Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Inventory Management Operations Management - 5 th Edition Chapter 12 Roberta Russell & Bernard W. Taylor, III

Copyright 2006 John Wiley & Sons, Inc.12-2 Lecture Outline   Elements of Inventory Management Types of inventory Inventory costs ABC classification   Inventory Control Systems   Economic Order Quantity Models   Reorder Point

Copyright 2006 John Wiley & Sons, Inc.12-3 What Is Inventory?   Stock of items kept to meet future demand   Importance of inventory management   Purpose of inventory management how many units to order when to order

Copyright 2006 John Wiley & Sons, Inc.12-4 Types of Inventory   Raw materials   Purchased parts and supplies   Work-in-process (partially completed) products (WIP)   Items being transported   Tools and equipment

Copyright 2006 John Wiley & Sons, Inc.12-5 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Types of Inventory (Purpose)  Cycle stock  Safety stock  Anticipation inventory  Pipeline inventory

Copyright 2006 John Wiley & Sons, Inc.12-6 Two Forms of Demand (Two Types of Items)  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 2006 John Wiley & Sons, Inc.12-7 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 2006 John Wiley & Sons, Inc.12-8 Inventory Placement  Special items (make-to-order) (make-to-order)  Standard items (make-to-stock) (make-to-stock)

Copyright 2006 John Wiley & Sons, Inc.12-9 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e ABC Classification  The purpose  The process  The classifications

Copyright 2006 John Wiley & Sons, Inc ABC Classification  Class A 5 – 20 % of units 5 – 20 % 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 2006 John Wiley & Sons, Inc ABC Classification: Example 1$ PARTUNIT COSTANNUAL USAGE

Copyright 2006 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 2006 John Wiley & Sons, Inc Inventory Control Systems  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 2006 John Wiley & Sons, Inc Economic Order Quantity (EOQ) Models   EOQ optimal order quantity that will minimize total inventory costs   Basic EOQ model

Copyright 2006 John Wiley & Sons, Inc 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 2006 John Wiley & Sons, Inc EOQ: Cost Trade-off Order Freq.Lot sizeAvg. Inv Order Freq.Lot sizeAvg. Inv Daily 105 Weekly Monthly Ordering Cost Carrying cost Ordering Cost Carrying cost

Copyright 2006 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 2006 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 2006 John Wiley & Sons, Inc EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc 2(150)(10,000)(0.75) Q opt = 2,000 yards 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 2006 John Wiley & Sons, Inc Inventory Order Cycle Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q 0

Copyright 2006 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 2006 John Wiley & Sons, Inc Reorder Point: Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = yards/day Lead time = L = 10 days R = dL = (32.154)(10) = yards

Copyright 2006 John Wiley & Sons, Inc Safety Stocks  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

Copyright 2006 John Wiley & Sons, Inc Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0

Copyright 2006 John Wiley & Sons, Inc Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

Copyright 2006 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 2006 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 2006 John Wiley & Sons, Inc Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d= 30 yards per day L= 10 days  d = 5 yards per day For a 95% service level, z = 1.65 R= dL + z  d L = 30(10) + (1.65)(5)( 10) = yards Safety stock= z  d L = (1.65)(5)( 10) = 26.1 yards