Copyright 2009 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Inventory Management Operations Management - 6 th Edition Chapter 13 Roberta Russell & Bernard W. Taylor, III

Copyright 2009 John Wiley & Sons, Inc.13-2 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 2009 John Wiley & Sons, Inc.13-3 What Is Inventory?   Stock of items kept to meet future demand   Purpose of inventory management how many units to order when to order

Copyright 2009 John Wiley & Sons, Inc.13-4 Reasons for Inventory and Bullwhip Effect  Bullwhip effect demand information is distorted as it moves away from the end-use customer demand information is distorted as it moves away from the end-use customer higher safety stock inventories to are stored to compensate 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 2009 John Wiley & Sons, Inc.13-5 Inventory and 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 2009 John Wiley & Sons, Inc.13-6 Types of Inventory   Raw materials   Work-in-process (partially completed) products (WIP)   Finished Goods   Purchased parts and supplies   Items being transported   Tools and equipment

Copyright 2009 John Wiley & Sons, Inc.13-7 Two Forms of Demand  Dependent  Demand for items used to produce final products   Tires stored at a Goodyear plant are an example of a dependent demand item  Independent  Demand for items used by external customers   Cars, appliances, computers, and houses are examples of independent demand inventory

Copyright 2009 John Wiley & Sons, Inc.13-8 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 2009 John Wiley & Sons, Inc.13-9 Inventory Control Systems  ABC Classification  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

Copyright 2009 John Wiley & Sons, Inc ABC Classification  Class A 5 – 15 % of units 5 – 15 % of units 70 – 80 % of value 70 – 80 % of value  Class B 30 % of units 30 % of units 15 % of value 15 % of value  Class C 50 – 60 % of units 50 – 60 % of units 5 – 10 % of value 5 – 10 % of value

Copyright 2009 John Wiley & Sons, Inc ABC Classification: Example 1$ PARTUNIT COSTANNUAL USAGE

Copyright 2009 John Wiley & Sons, Inc ABC Classification: Example (cont.) Example $ PARTUNIT COSTANNUAL USAGE TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE 9$30, , , , , , , , , , $85,400 AB C % OF TOTAL CLASSITEMSVALUEQUANTITY A9, 8, B1, 4, C6, 5, 10,

Copyright 2009 John Wiley & Sons, Inc Continuous Review: Economic Order Quantity (EOQ) Models   EOQ optimal order quantity that will minimize total inventory costs   Basic EOQ model   Production quantity model

Copyright 2009 John Wiley & Sons, Inc Assumptions of Basic EOQ Model Assuming Continuous REVIEW  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 2009 John Wiley & Sons, Inc Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q 0 Inventory Order Cycle Average inventory Q 2

Copyright 2009 John Wiley & Sons, Inc EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222

Copyright 2009 John Wiley & Sons, Inc EOQ Cost Model 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

Copyright 2009 John Wiley & Sons, Inc EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Total Cost Carrying Cost = CcQCcQ22CcQCcQ222 Slope = 0 Minimum total cost Optimal order Q opt Q opt Ordering Cost = CoDCoDQQCoDCoDQQQ

Copyright 2009 John Wiley & Sons, Inc EOQ Example C c = $0.75 per gallonC o = $150D = 10,000 gallons Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc 2(150)(10,000)(0.75) Q opt = 2,000 gallons TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 (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

Copyright 2009 John Wiley & Sons, Inc Production Quantity Model (Continuous Review with non- instantaneous receipt)   An EOQ Model in which an 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 2009 John Wiley & Sons, Inc Production Quantity Model (cont.) Q(1-d/p) Inventorylevel (1-d/p) Q2 Time 0 Order receipt period BeginorderreceiptEndorderreceipt Maximum inventory level Average

Copyright 2009 John Wiley & Sons, Inc Production Quantity Model (cont.) p = production rated = demand rate Maximum inventory level =Q - d =Q 1 - Qp dp Average inventory level = 1 - Q2 dp TC = dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Q opt = 2C o D C c 1 - dp

Copyright 2009 John Wiley & Sons, Inc Production Quantity Model: Example 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 - dp 2(150)(10,000) TC = = $1,329 dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = = days per order Qp2,

Copyright 2009 John Wiley & Sons, Inc Production Quantity Model: Example (cont.) Number of production runs = = = 4.43 runs/year DQDQ 10,000 2,256.8 Maximum inventory level =Q 1 - = 2, =1,772 gallons dpdp

Copyright 2009 John Wiley & Sons, Inc Solution of EOQ Models with Excel

Copyright 2009 John Wiley & Sons, Inc Solution of EOQ Models with Excel (Con’t)

Copyright 2009 John Wiley & Sons, Inc Solution of EOQ Models with OM Tools

Copyright 2009 John Wiley & Sons, Inc Continuous Review EOQ with Quantity Discounts Price per unit decreases as order quantity increases We have to add annual cost TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand

Copyright 2009 John Wiley & Sons, Inc Quantity Discount Model (cont.) Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 ) ORDER SIZE PRICE $ – ( d 1 ) ( d 2 )

Copyright 2009 John Wiley & Sons, Inc Quantity Discount: Example QUANTITYPRICE $1, , C o =$2,500 C c =$190 per TV D =200 TVs per year Q opt = = = 72.5 TVs 2CoD2CoDCcCc2CoD2CoDCcCc2(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 CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 For Q = 90

Copyright 2009 John Wiley & Sons, Inc Quantity-Discount Model Solution with Excel

Copyright 2009 John Wiley & Sons, Inc Reorder Point Level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

Copyright 2009 John Wiley & Sons, Inc Reorder Point: Example Demand = 10,000 gallons/year Store is open 311 days/year Daily demand = 10,000 / 311 = gallons/day Lead time = L = 10 days R = dL = (32.154)(10) = gallons

Copyright 2009 John Wiley & Sons, Inc Safety Stocks  Safety stock  A buffer that is added to on-hand inventory during lead time  Stockout  An inventory shortage  Service level  The probability that the inventory available during lead time will meet demand

Copyright 2009 John Wiley & Sons, Inc Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0

Copyright 2009 John Wiley & Sons, Inc Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

Copyright 2009 John Wiley & Sons, Inc Reorder Point With Variable Demand 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

Copyright 2009 John Wiley & Sons, Inc Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z  d L

Copyright 2009 John Wiley & Sons, Inc Reorder Point for Variable Demand 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

Copyright 2009 John Wiley & Sons, Inc Determining Reorder Point with Excel

Copyright 2009 John Wiley & Sons, Inc ANOTHER Control System: Order Quantity for a Periodic Inventory System 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 z  d t b + L= safety stock I= inventory level

Copyright 2009 John Wiley & Sons, Inc Periodic Inventory System

Copyright 2009 John Wiley & Sons, Inc Fixed-Period Model with Variable Demand 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

Copyright 2009 John Wiley & Sons, Inc Fixed-Period Model with Excel

Copyright 2009 John Wiley & Sons, Inc Copyright 2009 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.