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