Hmwk5sol

# Hmwk5sol - ISyE 3232 Stochastic Manufacturing and Service...

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Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 J. Dai and H. Ayhan Solutions to Homework 5 1. (a) Using the notation in Section 1.5 of the newsvendor notes: c f = 1000, c v = 40, h = 10, p = 100. The optimal order-up-to quantity S is the smallest one such that F ( S ) ≥ p- c v p + h = 100- 40 100 + 10 = 0 . 545 . Hence, S = 600. (b) L ( x ) = 100 E ( D- x ) + + 10 E ( x- D ) + The order-up-to quantity as computed in (a) is 600. For all x < 600, if we do not order the cost will be L ( x ) = 100(637 . 5- x ) if x ≤ 500 56875- 86 . 25 x if 500 < x ≤ 600 (1) if we choose to make the order the cost will be C ( x ) = 1000 + (600- x )40 + L (600) = 30125- 40 x we need to find x * such that L ( x * ) = C ( x * ) So x * ≈ 578 . 38. (c) If x = 0 we order 600 liters. Hence the cost is C (0) = 1000 + 600 * 40 + L (600) = 30125 . (2) If x = 700, we do not order. The cost is C (700) = L (700) = 2000 (3) 2. (a) Using the notation in Section 1.5 of the newsvendor notes: c f = 1000, c v = 40, h = 10, p = 100. The optimal order-up-to quantity S follows from F ( S ) = p- c v p + h = 100- 40...
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Hmwk5sol - ISyE 3232 Stochastic Manufacturing and Service...

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