# Example of a Decision Tree Problem: The Payoff Table

## Presentation on theme: "Example of a Decision Tree Problem: The Payoff Table"— Presentation transcript:

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

Example of a Decision Tree Problem: Step 1
Example of a Decision Tree Problem: Step 1. We start by drawing the three decisions A B C 22

Example of Decision Tree Problem: Step 2
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 \$200k \$25k -\$120k \$60k \$40k \$20k 23

Example of Decision Tree Problem: Step 3
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 EVA=.4(90)+.5(50)+.1(10)=\$62k \$62k 24

Example of Decision Tree Problem: Step 4. Make decision
High demand (.4) Medium demand (.5) Low demand (.1) A B C \$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. 25

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

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 .

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.

Location Factor Rating Example 2:
Key Scores Success (out of 100) Weighted Scores Factor Weight France Denmark France Denmark 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 © 2011 Pearson Education, Inc. publishing as Prentice Hall

Location Factor Rating Example 3:
Labor pool and climate Proximity to suppliers Wage rates Community environment Proximity to customers Shipping modes Airport service LOCATION FACTOR .30 .20 .15 .10 .05 WEIGHT 80 100 60 75 65 85 50 Site 1 91 95 90 92 Site 2 72 Site 3 SCORES (0 TO 100) Weighted Score for “Labor pool and climate” for Site 1 = (0.30)(80) = 24 Copyright 2011 John Wiley & Sons, Inc., R.Taylor

Location Factor Rating
24.00 20.00 9.00 11.25 6.50 4.25 2.50 77.50 Site 1 19.50 18.20 14.25 12.00 4.60 3.25 80.80 Site 2 27.00 15.00 10.80 9.50 4.50 82.05 Site 3 WEIGHTED SCORES Site 3 has the highest factor rating Copyright 2011 John Wiley & Sons, Inc.,R.Taylor

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? .

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.

Locational Break-Even Analysis Example 2
Three locations: Selling price = \$120 Expected volume = 2,000 units Akron \$30,000 \$75 \$180,000 Bowling Green \$60,000 \$45 \$150,000 Chicago \$110,000 \$25 \$160,000 Fixed Variable Total City Cost Cost Cost Total Cost = Fixed Cost + (Variable Cost x Volume) © 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 | | | | | | | ,000 1,500 2,000 2,500 3,000 Volume Bowling Green cost curve Akron cost curve Chicago cost curve Akron lowest cost Chicago lowest cost Bowling Green lowest cost Figure 8.2 © 2011 Pearson Education, Inc. publishing as Prentice Hall

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

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

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

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