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Lecture 2 Notes - Space IOE 202 Lecture 2 outline...

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Space IOE 202: Lecture 2 outline Announcements Last time... Inventory management problems and models: Economic Order Quantity models: continued A di ff erent inventory management situation (and a Linear Programming model) IOE 202: Operations Modeling, Fall 2009 Page 1 Space Last time Problems of maintaining and replenishing inventory One of the issues: balancing holding costs vs. ordering and shortage costs First example: a problem with Long-term planning: Known, steady demand Known costs (setup and per unit ordering, holding) that do not change over time Known lead time that does not change over time No (planned) shortages allowed Continuous review Approach to managing inventory: Select a batch size Q items Order a batch of size Q just as you are about to run out What value of Q maximizes net profits? What is the “Economic Order Quantity”? IOE 202: Operations Modeling, Fall 2009 Page 2
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Space Inventory level over time Q/a Q Time Inventory Level - a IOE 202: Operations Modeling, Fall 2009 Page 3 Space Inputs and outputs of EOQ models Definition Units a Demand per unit of time unit/unit of time L Lead time units of time K Setup cost for ordering one batch $ c Cost for purchasing one unit $/unit h Holding cost per unit per unit of time held $/(unit × unit of time) Q Order Quantity (batch size) unit Q / a Time between orders unit of time T ( Q ) Cost per unit of time $/unit of time Note: sales revenue does 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
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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 Duration of the cycle = aK Q + ac + hQ 2 This formula is a descriptive model: what happens when ordering quantity is Q ? IOE 202: Operations Modeling, Fall 2009 Page 6
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Space Prescriptive model: EOQ We want a prescriptive model: what value of Q is optimal, i.e., the best? Optimization problem: “minimize T ( Q ) over all Q 0” To find the minimum, compute the derivative of T ( Q ) and set it to 0: T ( Q ) = aK Q + ac + hQ 2 , so T ( Q ) = aK Q 2 + h 2 The value of Q that minimizes the annual inventory ordering and holding cost: Q = 2 aK h (the “Economic Order Quantity”) Time between orders: t = Q 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
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