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  • 1. Chapter 13Inventory Management
  • 2. Lecture Outline• Elements of Inventory Management• Inventory Control Systems• Economic Order Quantity Models• Quantity Discounts• Reorder Point• Order Quantity for a Periodic Inventory SystemCopyright 2011 John Wiley & Sons, Inc. 13-2
  • 3. What Is Inventory?• Stock of items kept to meet future demand• Purpose of inventory management • how many units to order • when to orderCopyright 2011 John Wiley & Sons, Inc. 13-3
  • 4. Supply Chain Management• Bullwhip effect • demand information is distorted as it moves away from the end-use customer • 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 stoppagesCopyright 2011 John Wiley & Sons, Inc. 13-4
  • 5. Quality Management in the Supply Chain• 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 QMCopyright 2011 John Wiley & Sons, Inc. 13-5
  • 6. Types of Inventory• Raw materials• Purchased parts and supplies• Work-in-process (partially completed) products (WIP)• Items being transported• Tools and equipmentCopyright 2011 John Wiley & Sons, Inc. 13-6
  • 7. Two Forms of Demand• Dependent • Demand for items used to produce final products • Tires for autos are a dependent demand item• Independent • Demand for items used by external customers • Cars, appliances, computers, and houses are examples of independent demand inventoryCopyright 2011 John Wiley & Sons, Inc. 13-7
  • 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 metCopyright 2011 John Wiley & Sons, Inc. 13-8
  • 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 timeCopyright 2011 John Wiley & Sons, Inc. 13-9
  • 10. ABC Classification• Class A • 5 – 15 % of units • 70 – 80 % of value• Class B • 30 % of units • 15 % of value• Class C • 50 – 60 % of units • 5 – 10 % of valueCopyright 2011 John Wiley & Sons, Inc. 13-10
  • 11. ABC Classification PART UNIT COST ANNUAL USAGE 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 120Copyright 2011 John Wiley & Sons, Inc. 13-11
  • 12. ABC Classification 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 A 15.0 1 5,400 6.3 9.0 24.0 4 4,800 5.6 6.0 B 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 C 83.0 7 1,700 2.0 17.0 100.0 $85,400 Example 10.1Copyright 2011 John Wiley & Sons, Inc. 13-12
  • 13. ABC Classification % OF TOTAL % OF TOTAL CLASS ITEMS VALUE QUANTITY A 9, 8, 2 71.0 15.0 B 1, 4, 3 16.5 25.0 C 6, 5, 10, 7 12.5 60.0 Example 10.1Copyright 2011 John Wiley & Sons, Inc. 13-13
  • 14. Economic Order Quantity (EOQ) Models• EOQ • optimal order quantity that will minimize total inventory costs• Basic EOQ model• Production quantity modelCopyright 2011 John Wiley & Sons, Inc. 13-14
  • 15. Assumptions of Basic EOQ Model• Demand is known with certainty and is constant over time• No shortages are allowed• Lead time for the receipt of orders is constant• Order quantity is received all at onceCopyright 2011 John Wiley & Sons, Inc. 13-15
  • 16. Inventory Order CycleOrder quantity, Q Demand Average rate inventory Inventory Level Q 2 Reorder point, R 0 Lead Lead Time time time Order Order Order Order placed receipt placed receiptCopyright 2011 John Wiley & Sons, Inc. 13-16
  • 17. EOQ Cost Model Co - cost of placing order D - annual demand Cc - annual per-unit carrying cost Q - order quantity Co D Annual ordering cost = Q CcQ Annual carrying cost = 2 CoD CcQ Total cost = + Q 2Copyright 2011 John Wiley & Sons, Inc. 13-17
  • 18. EOQ Cost Model Deriving Qopt Proving equality of costs at optimal point CoD CcQ TC = + Q 2 CoD CcQ = TC CoD Cc Q 2 = – Q2 + Q 2 2CoD C0D Cc Q2 = Cc 0 = – Q2 + 2 2CoD 2CoD Qopt = Qopt = Cc CcCopyright 2011 John Wiley & Sons, Inc. 13-18
  • 19. EOQ Cost Model Annual cost ($) Total Cost Slope = 0 CcQ Minimum Carrying Cost = 2 total cost CoD Ordering Cost = Q Optimal order Order Quantity, Q QoptCopyright 2011 John Wiley & Sons, Inc. 13-19
  • 20. EOQ Example Cc = $0.75 per gallon Co = $150 D = 10,000 gallons 2CoD CoD CcQ Qopt = TCmin = + Cc Q 2 2(150)(10,000) (150)(10,000) (0.75)(2,000) Qopt = (0.75) TCmin = 2,000 + 2 Qopt = 2,000 gallons TCmin = $750 + $750 = $1,500Orders per year = D/Qopt Order cycle time = 311 days/(D/Qopt) = 10,000/2,000 = 311/5 = 5 orders/year = 62.2 store daysCopyright 2011 John Wiley & Sons, Inc. 13-20
  • 21. Production Quantity Model• 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 demandedCopyright 2011 John Wiley & Sons, Inc. 13-21
  • 22. Production Quantity Model Inventory level Maximum Q(1-d/p) inventory level Average Q inventory (1-d/p) 2 level 0 Begin End Time order order Order receipt receipt receipt periodCopyright 2011 John Wiley & Sons, Inc. 13-22
  • 23. Production Quantity Model p = production rate d = demand rate Maximum inventory level = Q - Q d p =Q1- d 2CoD p Qopt = d Q d Cc 1 - Average inventory level = 1- p 2 p CoD CcQ d TC = Q + 2 1 - pCopyright 2011 John Wiley & Sons, Inc. 13-23
  • 24. Production Quantity Model Cc = $0.75 per gallon Co = $150 D = 10,000 gallons d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day 2CoD 2(150)(10,000) Qopt = = = 2,256.8 gallons Cc 1 - d 0.75 1 - 32.2 p 150 CoD CcQ d TC = Q + 2 1 - p = $1,329 Q 2,256.8 Production run = = = 15.05 days per order p 150Copyright 2011 John Wiley & Sons, Inc. 13-24
  • 25. Production Quantity Model D 10,000 Number of production runs = = = 4.43 runs/year Q 2,256.8 d 32.2 Maximum inventory level = Q 1 - = 2,256.8 1 - p 150 = 1,772 gallonsCopyright 2011 John Wiley & Sons, Inc. 13-25
  • 26. Solution of EOQ Models With Excel The optimal order size, Q, in cell D8Copyright 2011 John Wiley & Sons, Inc. 13-26
  • 27. Solution of EOQ Models With Excel The formula for Q in cell D10 =(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8)) =D10*(1-(D7/D8))Copyright 2011 John Wiley & Sons, Inc. 13-27
  • 28. Solution of EOQ Models With OM ToolsCopyright 2011 John Wiley & Sons, Inc. 13-28
  • 29. Quantity Discounts Price per unit decreases as order quantity increases CoD CcQ TC = + + PD Q 2 where P = per unit price of the item D = annual demandCopyright 2011 John Wiley & Sons, Inc. 13-29
  • 30. Quantity Discount Model ORDER SIZE PRICE 0 - 99 $10 TC = ($10 ) 100 – 199 8 (d1) 200+ 6 (d2) TC (d1 = $8 ) TC (d2 = $6 ) Inventory cost ($) Carrying cost Ordering cost Q(d1 ) = 100 Qopt Q(d2 ) = 200Copyright 2011 John Wiley & Sons, Inc. 13-30
  • 31. Quantity Discount QUANTITY PRICE Co = $2,500 1 - 49 $1,400 Cc = $190 per TV 50 - 89 1,100 D = 200 TVs per year 90+ 900 2CoD 2(2500)(200) Qopt = = = 72.5 TVs Cc 190 For Q = 72.5 CoD CcQopt TC = + 2 + PD = $233,784 Qopt For Q = 90 Co D CcQ TC = + 2 + PD = $194,105 QCopyright 2011 John Wiley & Sons, Inc. 13-31
  • 32. Quantity Discount Model With Excel =IF(D10>B10,D10,B10) =(D4*D5/E10)+(D3*E10/2)+C10*D5Copyright 2011 John Wiley & Sons, Inc. 13-32
  • 33. Reorder Point• Inventory level at which a new order is placed R = dL where d = demand rate per period L = lead time Copyright 2011 John Wiley & Sons, Inc. 13-33
  • 34. Reorder Point Demand = 10,000 gallons/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 gallons/day Lead time = L = 10 days R = dL = (32.154)(10) = 321.54 gallonsCopyright 2011 John Wiley & Sons, Inc. 13-34
  • 35. Safety Stock• 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 • P(Demand during lead time <= Reorder Point)Copyright 2011 John Wiley & Sons, Inc. 13-35
  • 36. Variable Demand With Reorder Point Q Inventory level Reorder point, R 0 LT LT TimeCopyright 2011 John Wiley & Sons, Inc. 13-36
  • 37. Reorder Point With Safety Stock Inventory level Q Reorder point, R Safety Stock 0 LT LT TimeCopyright 2011 John Wiley & Sons, Inc. 13-37
  • 38. 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 stockCopyright 2011 John Wiley & Sons, Inc. 13-38
  • 39. Reorder Point For a Service Level Probability of meeting demand during lead time = service level Probability of a stockout Safety stock z d L dL R DemandCopyright 2011 John Wiley & Sons, Inc. 13-39
  • 40. Reorder Point For Variable Demand The paint store wants a reorder point with a 95% service level and a 5% stockout probability d = 30 gallons per day L = 10 days d = 5 gallons per day For a 95% service level, z = 1.65 R = dL + z d L Safety stock = z d L = 30(10) + (1.65)(5)( 10) = (1.65)(5)( 10) = 326.1 gallons = 26.1 gallonsCopyright 2011 John Wiley & Sons, Inc. 13-40
  • 41. Determining Reorder Point with Excel The reorder point formula in cell E7Copyright 2011 John Wiley & Sons, Inc. 13-41
  • 42. Order Quantity for a Periodic Inventory System Q = d(tb + L) + z d tb + L - I where d = average demand rate tb = the fixed time between orders L = lead time d = standard deviation of demand z d tb + L = safety stock I = inventory levelCopyright 2011 John Wiley & Sons, Inc. 13-42
  • 43. Periodic Inventory SystemCopyright 2011 John Wiley & Sons, Inc. 13-43
  • 44. Fixed-Period Model With Variable Demand d = 6 packages per day d = 1.2 packages tb = 60 days L = 5 days I = 8 packages z = 1.65 (for a 95% service level) Q = d(tb + L) + z d tb + L - I = (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8 = 397.96 packagesCopyright 2011 John Wiley & Sons, Inc. 13-44
  • 45. Fixed-Period Model with Excel Formula for order size, Q, in cell D10Copyright 2011 John Wiley & Sons, Inc. 13-45
  • 46. Copyright 2011 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.Copyright 2011 John Wiley & Sons, Inc. 13-46