1998exam1-soln - = = + = -q z c c c q u u 3… (a) 395 . 2...

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IE 221 OPERATIONS RESEARCH – PROBABILISTIC MODELS EXAM 1 FALL 1998 1 … gal 4 . 516 3 ) 5000 )( 80 ( 2 2 * = = = n KD q 1 month shelf life life. shelf over demanded gal 66 . 416 12 5000 = 66 . 416 * q life. shelf month 2 over demand gal 3 . 833 15 . 365 6 ) 5000 )( 80 ( 2 (doubled) 6 h and facility better with EOQ let * < = = = = d q Old storage facility: TC(416.66) = (12)(80) + (3)(1/2)(416.66) = 1585 Better storage facility: TC(365.15) = 2191 ) 6 )( 5000 )( 80 )( 2 ( 2 = = KDh Therefore, order 1 month supply = 416.66, and store in old facility. 2 … let q = amount planned for monthly expenses (i.e., not invested) 100,000 – q = amount invested monthly interest = (24/12)% = 2% d ~ Normal: μ = 6000/mo. σ = 2000/mo.
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d q : expenses met from amount planned cost (d,q) = – .02 (100,000 – q) = .02q – 2000 c 0 = .02 d > q : d – q must be withdrawn from investment to cover expenses. cost (d,q) = .04 (d – q) – .02 (100,000 – d) = – .04q + .06d – 2000 c u = .04 93140/mo. invest 6860 ) 2000 )( 43 (. 6000 43 . 667 . 06 . 04 . 2000 6000 P * * 0 * = + = =
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Unformatted text preview: = = + = -q z c c c q u u 3… (a) 395 . 2 9917 . 100 ) 10 ( 12 1 1 1 ) ( P = → = -=-= z c Rh z B 391.1 stock safety 1 . 491 6 ) 400 ( ) 395 . 2 ( 6 1 ) 600 ( ) ( 2 = → = + = + + = + L R z L R D S s (b) 333 , 13 12 ) 400 ( 8 . ) var( mo. 1 2 2 R = = = = s L L 549 333 , 301 ) 8 (. ) 600 ( ) 400 ( 12 1 ) var( ) ( ) var( 2 2 2 2 = = + = + = L L L D E D L s s 561 666 , 314 333 , 13 333 , 301 2 2 2 = = + = + = + + L R R L L R s s s s S = 100 + (2.395)(561) = 1443.5 SScost(part a) = (391.1)(10) SScost(part b) = (1343.5)(10) ∆ SScost = (1343.5 – 391.1)(10) = $9523.78/yr. (c) 36 . 2 003063 . ) 3 . 163 ( ) 01 (. 12 1 600 ) 1 ( ) ( 1 = → = =-= + z SLM R D z NL L R s note : safety stock = L R z + s . ∴ since z is lower here, not as much protection is offered....
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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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1998exam1-soln - = = + = -q z c c c q u u 3… (a) 395 . 2...

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