26 (06 Three Technologies with Uncertainty The Rams is coming back to Southern C
ID: 458521 • Letter: 2
Question
26 (06 Three Technologies with Uncertainty
The Rams is coming back to Southern California and plans to build an NFL stadium in Inglewood. In this hypothetical situation, the Rams owner is considering three contractors to build the long awaited stadium: SOCAL Builders, LA Constructions, and OC Developers. Even though, the three construction companies pledge to complete the stadium in 2018, a construction project of this magnitude can easily have time overruns. The Rams owner assessed different scenarios and the three companies, and came up with the following total cost estimates, in billions of dollars, to have a completed NFL stadium for the Rams:
Contractor
Early Completion (Probability = 0.1)
Ontime Completion (Probability = 0.5)
6+Month Overrun
(Probability = 0.4)
SOCAL Builders
2.10
2.40
3.30
LA Constructions
2.00
2.60
3.10
OC Developers
1.90
2.50
3.40
The total cost accounts for the stadium construction costs and all other relevant commercial values tied to the completion time. Subject probabilities of the three scenarios are also provided, based on other stadium projects. You need to use 2 decimals in calculations. (a)[2] Given the expected value approach, which contractor would the owner choose? Explain.
(b)[1] Given the minimax approach, which contractor would the owner choose? Explain.
(c)[1] Given the minimin approach, which contractor would the owner choose? Explain.
(d)[2] Given the minimax regret approach, which contractor would the owner choose? Explain.
Contractor
Early Completion (Probability = 0.1)
Ontime Completion (Probability = 0.5)
6+Month Overrun
(Probability = 0.4)
SOCAL Builders
2.10
2.40
3.30
LA Constructions
2.00
2.60
3.10
OC Developers
1.90
2.50
3.40
Explanation / Answer
(a)[2] Given the expected value approach, which contractor would the owner choose? Explain.
Expected monetary value of an alternative = (Probability of event x respective payoff)
For Alternative 1, giving contract to SOCAL Builders,
EMV1 = (0.1 x 2.7) + (0.5 x 3.9) + (0.4 x 6.3) = 4.74
EMV2 = (0.1 x 2.1) + (0.5 x 3.8) + (0.4 x 6.5) = 4.71
EMV3 = (0.1 x 1.7) + (0.5 x 4.3) + (0.4 x 6.1) = 4.76
According to Expected value approach, alternative giving maximum EMV is selected. Thus, Maximum EMV is 4.76 for alternative of giving contract to OC developers.
(b)[1] Given the minimax approach, which contractor would the owner choose? Explain.
This approach selects the alternative which minimizes the maximum payoff among all events
Minimum of (6.3, 6.5, 6.1) = 6.1.
Thus, alternative of giving contract to OC developers minimizes the maximum payoff among all events.
(c)[1] Given the minimin approach, which contractor would the owner choose? Explain.
This approach selects the alternative which minimizes the minimum payoff among all the events.
Minimum of (2.7, 2.1, 1.7) = 1.7
Thus, alternative of giving contract to OC developers minimizes the minimum payoff among all events.
(d)[2] Given the minimax regret approach, which contractor would the owner choose? Explain.
This approach selects the alternative which minimizes the maximum regret of opportunity loss among all the events.
First develop regret table by subtracting maximum payoff among the each event and subtracting each payoff from this value. Then select maximum regret value for each alternative. Then select the minimum value from this maximum regret.
Minimum value among maximum regret = 0.4 for alternative 1
Thus, alternative of giving contract to SOCAL developers minimizes the maximum regret payoff among all events.
Possible Events
Probabilities
0.1
0.5
0.4
Contractor
Early Completion
Ontime Completion
6+Month Overrun
Minimum Payoff
Maximum Payoff
Average
Expected Payoff
SOCAL Builders
2.7
3.9
6.3
2.7
6.3
4.30
4.74
LA Constructions
2.1
3.8
6.5
2.1
6.5
4.13
4.71
OC Developers
1.7
4.3
6.1
1.7
6.1
4.03
4.76
Maximum for each event
2.7
4.3
6.5
Opportunity Loss Table (Regret Table)
Possible Events
Contractor
Early Completion
Ontime Completion
6+Month Overrun
Maximum
SOCAL Builders
0
0.4
0.2
0.4
LA Constructions
0.6
0.5
0
0.6
OC Developers
1
0
0.4
1
The result table is summarized as follows:
Decision Table
Criterion
Resulting Payoff
Best Alternative
Minmin
1.7
OC Developers
Minimax
6.1
OC Developers
Minimax Regret
0.4
SOCAL Builders
Expected Monetry Value
4.76
OC Developers
Possible Events
Probabilities
0.1
0.5
0.4
Contractor
Early Completion
Ontime Completion
6+Month Overrun
Minimum Payoff
Maximum Payoff
Average
Expected Payoff
SOCAL Builders
2.7
3.9
6.3
2.7
6.3
4.30
4.74
LA Constructions
2.1
3.8
6.5
2.1
6.5
4.13
4.71
OC Developers
1.7
4.3
6.1
1.7
6.1
4.03
4.76
Maximum for each event
2.7
4.3
6.5
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