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**Operations Management**

William J. Stevenson 8th edition

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**11 Inventory Management CHAPTER**

Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

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**Economic Order Quantity Models**

Economic production model Quantity discount model

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**Assumptions of EOQ Model**

Only one product is involved Annual demand requirements known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts

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**Profile of Inventory Level Over Time**

The Inventory Cycle Figure 11.2 Profile of Inventory Level Over Time Quantity on hand Q Receive order Place Lead time Reorder point Usage rate Time

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**Total Cost Annual carrying cost ordering Total cost = + Q 2 H D S TC =**

TC= Total annual cost Q= Order quantity in units H= Holding cost per unit D= Annual Demand S= Ordering cost Annual carrying cost ordering Total cost = + Q 2 H D S TC =

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**Cost Minimization Goal**

Figure 11.4C The Total-Cost Curve is U-Shaped Annual Cost Ordering Costs Order Quantity (Q) QO (optimal order quantity)

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Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal. QOPT= Optimum order quantity Q= Order quantity in units H= Holding cost per unit D= Annual Demand S= Ordering cost

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EOQ MODEL EXAMPLE A local distributor for a national tire company expects to sell approximately 9600 steel-belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year. D= $ 9600 H= $ 16 S= $ 75 a) What is the EOQ? b) No. Of orders per year=D/Q=9600/300=32

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**EOQ MODEL EXAMPLE D= $ 9600 H= $ 16 S= $ 75**

c) Length of order cycle= Q/D= 300/9600 =1/32 of a year*288 =9 work days. d) Total Cost=Carrying cost+Ordering cost =(Q/2)H+(D/Q)S =(300/2)16+(9600/300)75 = =$ 4800

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**Economic Production Quantity Assumptions**

Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts

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**Economic Run (Batch) Size**

Qp= Optimum production quantity H= Holding cost per unit D= Annual Demand S= Setup cost P= Production or delivery rate U= Usage rate

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**Economic Run (Batch) Size Example**

A toy manufacturer uses rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $ $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year. D= S=$45 H=$1 per year p=800 wheels per day u= wheels per 240 days or 200 wheels per day. Optimal run size Minimum total annual cost

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**Economic Run (Batch) Size Example**

D= S=$45 H=$1 per year p=800 wheels per day u= wheels per 240 days or 200 wheels per day. c) Thus, a run of wheels will be made every 12 days. d) Thus, each run will require three days to complete.

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