ENGI 5708 Design of Civil Engineering Systems

Transcription

1 ENGI 5708 Design of Civil Engineering Systems Lecture 22: Decision Tree Analysis Part 1 Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr.mun.ca

2 Lecture 22 Objective to understand concepts of decision tree analysis S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

3 Decision Tree Overview to understand concepts of decision tree analysis S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

4 Example Product Development To absorb some short-term excess production capacity at its plant, Special Instrument Products is considering a short manufacturing run for either of two new products, a temperature sensor or a pressure sensor. The market for each product is known if the products can be successfully developed. However, there is some chance that it will not be possible to successfully develop them. Revenue of $1,000,000 would be realized from selling the temperature sensor and revenue of $400,000 would be realized from selling the pressure sensor. Both of these amounts are net of production cost but do not include development cost. If development is unsuccessful for a product, then there will be no sales, and the development cost will be totally lost. Development cost would be $100,000 for the temperature sensor and $10,000 for the pressure sensor. Ref: Kirkwood S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

5 Example Product Development (cont.) Development Cost Outcome Revenue Net Profit Success $1,000,000 $900,000 -$100,000 Temperature Sensor Failure -$100,000 -$10,000 Pressure Sensor Success $400,000 $390,000 Do Nothing Failure -$10,000 Ref: Kirkwood S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

6 Example Product Development Additional information has been obtained where the success rate of product development for the temperature sensor is 50% and the pressure sensor is 80%. Ref: Kirkwood S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

7 Example Product Development (cont.) Development Cost Outcome Revenue Net Profit 0.5 $1,000,000 $900,000 -$100,000 Temperature Sensor 0.5 -$100,000 -$10,000 Pressure Sensor 0.8 $400,000 $390,000 Do Nothing 0.2 -$10,000 Ref: Kirkwood S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

8 Performance Criteria Expected Value Decision criteria for uncertain alternative Multiply each possible outcome of the uncertain alternative by the associated probability and sum the results Select the best expected value (profit, cost) S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

9 Example Die Toss A friend proposes a wager: You will pay her $9.00, and then a fair die will be rolled. If the die comes up a 3, 4, 5, or 6, then your friend will pay you $ If the die comes up 1 or 2, she will pay you nothing. Furthermore, your friend agrees to repeat this game as many times as you wish to play. Should you agree to play this game? S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

10 Example Die Toss (cont.) EV = (2/3)($6) - (1/3)(-$9) = $1 -$9 Roll Die 2/3 1/3 $6 -$9 Do Nothing EV = 1() = S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

11 Example Construction Bid Overview A contractor has the opportunity to bid on major projects to construct a highway system and reservoir dam. The contractor only has sufficient resources to bid on one job. Historical Contract Award Data on Project Bids Highway Low bid 20% success rate High bid 10% success rate Dam Low bid 40% success rate High bid 20% success rate S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

12 Example Construction Bid (cont.) Historical Profit Data on Projects Dam High bid $800, $400, $200, Low bid $500, $100, $400, = 1 = S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

13 Example Construction Bid (cont.) Historical Profit Data on Projects Highway High bid $2,000, $1,000, $400, Low bid $800, $400, $400, = 1 = S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

14 Example Construction Bid (cont.) $20,000 $300, $800,000 Win $400,000 $20,000 High Bid Lose $50,000 -$200,000 Dam Low Bid $18,000 Win 0.40 $120, $500,000 $100,000 No Bid Lose $50, $400,000 $26,000 Highway High Bid Win 0.10 Lose 0.90 $1,160,000 -$100, $2,000,000 $1,000,000 -$400,000 $26,000 Low Bid -$16,000 Win 0.20 Lose 0.80 $320,000 -$100, $800,000 $400,000 -$400, S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

15 Reading List am uff/decisiontrees/index.html S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22

16 References ReVelle, C.S., E.E. Whitlatch, Jr. and J.R. Wright (2004). Civil and Environmental Systems Engineering 2nd Edition, Pearson Prentice Hall ISBN uff/decisiontrees/index.html S. Kenny, Ph.D., P.Eng. ENGI 5708 Civil Engineering Systems Lecture 22