by means at our disposal

Decision Diagram

Num of Αlpha

Failures

Value

Train UDC engineers OR

Outsource

Continue with Existing

Arrangement

Total Beta Failure Cost

Num of Beta

FailuresCost of Alpha

Failures

Cost of Beta

Failures

Units Sold

Total Revenue

Total Alpha Failure Cost

Sell ROE-II to UDC

Training Cost

Initial Cost (Training + Installation)

NPV of Each Strategy at Base Case

Existing Train UDC Contract IPX Do not Sell

-150

-100

-50

0

50

100

150

200

-105

178

150

-8

N P V

in

$ 1 0 0 0 s

We can see that in the base case • “Training UDC” is the best option • Contracting with IPX is also an attractive• Existing option is far worse than either training or

contracting

Comparison of Alternatives (100% range)

Existing

Train WDC

Contract IPX

Do not Sell

-800 -600 -400 -200 0 200 400 600 800

Range of Profit for the 4 Alternatives

Profit in $1000s

Mid: 147K

Mid:178K

Mid:-105K

The Key takeaway here is that the “Training UDC” option is the more profitable option in the base case. However the “Train UDC” option also has a higher range (-88, 595) than Contract IPX(0, 347). This “can” imply more risk associated with the “Training WDC” Option

Assessing Important Uncertainties (95%)

Alpha Repair Cost

Units Sold

Num of Alpha Failures

Num of Beta Failures

Beta Repair Cost

-$300.00 -$250.00 -$200.00 -$150.00 -$100.00 -$50.00 $0.00

Existing Arrangement

Avg Cost

Num of Alpha Failures

Units Sold

Training Cost

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00

Train UDC

From the tornado diagrams above we observe that. • 4 Uncertainties to be assessed for Alternative 1 (Existing arrangement). • 3 Uncertainties for Alternative 2 (Training UDC for servicing)• 1 Uncertainty for Alternative 3 (Contract with IPX)• Alternative 4(Do not Sell) has no uncertainties

Probabilistic AssessmentDiscretizing (Equal Areas – Shortcut)

Low(0-25%) Mid(25-75%) High(75-100)

Avg Repair Cost(alpha)8.91 9.95 12.5

Avg Repair Cost (Beta)6.92 8 9.5

Num Alpha failures (per yr) 11.90% 15.00% 19.00%

Num Beta failures (per yr) 64.50% 70.00% 75.50%

Units Sold 24.5 30 49.5

Training Cost 3.55 8 12.44

We divided the continuous probabilities into the range {0-25%, 25-75%, 75-100%}.We then arrived at the the values in the table above as the cumulative mean over the individual ranges.We will use these values to further refine our model.

Decision Tree (Condensed)

Value Measure U-Value

Existing Alternative-116.92 -116.92

Train UDC195.91 195.91

195.9063 Contract IPX161.75 161.75

Do not Sell-8.00 -8.00

• Alternative 2 (Train UDC) has the best CE and is the initial recommendation if there is no room for further analysis

• We do recommend further analysis on uncertainties to assess their impact and devise plans to control them or mitigate their impact

Probabilistic Dominance

-400 -300 -200 -100 0 100 200 300 400 500 6000.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

Train UDC

Contract IPX

Do not Sell

Existing

Profit in $1000s

This graph shows the CDF of the Certain Equivalent of 4 alternatives

Dominance Contd..Type Dominance Exists Comments/Insight

Deterministic No There is always a point where any Alternative X is greater than any other

Alternative Y.Therefore you are never 100% sure that the alternative you select is better than

any other for the entire universe of possibilities

1st Order Yes“Train UDC” Dominates “Existing Option”

This implies that “Train UDC” is a better alternative than the “Existing” alternative

over the entire probability space.We can discard “Existing” option for

further analysis for almost all practical cases (See note on slide)

2nd Order Yes“Train UDC” Dominates “Contract with IPX”

and “Do not Sell”“Contract IPX” Dominates “Do not Sell”

Value of Information

Units Sold Training Cost Num of Alpha Failures0

5

10

15

20

25

30

35

Value of Information

14.31

28.6

6.28

• If LIM is able to get information on “Training Cost” in advance then $28.6K is the highest it should be willing to pay

• Similarly $14.31K for information on “Units Sold” and $6.28K for Alpha failures

Value of Control (1 degree)

Units Sold = 50 Training Cost = $12.44K146.5

147147.5

148148.5

149149.5

150150.5

151151.5

VoC

VoC

If LIM can control the value of “Units Sold” to 50 units then $151.09K is the most it should be willing to pay, likewise $148.28K for pegging Training Cost to $12.44K

151.09

148.28

Sensitivity Analysis: Unit Cost

Low Base High0

50

100

150

200

250

300

350

400

142.625

175.625

289.75

142.625

175.625

347

Closed/Open Loop Sensitivity Analysis (Units Sold)

Open Loop

Closed Loop

Train UDC

Train UDC

ContractIPX

Sensitivity Analysis (Training Cost)

Low Base High0

50

100

150

200

250

300

350

400

344.1875

196.0625

47.3125

344.1875

196.063

161.75

Closed/Open Loop Sensitivty on Training Cost

Open

Closed

Train UDC

Train UDC

ContractIPX

Sensitivity Analysis— Num of Alpha Failures

Low Base High0

50

100

150

200

250

300

248.375

199.313

161.75

248.375

199.313

136.625

Sensitivity to Num of Alpha Repairs

Closed

Open

Contract IPX

Train UDC

Train UDC

Train UDC

Sensitivity Analysis— Risk Aversion

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450.001

0.01

0.1

1

Sensitivity To Risk Aversion

CE

Risk Aversion Coefficient (γ)

CE

The decision does not change with change in risk aversion and Train UDC is the best option

Conclusions

Items for a second-round assessment Determine Value of Information and VoC for multiple degrees

e.g (Units Sold & Training Cost) Identify tools that can effectively provide Control or Information

on the uncertainty parameters and evaluate their effectiveness.

Revaluate Risk-Preference Study if options be used as a tool to mitigate risk ? Instead

of Contracting with IPX, buy the option to contract with IPX. Evaluate an insurance purchase for uncertainties that cannot

be controlled.

F U L L D E C I S I O N T R E E

Appendix

Decision Tree (Train WDC Part 1)


0.25 Alpha Failures Low291 291

0.25 Units Sold Low 0.5 Alpha Failures Mid248 248

249 2490.25 Alpha Failures High

209 209


0.25 Training Low 0.5 Units Sold Base 0.5 Alpha Failures Mid312 312

344.188 344.188 309 3090.25 Alpha Failures High

256 256


0.25 Units Sold High 0.5 Alpha Failures Mid515 515

509.75 509.750.25 Alpha Failures High

422 422

Decision Tree: Train WDC Part 2




100 100


0.5 Training Base 0.5 Units Sold Base 0.5 Alpha Failures Mid179 179

196.063 196.063 175.5 175.50.25 Alpha Failures High

122 122




202 202

Decision Tree: Train WDC Part 3




-9 -9


0.25 Training High 0.5 Units Sold Base 0.5 Alpha Failures Mid46 46

47.3125 47.3125 42.5 42.50.25 Alpha Failures High

-11 -11




-18 -18

Decision Tree: Contract IPX


0.25 Units Sold Low-15 -15

0.5 Units Sold Medium150 150

161.75

0.25 Units Sold High347 347

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ARUNABHA SAHA Final Exam: Large Instrument Manufacturer, Inc