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Chapter 13 Inventory Management

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Lecture Outline Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts Reorder Point Order Quantity for a Periodic Inventory System Copyright 2011 John Wiley & Sons, Inc.13-2

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What Is Inventory? Stock of items kept to meet future demand Purpose of inventory management how many units to order when to order Copyright 2011 John Wiley & Sons, Inc.13-3

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Supply Chain Management Bullwhip effect demand information is distorted as it moves away from the end-use customer higher safety stock inventories to are stored to compensate Seasonal or cyclical demand Inventory provides independence from vendors Take advantage of price discounts Inventory provides independence between stages and avoids work stoppages Copyright 2011 John Wiley & Sons, Inc.13-4

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Quality Management in the Supply Chain Customers usually perceive quality service as availability of goods they want when they want them Inventory must be sufficient to provide high- quality customer service in QM Copyright 2011 John Wiley & Sons, Inc.13-5

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Types of Inventory Raw materials Purchased parts and supplies Work-in-process (partially completed) products (WIP) Items being transported Tools and equipment Copyright 2011 John Wiley & Sons, Inc.13-6

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Two Forms of Demand Copyright 2011 John Wiley & Sons, Inc.13-7 Dependent Demand for items used to produce final products Tires for autos are a dependent demand item Independent Demand for items used by external customers Cars, appliances, computers, and houses are examples of independent demand inventory

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Inventory Costs Carrying cost cost of holding an item in inventory Ordering cost cost of replenishing inventory Shortage cost temporary or permanent loss of sales when demand cannot be met Copyright 2011 John Wiley & Sons, Inc.13-8

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Inventory Control Systems Copyright 2011 John Wiley & Sons, Inc.13-9 Continuous system (fixed-order-quantity) constant amount ordered when inventory declines to predetermined level Periodic system (fixed-time-period) order placed for variable amount after fixed passage of time

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ABC Classification Class A 5 – 15 % of units 70 – 80 % of value Class B 30 % of units 15 % of value Class C 50 – 60 % of units 5 – 10 % of value Copyright 2011 John Wiley & Sons, Inc.13-10

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ABC Classification Copyright 2011 John Wiley & Sons, Inc $ PARTUNIT COSTANNUAL USAGE

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ABC Classification Copyright 2011 John Wiley & Sons, Inc Example $30, , , , , , , , , , TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE A B C $85,400

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ABC Classification Copyright 2011 John Wiley & Sons, Inc Example 10.1 % OF TOTAL CLASSITEMSVALUEQUANTITY A9, 8, B1, 4, C6, 5, 10,

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Economic Order Quantity (EOQ) Models EOQ optimal order quantity that will minimize total inventory costs Basic EOQ model Production quantity model Copyright 2011 John Wiley & Sons, Inc.13-14

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Assumptions of Basic EOQ Model Demand is known with certainty and is constant over time No shortages are allowed Lead time for the receipt of orders is constant Order quantity is received all at once Copyright 2011 John Wiley & Sons, Inc.13-15

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Inventory Order Cycle Copyright 2011 John Wiley & Sons, Inc Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q 0 Average inventory Q 2

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EOQ Cost Model Copyright 2011 John Wiley & Sons, Inc C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDQCoDQ Annual carrying cost = CcQ2CcQ2 Total cost = + CoDQCoDQ CcQ2CcQ2

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EOQ Cost Model Copyright 2011 John Wiley & Sons, Inc TC = + CoDQCoDQ CcQ2CcQ2 = – + CoDQ2CoDQ2 Cc2Cc2 TC Q 0 = – + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = CoDQCoDQ CcQ2CcQ2 Q 2 = 2CoDCc2CoDCc Q opt = 2CoDCc2CoDCc

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EOQ Cost Model Copyright 2011 John Wiley & Sons, Inc Order Quantity, Q Annual cost ($) Total Cost Carrying Cost = CcQ2CcQ2 Slope = 0 Minimum total cost Optimal order Q opt Ordering Cost = CoDQCoDQ

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EOQ Example Copyright 2011 John Wiley & Sons, Inc C c = $0.75 per gallonC o = $150D = 10,000 gallons Q opt = 2CoDCc2CoDCc 2(150)(10,000) (0.75) Q opt = 2,000 gallons TC min = + CoDQCoDQ CcQ2CcQ2 (150)(10,000) 2,000 (0.75)(2,000) 2 TC min = $750 + $750 = $1,500 Orders per year =D/Q opt =10,000/2,000 =5 orders/year Order cycle time =311 days/(D/Q opt ) =311/5 =62.2 store days

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Production Quantity Model Order is received gradually, as inventory is simultaneously being depleted AKA non-instantaneous receipt model assumption that Q is received all at once is relaxed p - daily rate at which an order is received over time, a.k.a. production rate d - daily rate at which inventory is demanded Copyright 2011 John Wiley & Sons, Inc.13-21

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Production Quantity Model Copyright 2011 John Wiley & Sons, Inc Q(1-d/p) Inventory level (1-d/p) Q2Q2 Time 0 Order receipt period Begin order receipt End order receipt Maximum inventory level Average inventory level

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Production Quantity Model Copyright 2011 John Wiley & Sons, Inc p = production rated = demand rate Maximum inventory level =Q - d =Q 1 - QpQp dpdp Average inventory level = 1 - Q2Q2 dpdp TC = dpdp CoDQCoDQ CcQ2CcQ2 Q opt = 2C o D C c 1 - dpdp

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Production Quantity Model Copyright 2011 John Wiley & Sons, Inc C c = $0.75 per gallonC o = $150D = 10,000 gallons d = 10,000/311 = 32.2 gallons per dayp = 150 gallons per day Q opt = = = 2,256.8 gallons 2C o D C c 1 - dpdp 2(150)(10,000) TC = = $1,329 dpdp CoDQCoDQ CcQ2CcQ2 Production run = = = days per order QpQp 2,

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Production Quantity Model Copyright 2011 John Wiley & Sons, Inc Number of production runs = = = 4.43 runs/year DQDQ 10,000 2,256.8 Maximum inventory level =Q 1 - = 2, =1,772 gallons dpdp

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Solution of EOQ Models With Excel Copyright 2011 John Wiley & Sons, Inc The optimal order size, Q, in cell D8

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Solution of EOQ Models With Excel Copyright 2011 John Wiley & Sons, Inc The formula for Q in cell D10 =(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8)) =D10*(1-(D7/D8))

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Solution of EOQ Models With OM Tools Copyright 2011 John Wiley & Sons, Inc.13-28

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Quantity Discounts Copyright 2011 John Wiley & Sons, Inc Price per unit decreases as order quantity increases TC = + + PD CoDQCoDQ CcQ2CcQ2 where P = per unit price of the item D = annual demand

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Quantity Discount Model Copyright 2011 John Wiley & Sons, Inc Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 ) ORDER SIZE PRICE $ – ( d 1 ) ( d 2 )

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Quantity Discount Copyright 2011 John Wiley & Sons, Inc QUANTITYPRICE $1, , C o =$2,500 C c =$190 per TV D =200 TVs per year Q opt = = = 72.5 TVs 2CoDCc2CoDCc 2(2500)(200) 190 TC = + + PD = $233,784 C o D Q opt C c Q opt 2 For Q = 72.5 TC = + + PD = $194,105 CoDQCoDQ CcQ2CcQ2 For Q = 90

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Quantity Discount Model With Excel Copyright 2011 John Wiley & Sons, Inc =(D4*D5/E10)+(D3*E10/2)+C10*D5 =IF(D10>B10,D10,B10)

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Reorder Point Copyright 2011 John Wiley & Sons, Inc Inventory level at which a new order is placed R = dL where d = demand rate per period L = lead time

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Reorder Point Copyright 2011 John Wiley & Sons, Inc Demand = 10,000 gallons/year Store open 311 days/year Daily demand = 10,000 / 311 = gallons/day Lead time = L = 10 days R = dL = (32.154)(10) = gallons

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Safety Stock Safety stock buffer added to on hand inventory during lead time Stockout an inventory shortage Service level probability that the inventory available during lead time will meet demand P(Demand during lead time <= Reorder Point) Copyright 2011 John Wiley & Sons, Inc.13-35

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Variable Demand With Reorder Point Copyright 2011 John Wiley & Sons, Inc Reorder point, R Q LT Time LT Inventory level 0

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Reorder Point With Safety Stock Copyright 2011 John Wiley & Sons, Inc Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

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Reorder Point With Variable Demand Copyright 2011 John Wiley & Sons, Inc R = dL + z d L where d=average daily demand L=lead time d =the standard deviation of daily demand z=number of standard deviations corresponding to the service level probability z d L=safety stock

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Reorder Point For a Service Level Copyright 2011 John Wiley & Sons, Inc Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z d L

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Reorder Point For Variable Demand Copyright 2011 John Wiley & Sons, Inc The paint store wants a reorder point with a 95% service level and a 5% stockout probability d= 30 gallons per day L= 10 days d = 5 gallons per day For a 95% service level, z = 1.65 R= dL + z d L = 30(10) + (1.65)(5)( 10) = gallons Safety stock= z d L = (1.65)(5)( 10) = 26.1 gallons

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Determining Reorder Point with Excel Copyright 2011 John Wiley & Sons, Inc The reorder point formula in cell E7

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Order Quantity for a Periodic Inventory System Copyright 2011 John Wiley & Sons, Inc Q = d(t b + L) + z d t b + L - I where d= average demand rate t b = the fixed time between orders L= lead time d = standard deviation of demand z d t b + L= safety stock I= inventory level

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Periodic Inventory System Copyright 2011 John Wiley & Sons, Inc.13-43

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Fixed-Period Model With Variable Demand Copyright 2011 John Wiley & Sons, Inc d= 6 packages per day d = 1.2 packages t b = 60 days L= 5 days I= 8 packages z= 1.65 (for a 95% service level) Q= d(t b + L) + z d t b + L - I = (6)(60 + 5) + (1.65)(1.2) = packages

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Fixed-Period Model with Excel Copyright 2011 John Wiley & Sons, Inc Formula for order size, Q, in cell D10

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Copyright 2011 John Wiley & Sons, Inc Copyright 2011 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.

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