W15_LUCKY_Decision to repair or to trade in a car using Decision Tree

W15_LUCKY_Decision to repair or to trade in a car using Decision Tree

1.      Problem Recognition

I have been asked for advice by a colleague. He has an old Hyundai saloon car valued at $1,592. He has a budget of $600 for the project.  An experienced Honda mechanic, a close associate, has offered to refurbish the car at an estimated cost of $250 in one week, hopefully, before my colleague travels to Ghana. A certified OEM (Hyundai) Centre offered to revamp the car at a cost of $350 to make it look like new. The Centre also offered to accept a trade in of the car at a cost of $2,290.

2.      Problem Definition

A set of quick calculation reveals there is problem. My colleague has a budget of $600. 

Honda mechanic repair cost - $250

OEM repair cost - $350

Second hand value of car - $1,592

Trade-in car option cost - $2,290

Given his budget, which alternative will be the best? This is a replacement problem that I would like to solve using the Decision Tree Tool and Technique.

a.      Assumptions

Key assumptions include:

·         The second hand value estimate of the car is reliable with 90 percent probability

·         The Honda mechanic estimate is good, and will meet deadline of one week with 80 per cent probability

·         The OEM Centre estimates are correct and cast in stone with 100 percent probability

·         The OEM will be willing to buy the car upon seeing it and replacement car available with 90 percent probability

 

3.      Feasible Alternatives

Feasible alternatives include:

A.    Do nothing – abandon the idea altogether

B.     Engage the Honda mechanic

C.     Engage the OEM Centre

D.    Trade in the car with the OEM Centre

In an earlier blog, W7_Lucky_Decision to repair or to trade in a car, the proposed feasible alternative arrived at was alternative #3 above.  Suppose the replacement car is available at the OEM Centre for the one week period. As each day passes a decision point is reached until the replacement is finally consummated. In this case, the problem has changed into a replacement problem. There is no chance of time-value-of-money due to the short duration of the envisaged transaction – one week- at this instance. Thus I would like to solve it using the Decision Tree Tool and Technique.

4.      Development of outcomes  for each alternative

The decision tree outlining the scenarios is shown in figure 1 below. On this tree there is one decision point:

The outcomes for each alternative are as follows:

1.      Do nothing or

2.      Fix the car

Along the way to the ultimate outcomes is one event node, node X from which I can chose any of the following:

1.      Engage the Honda mechanic

2.      Engage the OEM Centre

3.      Trade in the car with the OEM Centre

Taking each ultimate outcome in turn, the following calculations result:

Outcome A: For the ‘Don’t fix the car’ option, the outcome is zero

Outcome B: If the Honda mechanic is engaged,

                        $500 (10%) = 50

                        $300 (20%) = 60

                        $250 (70%) = 175

                              Value    = $285              

Outcome C: If the OEM Centre is engaged,

                        $500 (10%) = 50

                        $450 (20%) = 90

                        $350 (70%) = 245

                              Value    = $385              

Outcome D: If I advise trade-in the car,

                        $3000 (10%) = 300

                        $2500 (10%) = 250

                        $2290 (80%) = 1832

                              Value    = $2382        

4.      Selection Criteria

The selection criterion is the expected value that is LOWEST and assures

1.      On time delivery

2.      Quality standard

3.      Cost (within budget)

 

5      Analysis and Comparison of the alternatives

Working back through the paths:

The Expected value E_V for activity ‘Don’t fix the car’ is $0

 

Net outcome A: Zero

 

The Expected value E_V for activity ‘Engage Honda mechanic’ is $285

 

Net outcome B: $285

Percent Probability = 30%

 

The Expected value E_V for activity ‘Engage OEM Centre’ is $385

 

Net outcome C: $385

Percent Probability = 60%

 

The Expected value E_V for activity ‘Trade-in Car’ is $2382

 

Net outcome D: $2382

Percent Probability = 10%

 

 

·         Monetary consideration

To stay within budget, alternatives A, B and C are the only acceptable feasible alternatives, with alternative C being the best option due to its high probability.

·         Introducing risk into the solution

This applies to all three alternatives.

                                                              i.      Failure for on-time delivery – Travel to Ghana in public car [Best option is Alternative D]

                                                            ii.      Quality issue – Instigate rework; make alternative travel arrangement [Best options are alternatives C and D]

                                                          iii.      Cost changes – Request for firm price from service providers [All three options are acceptable alternatives]

 

·         Nonmonetary consideration

 

These include schedule and quality standard.

If schedule is considered, alternative D becomes the only feasible solution.

If quality is considered, alternatives C and D become better feasible alternatives.

 

 

6.      Selection of preferred alternative

I am prepared to advice my colleague to choose alternative C as my preferred alternative. He is would save $215 to cover any quality or schedule risk.

7.      Performance monitoring and post evaluation of results

The car shall be driven within town on test drives. Hopefully all performance issues with the car will surface and be resolved before being driven to Ghana.

 

 

Reference

1.      Sullivan, W., Wicks, E., Koelling, P., Kumar, p., & Kumar, N. (2012).Chapter 12 Probabilistic Risk Analysis (pp. 528 - 533). Engineering economy (15^th edition). England: Pearson Education Limited.

2.       Brassard, M. & Ritter D. (2010). Chapter 24 Tree Diagram (pp.200 – 209). The Memory Jogger 2 (2^nd edition). USA:GOAL/QPC

3.      Giammalvo, P. (2012, October 22). Integrated portfolio (asset), program (operations) and project management methodology course (cost engineering) slides (An AACE methodology course). Lagos, Nigeria: Lonadek