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KATYUSHA COMPUTATIONS OR QANATATIVE MANAGEMENT: USING ECONOMIC ORDER QUANTITY TO ASSESS SUSTAINABILITY OF HOSTILE ROCKET OFFENSIVES Johnnie B. Linn III, Ph.D. Concord University
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The Problem if Hezbollah is modeled as a “firm” that “delivers” launched rockets at a constant rate, given the number of rockets in stock and the frequency and size of additions to that stock, how many rockets ought Hezbollah fire off each day?
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The Standard EOQ Cost Function
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The Economic Order Quantity (EOQ)
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Modifications to Cost Function Demand (D) adjusted for casualty rate z of rockets at launch. Order Cost (c) adjusted for proportion n of shipments intercepted. Holding Cost (h) adjusted for daily casualty rate s of rockets in inventory.
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Adjusted EOQ
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What about extra inventory at the start? Let release from inventory be designated as Q 1. Order cost will have Q + Q 1 in the denominator instead of Q only to reflect longer waiting period between shipments. Holding cost will incorporate Q 1 as well as Q. First-order conditions for Q and Q 1 will be identical.
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Draw per Shipment
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Interval Between Shipments
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Two Inventory Release Methods “Straight-Line”: Inventory is released in a constant amount over a pre-specified number of days. “Accelerated”: Daily Inventory release is proportional to remaining inventory and is scaled to meet all of draw before first shipment arrives.
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Estimate of Total Available Inventory, Straight-Line Method
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Release From Inventory, Straight-Line Method
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Release from Inventory, Accelerated Method
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A Sample Calculation Initial inventory of 10,000 rockets 100 strikes per day a ratio of order cost to unit holding cost of 100 an offensive length of 50 days 5 percent casualty rate for launches 5 percent casualty rate for shipments 5 percent daily casualty rate for rockets in inventory.
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A Sample Calculation
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