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Optimal Inventory Management: Continuous Review and Economic Order Quantity Analysis

This document explores continuous review inventory theory, emphasizing the differences from periodic review practices. It discusses essential components of an inventory policy, including when and how much to order. Key cost factors are analyzed, such as ordering costs, holding costs, and shortage costs. A deterministic model is presented, detailing an example from manufacturing speakers for TVs, with calculations for the Economic Order Quantity (EOQ) and the cycle costs associated. The implications of shortages are examined, providing insights for effective inventory management.

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Optimal Inventory Management: Continuous Review and Economic Order Quantity Analysis

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  1. Inventory TheoryContinuous ReviewMath 305 12/7/08

  2. Continuous Review Previous model: periodic review • orders placed at the begining of periods Continuous review: an order may be placed at any time What is an inventory policy? • when to order more • how much to order Costs • ordering /production (paperwork, delivery charges, per unit charges) • holding (storage, spoilage, opportunity • shortage (possible loss of sale, cost of filling back order) • revenues (not usually counted) • salvage value (at end of inventory period)

  3. Deterministic Example, No Shortages My factory needs 8000 speakers/month for the TVs it makes • speakers are produced in batches • setup cost per batch: $12,000 per run (retooling, startup,...) • per speaker cost of $10 How much do I produce/order at a time? (Q) Q (speakers) Q/a (time) In general K = set up cost c = per unit cost → production cost/cycle = K + cQ a = rate of demand → cycle length = Q/a h = holding cost → holding cost per cycle = (Q/a)(Q/a) h = (hQ2)/2a

  4. No Shortages Total cost per cycle = K + cQ + (hQ2)/2a Cost per unit time T(Q) = K + cQ + (hQ2)/2a = aK/Q + ac + hQ/2 Q/a T(Q) dT/dQ = -aK/Q2 +h/2 Q* = √2aK/h = EOQ t = Q/a = √ 2K/ah Q* Q TVs: T(Q) = (8000)(12,000)/Q + 8000 + .30Q/2 Q* = 25,298 t* = 3.2 months

  5. Shortages Allowed Shortage cost p per unfilled unit of demand per unit time S Q S/a Q/a shortage: p(Q/a-S/a)(Q-s)/2 = p(Q-S)2 /2a T(Q,S) = K + cQ - hS2/2a + p(Q-S)2/2a = aK/Q + ac + hS2/2Q + p(Q-S) 2/2a Q/a (... messy partial derivatives...) S* = √2aK/h √ p/(p+h) Q* = √2aK/h √(p+h)/p What happens as p → ∞? as p↓ P for speakers = 1.10 S* = EOQ(√ 1.1/(1.1+.3) = 22,424 Q* = EOQ(√ (1.1+.3)/1.1) = 28,540 Q-S = max shortage = 6116

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