Chapt 12 - Waiting Line Models 7. a. L q =- =- = 2 2 2 5 5...

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Unformatted text preview: Waiting Line Models 7. a. L q =- =- = 2 2 2 5 5 5 2 5 05000 ( ) ( . ) ( . ) . b. W L q q = = = 05000 2 5 0 20 . . . hours (12 minutes) c. W W q = + = + = 1 0 20 1 5 0 40 . . hours (24 minutes) d. P w = = = 2 5 5 050 . . 10. a. = 2 = 3 = 4 Average number waiting ( L q ) 1.3333 0.5000 Average number in system ( L ) 2.0000 1.0000 Average time waiting ( W q ) 0.6667 0.2500 Average time in system ( W ) 1.0000 0.5000 Probability of waiting ( P w ) 0.6667 0.5000 b. New mechanic = $30( L ) + $14 = 30(2) + 14 = $74 per hour Experienced mechanic = $30( L ) + $20 = 30(1) + 20 = $50 per hour Hire the experienced mechanic 14. a. = = 60 7 5 8 . customers per hour b. 5 1 1 0.3750 8 P =- =- = c. L q =- =- = 2 2 5 8 8 5 10417 ( ) ( ) . d. W L q q = = = 10417 5 0 2083 . . hours (12.5 minutes) e. P w = = = 5 8 0 6250 . f. 62.5% of customers have to wait and the average waiting time is 12.5 minutes. Ocala needs to add more consultants to meet its service guidelines. L L q = + = + = 05000 2 5 5 1 . . L q = 2 2 + ( / ) 2 2 (1 - / ) = (0.25) 2 (2) 2 + (0.25 / 0.3125) 2 2 (1 - 0.25 / 0.3125) = 2.225 W q = L q = 2.225 0.25 = 8.9 hours W = W q + 1 = 8.9 + 1 1.3125 = 12.1 hours Same at P w = = 0.25 0.3125 = 0.80 L q = 2 2 + ( / ) 2 2 (1 - / ) = (.375) 2 (1.5) 2 + (.375/ .5) 2 2 (1 - .375 / .5) = 1.7578 Chapter 12 22. = 24 Characteristic System A ( k = 1, = 30) System B ( k = 1, = 48) System C ( k = 2, = 30) a. P 0.2000 0.5000 0.4286 b. L q 3.2000 0.5000 0.1524 c. W q 0.1333 0.0200 0.0063 d. W 0.1667 0.0417 0.0397 e. L 4.0000 1.0000 0.9524 f. P w 0.8000 0.5000 0.2286 System C provides the best service. 27. a. 2/8 hours = 0.25 per hour b. 1/3.2 hours = 0.3125 per hour c. d. e. f. 80% of the time the welder is busy. 29. a. = 3/8 = .375 = 1/2 = .5 b. L = L q + / = 1.7578 + .375 / .5 = 2.5078 TC = c w L + c s k = 35 (2.5078) + 28 (1) = $115.71 c. Current System ( = 1.5) New System ( = 0) L q = 1.7578 L q = 1.125 L = 2.5078 L = 1.875 W q = 4.6875 W q = 3.00 W = 6.6875 W = 5.00 TC = $115.77 TC = c w L + c s k = 35 (1.875) + 32 (1) = $97.63 d. Yes; Savings = 40 ($115.77 - $97.63) = $725.60 Waiting Line Models Note: Even with the advantages of the new system, W q = 3 shows an average waiting time of 3 hours. The company should consider a second channel or other ways of improving the emergency repair service....
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This note was uploaded on 04/20/2010 for the course IE ie200 taught by Professor . during the Spring '10 term at 카이스트, 한국과학기술원.

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Chapt 12 - Waiting Line Models 7. a. L q =- =- = 2 2 2 5 5...

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