1999exam1-soln - 3 … (a) 52 . 1 28 . ) 300 )( 7 ( ) 99 ....

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IE 221 OPERATIONS RESEARCH – PROBABILISTIC MODELS EXAM 1 FALL 1999 1 … (a) 2 . 2571 ) 3 . 0 ( 9 ) 25500 )( 350 ( 2 2 = = = d ph KD EOQ (b) 24206 136 . 9 3471 ) 236442 )( 95 . 0 ( 26794 136 . 9 3471 ) 236442 )( 05 . 1 ( 136 . 9 3471 9 2571 350 2 ) 7 . 2 ( 2571 2 2 2 . 2571 with 236442 2 = - = = - = - = + - = + - = + = - = = + + = - + D D TC TC p q K p qh TC D p q K D p qh TC q pD p qh q KD TC d d d (c) 45649 3 . 0 25500 9 9 5 . 13 ) 3 . 0 ( 9 ) 3 . 0 )( 5 . 13 )( 25500 )( 350 ( 2 2 * 5 . 13 , 9 1 1 2 1 2 2 1 = - + = - + = = = d d d h D p p p h p h KDp Q p p 2 … (a) 9 , 40 51 , 60 , 100 = - = = - = = = = g c p c g p o u u u u Find smallest q* such that 816 . 0 49 40 *) ( = = - - = + g p p c c c q F u o u u K 300 400 500 600 700 800 F(K) 0.1 0.2 0.6 0.8 0.9 1.0 q*=700
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(b) Expected revenue = [(0.1)(300) + (0.1)(400) + (0.4)(500) + (0.2)(600) + (0.2)(700)].(100) = 53000 Expected salvage = [(0.1)(400) + (0.1)(300) + (0.4)(200) + (0.2)(100)].(51) = 8670 Purchase cost = 700(60) = 42000 Expected profit = 53000 + 8670 – 42000 = 19670
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Unformatted text preview: 3 … (a) 52 . 1 28 . ) 300 )( 7 ( ) 99 . ( ) 01 . )( 550 )( 4 ( . ) 1 ).( ( . ) ( NL 2 1 1 = → = =-= + z SLM SLM D E R z L R s SS = z s R+L = (1.52)(793.73) = 1206.46 S = (R+L).E(D) + SS = (7)(550) + 1206.46 = 5056.46 (b) 1 SLM cycle} in inventory ient P{insuffic cycle}) in inventory nt P{sufficie ( 1 ) 52 . 4 ( P ). ( P = ≈ ∴ = ≈ = -D L L D E r s 00364 . 520 ) 300 ( 3 ) 1 ( ) 10 ( 7 ) 52 . 4 ( 1 1 6 < ∴ =-= <-q SLM q SLM q NL If q=1, smallest order quantity, policy is to order a replacement whenever a demand occurs....
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This note was uploaded on 05/05/2008 for the course IE 221 taught by Professor Georgewilson during the Spring '08 term at Lehigh University .

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1999exam1-soln - 3 … (a) 52 . 1 28 . ) 300 )( 7 ( ) 99 ....

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