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Beni Asllani University of Tennessee at Chattanooga Inventory Management Operations Management - 5 th Edition Chapter 12 Roberta Russell & Bernard W. Taylor, III
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Lecture Outline <ul><li>Elements of Inventory Management </li></ul><ul><li>Inventory Control Systems </li></ul><ul><li>Economic Order Quantity Models </li></ul><ul><li>Quantity Discounts </li></ul><ul><li>Reorder Point </li></ul><ul><li>Order Quantity for a Periodic Inventory System </li></ul>
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What Is Inventory? <ul><li>Stock of items kept to meet future demand </li></ul><ul><li>Purpose of inventory management </li></ul><ul><ul><li>how many units to order </li></ul></ul><ul><ul><li>when to order </li></ul></ul>
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Types of Inventory <ul><li>Raw materials </li></ul><ul><li>Purchased parts and supplies </li></ul><ul><li>Work-in-process (partially completed) products (WIP) </li></ul><ul><li>Items being transported </li></ul><ul><li>Tools and equipment </li></ul>
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Inventory and Supply Chain Management <ul><li>Bullwhip effect </li></ul><ul><ul><li>demand information is distorted as it moves away from the end-use customer </li></ul></ul><ul><ul><li>higher safety stock inventories to are stored to compensate </li></ul></ul><ul><li>Seasonal or cyclical demand </li></ul><ul><li>Inventory provides independence from vendors </li></ul><ul><li>Take advantage of price discounts </li></ul><ul><li>Inventory provides independence between stages and avoids work stop-pages </li></ul>
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Two Forms of Demand <ul><li>Dependent </li></ul><ul><ul><li>Demand for items used to produce final products </li></ul></ul><ul><ul><li>Tires stored at a Goodyear plant are an example of a dependent demand item </li></ul></ul><ul><li>Independent </li></ul><ul><ul><li>Demand for items used by external customers </li></ul></ul><ul><ul><li>Cars, appliances, computers, and houses are examples of independent demand inventory </li></ul></ul>
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Inventory and Quality Management <ul><li>Customers usually perceive quality service as availability of goods they want when they want them </li></ul><ul><li>Inventory must be sufficient to provide high-quality customer service in TQM </li></ul>
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Inventory Costs <ul><li>Carrying cost </li></ul><ul><ul><li>cost of holding an item in inventory </li></ul></ul><ul><li>Ordering cost </li></ul><ul><ul><li>cost of replenishing inventory </li></ul></ul><ul><li>Shortage cost </li></ul><ul><ul><li>temporary or permanent loss of sales when demand cannot be met </li></ul></ul>
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Inventory Control Systems <ul><li>Continuous system (fixed-order-quantity) </li></ul><ul><ul><li>constant amount ordered when inventory declines to predetermined level </li></ul></ul><ul><li>Periodic system (fixed-time-period) </li></ul><ul><ul><li>order placed for variable amount after fixed passage of time </li></ul></ul>
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ABC Classification <ul><li>Class A </li></ul><ul><ul><li>5 – 15 % of units </li></ul></ul><ul><ul><li>70 – 80 % of value </li></ul></ul><ul><li>Class B </li></ul><ul><ul><li>30 % of units </li></ul></ul><ul><ul><li>15 % of value </li></ul></ul><ul><li>Class C </li></ul><ul><ul><li>50 – 60 % of units </li></ul></ul><ul><ul><li>5 – 10 % of value </li></ul></ul>
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ABC Classification: Example (cont.) Example 10.1 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE 9 $30,600 35.9 6.0 6.0 8 16,000 18.7 5.0 11.0 2 14,000 16.4 4.0 15.0 1 5,400 6.3 9.0 24.0 4 4,800 5.6 6.0 30.0 3 3,900 4.6 10.0 40.0 6 3,600 4.2 18.0 58.0 5 3,000 3.5 13.0 71.0 10 2,400 2.8 12.0 83.0 7 1,700 2.0 17.0 100.0 $85,400 A B C % OF TOTAL % OF TOTAL CLASS ITEMS VALUE QUANTITY A 9, 8, 2 71.0 15.0 B 1, 4, 3 16.5 25.0 C 6, 5, 10, 7 12.5 60.0
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Economic Order Quantity (EOQ) Models <ul><li>EOQ </li></ul><ul><ul><li>optimal order quantity that will minimize total inventory costs </li></ul></ul><ul><li>Basic EOQ model </li></ul><ul><li>Production quantity model </li></ul>
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Assumptions of Basic EOQ Model <ul><li>Demand is known with certainty and is constant over time </li></ul><ul><li>No shortages are allowed </li></ul><ul><li>Lead time for the receipt of orders is constant </li></ul><ul><li>Order quantity is received all at once </li></ul>
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Inventory Order Cycle Demand rate Time Lead time Lead time Order placed Order placed Order receipt Order receipt Inventory Level Reorder point, R Order quantity, Q 0
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EOQ Cost Model C o - cost of placing order D - annual demand C c - annual per-unit carrying cost Q - order quantity Annual ordering cost = C o D Q Annual carrying cost = C c Q 2 Total cost = + C o D Q C c Q 2
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EOQ Cost Model TC = + C o D Q C c Q 2 = + C o D Q 2 C c 2 TC Q 0 = + C 0 D Q 2 C c 2 Q opt = 2 C o D C c Deriving Q opt Proving equality of costs at optimal point = C o D Q C c Q 2 Q 2 = 2 C o D C c Q opt = 2 C o D C c
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EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Total Cost Carrying Cost = C c Q 2 Slope = 0 Minimum total cost Optimal order Q opt Ordering Cost = C o D Q
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EOQ Example 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 C c = $0.75 per yard C o = $150 D = 10,000 yards Q opt = 2 C o D C c Q opt = 2(150)(10,000) (0.75) Q opt = 2,000 yards TC min = + C o D Q C c Q 2 TC min = + (150)(10,000) 2,000 (0.75)(2,000) 2 TC min = $750 + $750 = $1,500
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Production Quantity Model <ul><li>An inventory system in which an order is received gradually, as inventory is simultaneously being depleted </li></ul><ul><li>AKA non-instantaneous receipt model </li></ul><ul><ul><li>assumption that Q is received all at once is relaxed </li></ul></ul><ul><li>p - daily rate at which an order is received over time, a.k.a. production rate </li></ul><ul><li>d - daily rate at which inventory is demanded </li></ul>
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Production Quantity Model (cont.) Q (1- d/p ) Inventory level (1- d/p ) Q 2 Time 0 Order receipt period Begin order receipt End order receipt Maximum inventory level Average inventory level
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Production Quantity Model (cont.) p = production rate d = demand rate Maximum inventory level = Q - d = Q 1 - Q p d p Average inventory level = 1 - Q 2 d p TC = + 1 - d p C o D Q C c Q 2 Q opt = 2 C o D C c 1 - d p
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Production Quantity Model: Example C c = $0.75 per yard C o = $150 D = 10,000 yards d = 10,000/311 = 32.2 yards per day p = 150 yards per day Q opt = = = 2,256.8 yards 2 C o D C c 1 - d p 2(150)(10,000) 0.75 1 - 32.2 150 TC = + 1 - = $1,329 d p C o D Q C c Q 2 Production run = = = 15.05 days per order Q p 2,256.8 150
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Production Quantity Model: Example (cont.) Number of production runs = = = 4.43 runs/year D Q 10,000 2,256.8 Maximum inventory level = Q 1 - = 2,256.8 1 - = 1,772 yards d p 32.2 150
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Quantity Discounts Price per unit decreases as order quantity increases TC = + + PD C o D Q C c Q 2 where P = per unit price of the item D = annual demand
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Quantity Discount Model (cont.) Q opt Carrying cost Ordering cost Inventory cost ($) 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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Quantity Discount: Example C o = $2,500 C c = $190 per computer D = 200 QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 90+ 900 Q opt = = = 72.5 PCs 2 C o D C c 2(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 C o D Q C c Q 2 For Q = 90
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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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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 = (32.154)(10) = 321.54 yards
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Safety Stocks <ul><li>Safety stock </li></ul><ul><ul><li>buffer added to on hand inventory during lead time </li></ul></ul><ul><li>Stockout </li></ul><ul><ul><li>an inventory shortage </li></ul></ul><ul><li>Service level </li></ul><ul><ul><li>probability that the inventory available during lead time will meet demand </li></ul></ul>
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Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0
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Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock
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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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Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock d L Demand z d L
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Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability For a 95% service level, z = 1.65 d = 30 yards per day L = 10 days d = 5 yards per day R = dL + z d L = 30(10) + (1.65)(5)( 10) = 326.1 yards Safety stock = z d L = (1.65)(5)( 10) = 26.1 yards
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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 I = inventory level
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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) 60 + 5 - 8 = 397.96 bottles
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