Presentation on theme: "Example of a Decision Tree Problem: The Payoff Table"— Presentation transcript:
1 Example of a Decision Tree Problem: The Payoff Table The management also estimates the profits when choosing from the three alternatives (A, B, and C) under the differing probable levels of demand. These costs, in thousands of dollars are presented in the table below:21
2 Example of a Decision Tree Problem: Step 1 Example of a Decision Tree Problem: Step 1. We start by drawing the three decisionsABC22
3 Example of Decision Tree Problem: Step 2 Example of Decision Tree Problem: Step 2. Add our possible states of nature, probabilities, and payoffsABCHigh demand (.4)Medium demand (.5)Low demand (.1)$90k$50k$10k$200k$25k-$120k$60k$40k$20k23
4 Example of Decision Tree Problem: Step 3 Example of Decision Tree Problem: Step 3. Determine the expected value of each decisionHigh demand (.4)Medium demand (.5)Low demand (.1)A$90k$50k$10kEVA=.4(90)+.5(50)+.1(10)=$62k$62k24
5 Example of Decision Tree Problem: Step 4. Make decision High demand (.4)Medium demand (.5)Low demand (.1)ABC$90k$50k$10k$200k$25k-$120k$60k$40k$20k$62k$80.5k$46kAlternative B generates the greatest expected profit, so our choice is B or to construct a new facility.25
6 Location Factor Rating Example 1: we are considering two different cities Richmond, Birmingham for the location of a medium-sized Red Bakery Firm. The bakery will produce an assortment of bakery goods on site and will sell directly to retail customers as well as whole sale do grocery stores, restaurants, etc. The factors shown in Table-1 have been evaluated for two cites.Good Excellent
7 The total score can be computed for each site The total score can be computed for each site. This is done by first converting the rating for each non-cost factor to a numerical score. The conversion for the example is shown in Table-2 using a 10-point scale.
8 The location with the highest total score is then the best choice The location with the highest total score is then the best choice. The total scores are as follows: S1 =15(8)+5(6)+5(10)+5(2)+10(8)+60(6) S2 =15(10)+5(4)+5(8)+5(6)+10(6)+60(10) S1 =650 S2 =900 This scoring system, therefore, indicates that alternative 2, Birmingham, is preferred.
10 Location Factor Rating Example 3: Labor pool and climateProximity to suppliersWage ratesCommunity environmentProximity to customersShipping modesAirport serviceLOCATION FACTOR.126.96.36.199.05WEIGHT801006075658550Site 191959092Site 272Site 3SCORES (0 TO 100)Weighted Score for “Labor pool and climate” forSite 1 = (0.30)(80) = 24Copyright 2011 John Wiley & Sons, Inc., R.Taylor
11 Location Factor Rating 24.0020.009.0011.256.504.252.5077.50Site 119.5018.2014.2512.004.603.2580.80Site 227.0015.0010.809.504.5082.05Site 3WEIGHTED SCORESSite 3 has the highest factor ratingCopyright 2011 John Wiley & Sons, Inc.,R.Taylor
12 Locational Break-even analysis: Example 1: Potential locations at Albany, Baker and Casper have the cost structures shown in Table for a product expected to sell for $130. a)Find the most economical location for an expected to sell volume of units per year. b)What is the expected profit if the site selected in (a) is used ? c)For what output range is each location best?.
13 a)A: TC:$ $75(6.000) =$B: TC:$ $50(6.000) =$ *C: TC:$ $25(6.000) =$Therefore the most economical location is Bb) Expected profit (using B )P=$130 (6.000)-$ =$ /Yrc) From the graph, for quantities between 0 and 2000 A is best, between B is best and C is best for greater than 8000 units.