KATYUSHA COMPUTATIONS OR QANATATIVE MANAGEMENT: USING ECONOMIC ORDER QUANTITY TO ASSESS SUSTAINABILITY OF HOSTILE ROCKET OFFENSIVES Johnnie B. Linn III,

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Presentation transcript:

KATYUSHA COMPUTATIONS OR QANATATIVE MANAGEMENT: USING ECONOMIC ORDER QUANTITY TO ASSESS SUSTAINABILITY OF HOSTILE ROCKET OFFENSIVES Johnnie B. Linn III, Ph.D. Concord University

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?

The Standard EOQ Cost Function

The Economic Order Quantity (EOQ)

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.

Adjusted EOQ

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.

Draw per Shipment

Interval Between Shipments

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.

Estimate of Total Available Inventory, Straight-Line Method

Release From Inventory, Straight-Line Method

Release from Inventory, Accelerated Method

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.

A Sample Calculation