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An Engineering Company has just been awarded a development contract by the US Army Aviation Systems Command to design, develop, and demonstrate critical components of a new rotor system. The system will be part of the Heavy Lift Helicopter program which is currently receiving much attention in the industry.An integral part of the rotor system is the blade spar. The blade spar is a metal tube which runs the length of and provides strength to the helicopter blade. Due to the unusual length and size of the Heav Lift Helicopter blade, Ventron is unable to produce a single - piece blade spar of the required dimensions, using existing extrusion equipment and material.The engineering department has prepared two alternatives for developing the blade spar:sectioningimprovement of the extrusion process.Ventron is faced with a decision as to which process it should select.Sectioning ( true and tried, guaranteed to work ) This process involves joining several shorter lengths of extruded metal into a blade spar of sufficient length. The work will require extensive rework and testing over a 1 2 - month period at a cost of $ 1 5 0 , 0 0 0 per month. It will produce an adequate blade spar. However, it merely represents an extension of existing technology.Extrusion ( two parts, not guaranteed to work, groundbreaking ) To extrude the blade spar as a single piece, it will be necessary tomodify the extrusion press at a monthly cost of $ 1 6 0 , 0 0 0 and improve the material used at a monthly cost of $ 5 0 , 0 0 0 Each of these steps would require six months of steady work. If successful, this process would produce a blade spar of superior quality at a lower overall cost. Unfortunately, as opposed to sectioning , there is some risk that Ventron will be unable to perfect the process.RiskWhile the sectioning process is guaranteed to work, proceeding with extrusion involves risk.Material DevelopmentAfter studying the technical problems, the engineering department feels there is a nine in ten chance of perfecting the material. However, the other possibility ( a one in ten chance ) is that at the end of the six - month development effort, it will know that a satisfactory material cannot be developed, and it will have to rely on sectioning to meet its time and cost constraints.Press ModificationThe engineers believe there is a three in four chance of successfully modifying the press, but a one in four chance that at the end of a six - month press development project, the extrusion process will have to be abandoned, because a press with the necessary capabilities will be shown to be infeasible.Time ConstraintsDevelopment of the blade spar must be completed within 1 8 months to avoid holding up the rest of the contract. If necessary, It has also been determined that the sectioning work could be done on an accelerated basis in a six - month period at a monthly cost of $ 4 0 0 , 0 0 0 . DilemmaThe Director of Engineering, Dr . Smith, is most interested in the opportunity provided by this contract to explore new technology in the extrusion process. She feels that if Ventron is successful in producing the blade spar as a single piece Ventron's reputation in the field will be greatly enhanced. In addition, Ventron would be able to complete development of the blade spar well under budget.After a preliminary review of the problem, Ventron's President, Bill Walters, has not yet reached a final decision. Like Dr . Smith, he is intrigued by the possibility of successfully developing the extrusion process.He feels that this would give Ventron an excellent chance at some additional contracts. He is concerned, however, about the possibility of wasting money on unsuccessful development or of being forced to do sectioning on an accelerated basis.Ventron's contract with the Army is for a fixed total amount spread over several years. Walters wants to minimize the expenditures on the blade spar portion to free up money for technical developments on other components of the rotor system, which would improve Ventron's position for future business, both defense and commercial.Question 1 .  Map out a decision tree using the probabilities above. Calculate the terminal cost for each branch . 2 . Fold back from the terminal nodes. For each chance node, calculate an EMV and for each decision box, choose from the available EMVs . 3 . Based on EMV criterion, determine what you would recommend to Dr . Smith and President Waters if you were strictly an EMV maximizer. Your decision must allow Ventron to meet all of the constraints. Do not consider unfeasible solutions . 4 . Comment on how risk aversion may influence the decision making process . 5 . Keeping all other variables unchanged, what if the probability of success for PM was 6 0 % Instead of 7 5 % , does that change your decision making? At what range of PM success would you recommend extrusion? 6 . Keeping all other variables unchanged, what if the probability of success for MD was 8 0 % instead of 9 0 % , does that change your decision making? At what range of MD success would you recommend extrusion? 7 . What if the cost of NS were $ 2 0 0 a month Instead of $ 1 5 0 ? Does that change your decision making?

Question:

An Engineering Company has just been awarded a development contract by the US Army Aviation Systems Command to design, develop, and demonstrate critical components of a new rotor system. The system will be part of the Heavy Lift Helicopter program which is currently receiving much attention in the industry.An integral part of the rotor system is the blade spar. The blade spar is a metal tube which runs the length of and provides strength to the helicopter blade. Due to the unusual length and size of the Heav Lift Helicopter blade, Ventron is unable to produce a single - piece blade spar of the required dimensions, using existing extrusion equipment and material.The engineering department has prepared two alternatives for developing the blade spar:sectioningimprovement of the extrusion process.Ventron is faced with a decision as to which process it should select.Sectioning ( true and tried, guaranteed to work ) This process involves joining several shorter lengths of extruded metal into a blade spar of sufficient length. The work will require extensive rework and testing over a 1 2 - month period at a cost of $ 1 5 0 , 0 0 0 per month. It will produce an adequate blade spar. However, it merely represents an extension of existing technology.Extrusion ( two parts, not guaranteed to work, groundbreaking ) To extrude the blade spar as a single piece, it will be necessary tomodify the extrusion press at a monthly cost of $ 1 6 0 , 0 0 0 and improve the material used at a monthly cost of $ 5 0 , 0 0 0 Each of these steps would require six months of steady work. If successful, this process would produce a blade spar of superior quality at a lower overall cost. Unfortunately, as opposed to sectioning , there is some risk that Ventron will be unable to perfect the process.RiskWhile the sectioning process is guaranteed to work, proceeding with extrusion involves risk.Material DevelopmentAfter studying the technical problems, the engineering department feels there is a nine in ten chance of perfecting the material. However, the other possibility ( a one in ten chance ) is that at the end of the six - month development effort, it will know that a satisfactory material cannot be developed, and it will have to rely on sectioning to meet its time and cost constraints.Press ModificationThe engineers believe there is a three in four chance of successfully modifying the press, but a one in four chance that at the end of a six - month press development project, the extrusion process will have to be abandoned, because a press with the necessary capabilities will be shown to be infeasible.Time ConstraintsDevelopment of the blade spar must be completed within 1 8 months to avoid holding up the rest of the contract. If necessary, It has also been determined that the sectioning work could be done on an accelerated basis in a six - month period at a monthly cost of $ 4 0 0 , 0 0 0 . DilemmaThe Director of Engineering, Dr . Smith, is most interested in the opportunity provided by this contract to explore new technology in the extrusion process. She feels that if Ventron is successful in producing the blade spar as a single piece Ventron's reputation in the field will be greatly enhanced. In addition, Ventron would be able to complete development of the blade spar well under budget.After a preliminary review of the problem, Ventron's President, Bill Walters, has not yet reached a final decision. Like Dr . Smith, he is intrigued by the possibility of successfully developing the extrusion process.He feels that this would give Ventron an excellent chance at some additional contracts. He is concerned, however, about the possibility of wasting money on unsuccessful development or of being forced to do sectioning on an accelerated basis.Ventron's contract with the Army is for a fixed total amount spread over several years. Walters wants to minimize the expenditures on the blade spar portion to free up money for technical developments on other components of the rotor system, which would improve Ventron's position for future business, both defense and commercial.Question 1 .  Map out a decision tree using the probabilities above. Calculate the terminal cost for each branch . 2 . Fold back from the terminal nodes. For each chance node, calculate an EMV and for each decision box, choose from the available EMVs . 3 . Based on EMV criterion, determine what you would recommend to Dr . Smith and President Waters if you were strictly an EMV maximizer. Your decision must allow Ventron to meet all of the constraints. Do not consider unfeasible solutions . 4 . Comment on how risk aversion may influence the decision making process . 5 . Keeping all other variables unchanged, what if the probability of success for PM was 6 0 % Instead of 7 5 % , does that change your decision making? At what range of PM success would you recommend extrusion? 6 . Keeping all other variables unchanged, what if the probability of success for MD was 8 0 % instead of 9 0 % , does that change your decision making? At what range of MD success would you recommend extrusion? 7 . What if the cost of NS were $ 2 0 0 a month Instead of $ 1 5 0 ? Does that change your decision making?

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Asked by: Umesh
Created at: 2025-08-02 00:09:33

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Let's walk through the scenario step by step, as requested: --- ## **1. Map out a decision tree and calculate terminal costs** ### **Approach Options:** - **Sectioning (S):** - Cost: $150,000/month for 12 months = **$1,800,000** - Guaranteed success - **Extrusion (E):** - Two parallel developments for 6 months: - **Press Modification (PM):** $160,000/month × 6 = **$960,000** - **Material Development (MD):** $50,000/month × 6 = **$300,000** - Total for 6 months: **$1,260,000** - **Probabilities:** - MD success: 0.9; failure: 0.1 - PM success: 0.75; failure: 0.25 - **If either fails:** Must use **accelerated Sectioning (AS)** - AS cost: $400,000/month × 6 = **$2,400,000** - Total cost of failed extrusion = $1,260,000 (lost on E) + $2,400,000 (AS) = **$3,660,000** - Still within 18 months (6 months E + 6 months AS = 12 months total) - **If both succeed:** - **Total cost:** $1,260,000 --- ### **Decision Tree Probabilities and Terminal Costs** - **Extrusion:** - **MD success (0.9):** - **PM success (0.75):** Success, cost = **$1,260,000** - **PM fail (0.25):** Fail, cost = **$3,660,000** - **MD fail (0.1):** Must use AS, cost = **$3,660,000** - **Sectioning:** - **Guaranteed:** Cost = **$1,800,000** --- #### **Tree Layout** ``` [Decision] | |-- Sectioning: $1,800,000 | |-- Extrusion: | |-- MD success (0.9) | | | |-- PM success (0.75): $1,260,000 | |-- PM fail (0.25): $3,660,000 | |-- MD fail (0.1): $3,660,000 ``` --- ## **2. Fold back from terminal nodes (EMV Calculation)** ### **Extrusion Branch** #### **Step 1: Calculate EMV at PM after MD success** - PM success: 0.75 × $1,260,000 = $945,000 - PM fail: 0.25 × $3,660,000 = $915,000 - **EMV at PM node = $945,000 + $915,000 = $1,860,000** #### **Step 2: Back to MD node** - MD success: 0.9 × $1,860,000 = $1,674,000 - MD fail: 0.1 × $3,660,000 = $366,000 - **EMV at MD node = $1,674,000 + $366,000 = $2,040,000** ### **Sectioning Branch** - **Cost = $1,800,000** --- ## **3. EMV Recommendation** - **Extrusion EMV:** $2,040,000 - **Sectioning EMV:** $1,800,000 **EMV Minimization (minimize cost):** **Choose Sectioning**. **Recommendation:** If you are a strict EMV minimizer, you would recommend **Sectioning**, as it is guaranteed and has a lower expected cost. --- ## **4. Risk Aversion Comments** - **Sectioning** is low risk (guaranteed success, known cost). - **Extrusion** has a small chance of being very cheap ($1,260,000), but a significant chance of being much more expensive ($3,660,000). - **Risk-averse decision makers** would strongly prefer Sectioning, as it avoids the possibility of massive cost overruns. - **Risk-neutral** or **risk-seeking** decision makers might consider Extrusion for the upside, but the downside is severe. --- ## **5. PM Success Probability at 60% Instead of 75%** Let PM success = 0.6, PM fail = 0.4. #### **Step 1: EMV at PM node (MD success)** - PM success: 0.6 × $1,260,000 = $756,000 - PM fail: 0.4 × $3,660,000 = $1,464,000 - **EMV at PM node = $756,000 + $1,464,000 = $2,220,000** #### **Step 2: EMV at MD node** - MD success: 0.9 × $2,220,000 = $1,998,000 - MD fail: 0.1 × $3,660,000 = $366,000 - **EMV at MD node = $1,998,000 + $366,000 = $2,364,000** - **Sectioning EMV = $1,800,000** **Recommendation:** Still **Sectioning** is better (lower EMV cost). ### **At what PM probability is Extrusion better?** Set up equation: Let p = PM success probability. - EMV at PM node: $1,260,000 × p + $3,660,000 × (1-p) - EMV at MD node: 0.9 × [EMV at PM node] + 0.1 × $3,660,000 Set EMV equal to $1,800,000 and solve for p: \[ EMV = 0.9 [1,260,000p + 3,660,000(1-p)] + 0.1 \times 3,660,000 \] \[ = 0.9 [1,260,000p + 3,660,000 - 3,660,000p] + 366,000 \] \[ = 0.9 [3,660,000 - 2,400,000p] + 366,000 \] \[ = 3,294,000 - 2,160,000p + 366,000 \] \[ = 3,660,000 - 2,160,000p \] Set equal to $1,800,000: \[ 3,660,000 - 2,160,000p = 1,800,000 \] \[ 2,160,000p = 1,860,000 \] \[ p = \frac{1,860,000}{2,160,000} \approx 0.861 \] **So, PM success probability must be greater than about 86.1% for Extrusion to be the EMV-minimizing choice.** --- ## **6. MD Success Probability at 80% Instead of 90%** Let MD success = 0.8, MD fail = 0.2. #### **Step 1: EMV at PM node (original PM success 0.75):** - PM success: 0.75 × $1,260,000 = $945,000 - PM fail: 0.25 × $3,660,000 = $915,000 - **EMV at PM node = $1,860,000** #### **Step 2: EMV at MD node** - MD success: 0.8 × $1,860,000 = $1,488,000 - MD fail: 0.2 × $3,660,000 = $732,000 - **EMV at MD node = $1,488,000 + $732,000 = $2,220,000** - **Sectioning EMV = $1,800,000** **Recommendation:** Sectioning is still better. ### **At what MD probability is Extrusion better?** Let q = MD success probability. - EMV = q × $1,860,000 + (1-q) × $3,660,000 Set equal to $1,800,000: \[ q \times 1,860,000 + (1-q) \times 3,660,000 = 1,800,000 \] \[ 1,860,000q + 3,660,000 - 3,660,000q = 1,800,000 \] \[ -1,800,000q = 1,800,000 - 3,660,000 \] \[ -1,800,000q = -1,860,000 \] \[ q = \frac{1,860,000}{1,800,000} = 1.033 \] Which is impossible (can't have >100% chance). This means that with these numbers, even with 100% chance of PM success, you'd still prefer Sectioning unless PM cost is much lower. --- ## **7. What if Sectioning cost is $200,000/month instead of $150,000?** - New Sectioning cost: $200,000 × 12 = $2,400,000 Now compare: - **Sectioning:** $2,400,000 - **Extrusion (EMV):** $2,040,000 (from earlier) **Recommendation:** Now **Extrusion** is better by EMV. --- # **Summary Table** | Scenario | Sectioning ($) | Extrusion EMV ($) | Recommend? | |----------------------------------------------|----------------|-------------------|----------------| | Base case | 1,800,000 | 2,040,000 | Sectioning | | PM success = 60% | 1,800,000 | 2,364,000 | Sectioning | | PM success > 86.1% | 1,800,000 | < 1,800,000 | Extrusion | | MD success = 80% | 1,800,000 | 2,220,000 | Sectioning | | Sectioning cost = $200k/mo ($2,400,000) | 2,400,000 | 2,040,000 | Extrusion | --- # **Conclusion** 1. **Map and costs:** See above for tree and costs. 2. **EMV foldback:** Sectioning = $1.8M; Extrusion = $2.04M. 3. **Recommend:** Sectioning (lower EMV, meets constraints). 4. **Risk aversion:** Would reinforce Sectioning. 5. **PM success 60%:** Sectioning preferred; need PM success > 86.1% for Extrusion to be better. 6. **MD success 80%:** Sectioning still preferred; MD would have to be >100% to make Extrusion better (impossible). 7. **Sectioning cost $200k/mo:** Extrusion preferred. --- **If you want a hand-drawn tree or Excel format, let me know.**

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