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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)

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Presentation on theme: "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)"— 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:

2 Example of a Decision Tree Problem: Step 1. We start by drawing the three decisions A B C

3 Example of Decision Tree Problem: Step 2. Add our possible states of nature, probabilities, and payoffs A B C High demand (.4) Medium demand (.5) Low demand (.1) $90k $50k $10k High demand (.4) Medium demand (.5) Low demand (.1) $200k $25k -$120k High demand (.4) Medium demand (.5) Low demand (.1) $60k $40k $20k

4 Example of Decision Tree Problem: Step 3. Determine the expected value of each decision High demand (.4) Medium demand (.5) Low demand (.1) A $90k $50k $10k EV A =.4(90)+.5(50)+.1(10)=$62k $62k

5 Example of Decision Tree Problem: Step 4. Make decision High demand (.4) Medium demand (.5) Low demand (.1) High demand (.4) Medium demand (.5) Low demand (.1) A B C High demand (.4) Medium demand (.5) Low demand (.1) $90k $50k $10k $200k $25k -$120k $60k $40k $20k $62k $80.5k $46k Alternative B generates the greatest expected profit, so our choice is B or to construct a new facility.

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. 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 total scores are as follows: S 1 =15(8)+5(6)+5(10)+5(2)+10(8)+60(6) S 2 =15(10)+5(4)+5(8)+5(6)+10(6)+60(10) S 1 =650 S 2 =900 This scoring system, therefore, indicates that alternative 2, Birmingham, is preferred.

9 © 2011 Pearson Education, Inc. publishing as Prentice Hall Location Factor Rating Example 2: KeyScores Success(out of 100)Weighted Scores FactorWeightFranceDenmarkFranceDenmark Labor availability and attitude (.25)(70) = 17.5(.25)(60) = 15.0 People-to- car ratio (.05)(50) = 2.5(.05)(60) = 3.0 Per capita income (.10)(85) = 8.5(.10)(80) = 8.0 Tax structure (.39)(75) = 29.3(.39)(70) = 27.3 Education and health (.21)(60) = 12.6(.21)(70) = 14.7 Totals Table 8.4

10 Location Factor Rating Example 3: Copyright 2011 John Wiley & Sons, Inc., R.Taylor Supplement 7-10 Labor pool and climate Proximity to suppliers Wage rates Community environment Proximity to customers Shipping modes Airport service LOCATION FACTOR WEIGHT Site Site Site 3 SCORES (0 TO 100) Weighted Score for “Labor pool and climate” for Site 1 = (0.30)(80) = 24

11 Location Factor Rating Copyright 2011 John Wiley & Sons, Inc.,R.Taylor Supplement Site Site Site 3 WEIGHTED SCORES Site 3 has the highest factor rating

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 B b) Expected profit (using B ) P=$130 (6.000)-$ =$ /Yr c) 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.

14 © 2011 Pearson Education, Inc. publishing as Prentice Hall Locational Break-Even Analysis Example 2 Three locations: Akron$30,000$75$180,000 Bowling Green$60,000$45$150,000 Chicago$110,000$25$160,000 FixedVariableTotal CityCostCostCost Total Cost = Fixed Cost + (Variable Cost x Volume) Selling price = $120 Expected volume = 2,000 units

15 © 2011 Pearson Education, Inc. publishing as Prentice Hall Locational Break-Even Analysis Example – $180,000 – – $160,000 – $150,000 – – $130,000 – – $110,000 – – $80,000 – – $60,000 – – $30,000 – – $10,000 – – Annual cost ||||||| 05001,0001,5002,0002,5003,000 Volume Akron lowest cost Bowling Green lowest cost Chicago lowest cost Chicago cost curve Akron cost curve Bowling Green cost curve Figure 8.2

16 North-West&VAM Warehouse Factory Supply Demand Solving: North-west: $1015 VAM : $779

17 / stages/station a. CT= production time per day/output per day b. Stages,worker,workstation number= Sum of task times/ CT LAYOUT - Line Balancing

18 d. Sum of task times/ (CT x number of stations,workers etc) d. Sum of task times/ number of stations,workers etc

19 /


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