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11-1Inventory Management William J. Stevenson Operations Management 8 th edition

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11-2Inventory Management CHAPTER 11 Inventory Management McGraw-Hill/Irwin Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.

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11-3Inventory Management Economic order quantity model Economic production model Quantity discount model Economic Order Quantity Models

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11-4Inventory Management 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 Assumptions of EOQ Model

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11-5Inventory Management The Inventory Cycle Figure 11.2 Profile of Inventory Level Over Time Quantity on hand Q Receive order Place order Receive order Place order Receive order Lead time Reorder point Usage rate Time

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11-6Inventory Management Total Cost Annual carrying cost Annual ordering cost Total cost =+ Q 2 H D Q S TC = + TC= Total annual cost Q= Order quantity in units H= Holding cost per unit D= Annual Demand S= Ordering cost

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11-7Inventory Management Cost Minimization Goal Order Quantity (Q) The Total-Cost Curve is U-Shaped Ordering Costs QOQO Annual Cost ( optimal order quantity) Figure 11.4C

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11-8Inventory Management 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. Q OPT = Optimum order quantity Q= Order quantity in units H= Holding cost per unit D= Annual Demand S= Ordering cost

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11-9Inventory Management 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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11-10Inventory Management 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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11-11Inventory Management 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 Economic Production Quantity Assumptions

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11-12Inventory Management Economic Run (Batch) Size Q p = 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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11-13Inventory Management 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. a)Optimal run size b) Minimum total annual cost

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11-14Inventory Management 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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