Example of a Decision Tree Problem The Payoff
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:
Example of a Decision Tree Problem: Step 1. We start by drawing the three decisions A B C
Example of Decision Tree Problem: Step 2. Add our possible states of nature, probabilities, and payoffs High demand (. 4) Medium demand (. 5) Low demand (. 1) A High demand (. 4) B Medium demand (. 5) Low demand (. 1) C High demand (. 4) Medium demand (. 5) Low demand (. 1) $90 k $50 k $10 k $200 k $25 k -$120 k $60 k $40 k $20 k
Example of Decision Tree Problem: Step 3. Determine the expected value of each decision High demand (. 4) $62 k Medium demand (. 5) Low demand (. 1) A EVA=. 4(90)+. 5(50)+. 1(10)=$62 k $90 k $50 k $10 k
Example of Decision Tree Problem: Step 4. Make decision High demand (. 4) $62 k A B $80. 5 k Medium demand (. 5) Low demand (. 1) High demand (. 4) Medium demand (. 5) Low demand (. 1) C High demand (. 4) $46 k Medium demand (. 5) Low demand (. 1) $90 k $50 k $10 k $200 k $25 k -$120 k $60 k $40 k $20 k Alternative B generates the greatest expected profit, so our choice is B or to construct a new facility.
Location Factor Rating Example 1: we are considering two different cities Richmond, Birmingham for the location of a mediumsized 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. 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 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.
Location Factor Rating Example 2: Key Success Factor Weight France Labor availability and attitude People-tocar ratio Per capita income Tax structure Education and health Scores (out of 100) Denmark Weighted Scores France Denm . 25 70 60 (. 25)(70) = 17. 5 . 05 50 60 (. 05)(50) = 2. 5 (. 05)(60) = 3. 0 . 10. 39 85 75 80 70 (. 10)(85) = 8. 5 (. 10)(80) = 8. 0 (. 39)(75) = 29. 3 (. 39)(70) = 27. 3 . 21 60 70 (. 21)(60) = 12. 6 70. 4 68. 0 Totals 1. 00 © 2011 Pearson Education, Inc. publishing as Prentice Hall (. 25)(60) = 15. 0 (. 21)(70) = 14. 7 Table 8. 4
Location Factor Rating Example 3: SCORES (0 TO 100) LOCATION FACTOR Labor pool and climate Proximity to suppliers Wage rates Community environment Proximity to customers Shipping modes Airport service WEIGHT Site 1 Site 2 Site 3 . 30. 20. 15. 10. 05 80 100 60 75 65 85 50 65 91 95 80 90 92 65 90 75 72 80 95 65 90 Weighted Score for “Labor pool and climate” for Site 1 = (0. 30)(80) = 24 Copyright 2011 John Wiley & Sons, Inc. , R. Taylor Supplement 7 -10
Location Factor Rating WEIGHTED SCORES Site 1 Site 2 Site 3 24. 00 20. 00 9. 00 11. 25 6. 50 4. 25 2. 50 77. 50 19. 50 18. 20 14. 25 12. 00 9. 00 4. 60 3. 25 80. 80 27. 00 15. 00 10. 80 12. 00 9. 50 3. 25 4. 50 82. 05 Copyright 2011 John Wiley & Sons, Inc. , R. Taylor Supplement 7 -11 Site 3 has the highest factor rating
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 6. 000 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: $150. 000+$75(6. 000) =$600. 000 B: TC: $200. 000+$50(6. 000) =$500. 000 * C: TC: $400. 000+$25(6. 000) =$550. 000 Therefore the most economical location is B b) Expected profit (using B ) P=$130 (6. 000)-$500. 000=$280. 000/Yr c) From the graph, for quantities between 0 and 2000 A is best, between 2000 -8000 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 Fixed Variable Total City Cost Akron $30, 000 $75 $180, 000 Bowling Green $60, 000 $45 $150, 000 Chicago $110, 000 $25 $160, 000 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 Annual cost $130, 000 $110, 000 $80, 000 $60, 000 $30, 000 $10, 000 Figure 8. 2 © 2011 Pearson Education, Inc. publishing as Prentice Hall – – – urve c t s co – ago c i h C – – een r – g Grve n i l – ow t cu s – B co st o – c – ron ve – Ak cur – Akron – lowest – cost – | | – 0 500 Chicago lowest cost Bowling Green lowest cost | | | 1, 000 1, 500 2, 000 2, 500 3, 000 Volume
North-West&VAM Warehouse Factory 1 2 3 4 1 19 30 50 10 2 70 30 40 60 3 40 8 70 20 Demand 5 8 7 14 Solving: North-west: $1015 VAM : $779 Supply 7 9 18 34
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
0. 62 0. 39 0. 27 0. 14/0. 56 0. 28 0. 35
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