Lecture 2 Notes

# We never run out of inventory so to maximize net prot

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Unformatted text preview: oes not depend on ordering policy, as long as we never run out of inventory. So, to maximize net proﬁt, we simply need to minimize the cost of ordering and holding inventory. IOE 202: Operations Modeling, Fall 2009 Page 4 Space One ordering cycle: details ￿ Cycle duration = Q /a units of time ￿ Production/ordering cost per cycle = K + cQ dollars ￿ Holding cost per cycle = ￿ Total cost per cycle = IOE 202: Operations Modeling, Fall 2009 Page 5 Space Descriptive model: Expression of cost Thus, the cost per unit of time is: T (Q ) = Total cost per unit time = Total cost per cycle aK hQ = +ac + Duration of the cycle Q 2 This formula is a descriptive model: what happens when ordering quantity is Q ? ✻ ✲ IOE 202: Operations Modeling, Fall 2009 Page 6 Space Prescriptive model: EOQ ￿ ￿ To ﬁnd the minimum, compute the derivative of T (Q ) and set it to 0: T (Q ) = aK hQ aK h + ac + , so T ￿ (Q ) = − 2 + Q 2 Q 2 We want a prescriptive model: what value of Q is optimal, i.e., the best? Optimization problem: “minimize T (Q ) over all Q ≥ 0” The value of Q that minimizes the annual inventory ordering and holding cost: ￿ 2aK Q￿ = h (the “Economic Order Quantity”) Time between orders: Q￿ t￿ = a IOE 202: Operations Modeling, Fall 2009 Page 7 Space Back to CubicleMin’s problem: Parameters (with units): ￿ a = 100 cameras per month = 1200 cameras per year ￿ L = 1 week ￿ K = \$35 ￿ c = \$100 per camera ￿ h = \$10 per camera per year Hence, th...
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## This note was uploaded on 03/17/2010 for the course IOE 202 taught by Professor Marinaepelman during the Fall '09 term at University of Michigan-Dearborn.

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