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Inventory Management

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12-2 Lecture Outline Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts Reorder Point Order Quantity for a Periodic Inventory System

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12-3 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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12-4 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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12-5 Inventory and Supply Chain Management 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 stop-pages

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12-6 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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12-7 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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12-8 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

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12-9 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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12-10 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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12-11 ABC Classification: Example 1$ 6090 235040 330130 48060 530100 620180 710170 832050 951060 1020120 PARTUNIT COSTANNUAL USAGE

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12-12 ABC Classification: Example (cont.) Example 10.1 1$ 6090 235040 330130 48060 530100 620180 710170 832050 951060 1020120 PARTUNIT COSTANNUAL USAGE TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE 9 8 2 16.39.024.0 44,8005.66.030.0 33,9004.610.040.0 63,6004.218.058.0 53,0003.513.071.0 102,4002.812.083.0 71,7002.017.0100.0 $85,400

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12-13 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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12-14 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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12-15 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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12-16 EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = Annual carrying cost = Total cost = +

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12-17 EOQ Cost Model TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2 TC Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = Deriving Q opt Proving equality of costs at optimal point = Q 2 = Q opt =

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12-18 EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Slope = 0 Minimum total cost Optimal order Q opt Q opt

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12-19 EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc Q opt = yards TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 TC min = = Orders per year =D/Q opt = = orders/year Order cycle time = days/(D/Q opt ) = = store days

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12-20 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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12-21 Production Quantity Model (cont.) Inventorylevel (1-d/p) Q2 Time 0 Order receipt period BeginorderreceiptEndorderreceipt Maximum inventory level Average

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12-22 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 = + 1 - dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Q opt = 2C o D C c 1 - dp

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12-23 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 = = = yards 2C o D C c 1 - dp TC = + 1 - = dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = = days per order Qp

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12-24 Production Quantity Model: Example (cont.) Number of production runs = = = runs/year DQDQ Maximum inventory level =Q 1 - = = yards dpdp

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12-25 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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12-26 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 0 - 99 $10 100 – 199 8 ( d 1 ) 200+ 6 ( d 2 )

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12-27 Quantity Discount: Example QUANTITYPRICE 1 - 49$1,400 50 - 891,100 90+900 C o =$2,500 C c =$190 per computer D =200 Q opt = = = PCs 2CoD2CoDCcCc2CoD2CoDCcCc TC = + + PD = C o D Q opt C c Q opt 2 For Q = 72.5 TC = + + PD = CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 For Q = 90

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12-28 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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12-29 Reorder Point: Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 yards/day Lead time = L = 10 days R = dL = = yards

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12-30 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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12-31 Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0

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12-32 Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

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12-33 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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12-34 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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12-35 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 = R= dL + z d L = = yards Safety stock= z d L = = yards

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12-36 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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12-37 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 = = bottles

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