Mgt Science Essay

3864 words - 16 pages

Chapter Nine: Multicriteria Decision Making
PROBLEM SUMMARY
1. Model formulation, product mix 2. Model formulation, transportation, computer solution 3. Model formulation, urban recreation facility allocation 4. Model formulation, crop determination, computer solution 5. Model formulation, product mix, computer solution 6. Model formulation, OSHA safety compliance, computer solution 7. Computer solution; graphical solution 8. Computer solution; graphical solution 9. Computer solution 10. Model formulation, computer solution 11. Model formulation, product mix, computer solution 12. Model formulation, product mix, computer solution 13. Model formulation, clinic personnel selection, computer ...view middle of the document...

b)

The noninteger solution values were rounded to integer values (making sure no rim requirements were violated.) 3. a)

– – b) The goal constraint d3 + d7 d8 = 100 must be – + converted to 10x + 12x2 + 18x3 + d7 d7 = 900 for QM for Windows input. The solution is x1 = 25, d 1– = 1,975, d 3– = 550, d 4– = 775, d 5– = 900, – d 6– = 1,100, d 7 = 650. P 1 and P 2 are achieved; P3 (6,000), P4 (1,975), and P5 (550) are not achieved.

+

6. a)

b) x1 d2 d7 4. a)

6, x2 5, x3 x4 0, 4,000, d3 14, d4 4, d5 8, d8 12

1, d6

5, b)

7.

b)

5. a)

x1 20, d2 satisfied

10, d3

50

137

8.

b) x1 = 30 x2 = 15 Goal achievement: P1: achieved P2: achieved – P3: not achieved, d3 = 5 – P4: not achieved, d4 = 6
+ + + + – – – – 14. a) minimize P1(d1 , d2 , d3 , d4 ), P2(d5 , d6 , d7 , d8 ), – + P3d9 , P3d10 subject to
– + .06x1 + .17x2 + .10x3 + .14x4 + d1 – d1 = 700 – + .18x1 + .20x2 + .14x4 + d2 – d2 = 700 – + .07x1 + .20x2 + .08x3 + .12x4 + d3 – d3 = 800 – + .09x1 + .12x2 + .07x3 + .15x4 + d4 – d4 = 600 – + x1 + d5 – d5 = 2,600 – + x2 + d6 – d6 = 1,800 – + x3 + d7 – d7 = 4,100 – + x4 + d8 – d8 = 1,200 – + 90x1 + 100x2 + 80x3 + 120x4 + d9 – d9 = 700,000 – + 2.6x1 + 1.4x2 + 2.5x3 + 3.2x4 + d10– d10 = 15,000

x1 500, x2 satisfied 9. 10. a) x1 15, d1 satisfied

300, d3 12, d2

500 10, d4 6

b) x1 40, x2 satisfied 11.a)

50, d1

140, d4

120

b) x1 60, x2 satisfied 12. a)

30, d1

10, d3

5

b) x1 = 2,600 x2 = 0 x3 = 0 x4 = 1657.14 Goal achievement: P1: achieved; no overtime P2: not achieved; demand not met for parts 2 – (d6 = 1800) and 4 (d7– = 4100) P3: not achieved; profit goal not met by – $72,166.67 (d9 = 267,143) c) x1 = 2,600 x2 = 1,800 x3 = 4,100 x4 = 1,200 Goal achievement: P1: achieved, demand met P2: not achieved; overtime required for all + + + processes (d1 = 340, d2 = 296, d3 = + 214, d4 = 317) P3: achieved, profit goal met + P4: not achieved; 8,370 ft2 (d10 = 8,370) extra material required.

b)

The solution is x1 = 500,x2 = 317.5, + – – d1 = 480, d2 = 113.125, d4 = 52.5.

13. a)

138

+ – – – – – 15. a) minimize P1d1 , P2(d2 , d8 ), P3(d7 ), P4(d3 , d4 , – – d5 , d6 )

+ + + – – – + 16. a) minimize P1d1 , P2 d2 , P3 d3 , P4(d4 , d5 ), P5 d6 , – P6 d7

subject to – + x1 + x2 + x3 + x4 + x5 + x6 + x7 + d1 – d1 = 60 – + x1 + x4 + x5 + x6 + x7 + d2 – d2 = 47 – x1 + x2 + x5 + x6 + x7 + d3 – d3+ = 22 – + x1 + x2 + x3 + x6 + x7 + d4 – d4 = 28 – + x1 + x2 + x3 + x4 + x7 + d5 – d5 = 35 + x1 + x2 + x3 + x4 + x5 + d6– – d6 = 34 – + x2 + x3 + x4 + x5 + x6 + d7 – d7 = 43 – + x3 + x4 + x5 + x6 + x7 + d8 – d8 = 53 – xi, d i , di+ ≥ 0 b) Employees beginning work on day i = xi x1 = 0 – Sunday x2 = 7 – Monday x3 = 0 – Tuesday x4 = 27 – Wednesday x5 = 0 – Thursday x6 = 25 – Friday x7 = 1 – Saturday Goal achievement: P1: achieved P2: achieved P3: achieved P4: achieved 17. Normalized Matrices:

subject to .675x1 + 1.05x2+ .725x3 + .430x4 + 1.24x5 + – + .890x6 + 1.620x7 + 1.20x8 + d1 – d1 =...

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