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Copyright 2006 John Wiley & Sons, Inc. Inventory Management

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Copyright 2006 John Wiley & Sons, Inc. Lecture Outline Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts Reorder Point Order Quantity for a Periodic Inventory System

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

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

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Copyright 2006 John Wiley & Sons, Inc.12-5 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

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Copyright 2006 John Wiley & Sons, Inc.12-6 Inventory and Quality Management 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 TQM

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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

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Copyright 2006 John Wiley & Sons, Inc.12-8 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

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Copyright 2006 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

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Copyright 2006 John Wiley & Sons, Inc. ABC Classification: Example 1$ PARTUNIT COSTANNUAL USAGE

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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,

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Copyright 2006 John Wiley & Sons, Inc. Economic Order Quantity (EOQ) Models EOQ optimal order quantity that will minimize total inventory costs Basic EOQ model Production quantity model

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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

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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

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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

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Copyright 2006 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

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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

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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

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Copyright 2006 John Wiley & Sons, Inc. Production Quantity Model An inventory system 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

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Copyright 2006 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

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Copyright 2006 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

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Copyright 2006 John Wiley & Sons, Inc. Production Quantity Model: Example C c = $0.75 per yardC o = $150D = 10,000 yards d = 10,000/311 = 32.2 yards per dayp = 150 yards per day Q opt = = = 2,256.8 yards 2C o D C c 1 - dp 2(150)(10,000) TC = = $1,329 dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = = days per order Qp2,

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Copyright 2006 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 yards dpdp

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Copyright 2006 John Wiley & Sons, Inc. Quantity Discounts Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand

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Copyright 2006 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 )

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Copyright 2006 John Wiley & Sons, Inc. Quantity Discount: Example QUANTITYPRICE $1, , C o =$2,500 C c =$190 per computer D =200 Q opt = = = 72.5 PCs 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

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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

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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

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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

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

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

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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

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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

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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

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Copyright 2006 John Wiley & Sons, Inc 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

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Copyright 2006 John Wiley & Sons, Inc Fixed-Period Model with Variable Demand d= 6 bottles per day d = 1.2 bottles t b = 60 days L= 5 days I= 8 bottles 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) = bottles

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