Inventory managementppt@ doms

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Inventory managementppt@ doms

  1. 1. Inventory Management
  2. 2. 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>13-
  3. 3. 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>13-
  4. 4. 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 stoppages </li></ul>13-
  5. 5. Quality Management in the Supply Chain <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 QM </li></ul>13-
  6. 6. 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>13-
  7. 7. Two Forms of Demand 13- <ul><li>Dependent </li></ul><ul><ul><li>Demand for items used to produce final products </li></ul></ul><ul><ul><li>Tires for autos are 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>
  8. 8. 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>13-
  9. 9. Inventory Control Systems 13- <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>
  10. 10. 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>13-
  11. 11. ABC Classification 13- 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
  12. 12. ABC Classification 13- Example 10.1 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 TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE A B C $85,400
  13. 13. ABC Classification 13- Example 10.1 % OF TOTAL % OF TOTAL CLASS ITEMS VALUE QUANTITY A 9, 8, 2 71.0 15.0 B 1, 4, 3 16.5 25.0 C 6, 5, 10, 7 12.5 60.0
  14. 14. Economic Order Quantity (EOQ) Models <ul><li>EOQ </li></ul><ul><ul><li>optimal order quantity that will minimize total inventory costs </li></ul></ul><ul><li>Basic EOQ model </li></ul><ul><li>Production quantity model </li></ul>13-
  15. 15. Assumptions of Basic EOQ Model <ul><li>Demand is known with certainty and is constant over time </li></ul><ul><li>No shortages are allowed </li></ul><ul><li>Lead time for the receipt of orders is constant </li></ul><ul><li>Order quantity is received all at once </li></ul>13-
  16. 16. Inventory Order Cycle 13- Demand rate Time Lead time Lead time Order placed Order placed Order receipt Order receipt Inventory Level Reorder point, R Order quantity, Q 0 Average inventory Q 2
  17. 17. EOQ Cost Model 13- C o - cost of placing order D - annual demand C c - annual per-unit carrying cost Q - order quantity Annual ordering cost = C o D Q Annual carrying cost = C c Q 2 Total cost = + C o D Q C c Q 2
  18. 18. EOQ Cost Model 13- TC = + C o D Q C c Q 2 = – + C o D Q 2 C c 2  TC  Q 0 = – + C 0 D Q 2 C c 2 Q opt = 2 C o D C c Deriving Q opt Proving equality of costs at optimal point = C o D Q C c Q 2 Q 2 = 2 C o D C c Q opt = 2 C o D C c
  19. 19. EOQ Cost Model 13- Order Quantity, Q Annual cost ($) Total Cost Carrying Cost = C c Q 2 Slope = 0 Minimum total cost Optimal order Q opt Ordering Cost = C o D Q
  20. 20. EOQ Example 13- C c = $0.75 per gallon C o = $150 D = 10,000 gallons Q opt = 2 C o D C c Q opt = 2(150)(10,000) (0.75) Q opt = 2,000 gallons 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 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
  21. 21. Production Quantity Model <ul><li>Order is received gradually, as inventory is simultaneously being depleted </li></ul><ul><ul><li>AKA non-instantaneous receipt model </li></ul></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>13-
  22. 22. Production Quantity Model 13- 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
  23. 23. Production Quantity Model 13- 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
  24. 24. Production Quantity Model 13- C c = $0.75 per gallon C o = $150 D = 10,000 gallons d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day Q opt = = = 2,256.8 gallons 2 C o D C c 1 - d p 2(150)(10,000) 0.75 1 - 32.2 150 TC = + 1 - = $1,329 d p C o D Q C c Q 2 Production run = = = 15.05 days per order Q p 2,256.8 150
  25. 25. Production Quantity Model 13- Number of production runs = = = 4.43 runs/year D Q 10,000 2,256.8 Maximum inventory level = Q 1 - = 2,256.8 1 - = 1,772 gallons d p 32.2 150
  26. 26. Solution of EOQ Models With Excel 13- The optimal order size, Q , in cell D8
  27. 27. Solution of EOQ Models With Excel 13- The formula for Q in cell D10 =(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8)) =D10*(1-(D7/D8))
  28. 28. Solution of EOQ Models With OM Tools 13-
  29. 29. Quantity Discounts 13- Price per unit decreases as order quantity increases TC = + + PD C o D Q C c Q 2 where P = per unit price of the item D = annual demand
  30. 30. Quantity Discount Model 13- Q opt Carrying cost Ordering cost Inventory cost ($) 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 )
  31. 31. Quantity Discount 13- QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 90+ 900 C o = $2,500 C c = $190 per TV D = 200 TVs per year Q opt = = = 72.5 TVs 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
  32. 32. Quantity Discount Model With Excel 13- =(D4*D5/E10)+(D3*E10/2)+C10*D5 =IF(D10>B10,D10,B10)
  33. 33. Reorder Point 13- <ul><li>Inventory level at which a new order is placed </li></ul>R = dL where d = demand rate per period L = lead time
  34. 34. Reorder Point 13- 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 gallons
  35. 35. Safety Stock <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><ul><ul><li>P(Demand during lead time <= Reorder Point) </li></ul></ul>13-
  36. 36. Variable Demand With Reorder Point 13- Reorder point, R Q LT Time LT Inventory level 0
  37. 37. Reorder Point With Safety Stock 13- Reorder point, R Q LT Time LT Inventory level 0 Safety Stock
  38. 38. Reorder Point With Variable Demand 13- 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
  39. 39. Reorder Point For a Service Level 13- Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock d L Demand z  d L
  40. 40. Reorder Point For Variable Demand 13- 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 = 30(10) + (1.65)(5)( 10) = 326.1 gallons Safety stock = z  d L = (1.65)(5)( 10) = 26.1 gallons
  41. 41. Determining Reorder Point with Excel 13- The reorder point formula in cell E7
  42. 42. Order Quantity for a Periodic Inventory System 13- 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
  43. 43. Periodic Inventory System 13-
  44. 44. Fixed-Period Model With Variable Demand 13- d = 6 packages per day  d = 1.2 packages t b = 60 days L = 5 days I = 8 packages 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 packages
  45. 45. Fixed-Period Model with Excel 13- Formula for order size, Q , in cell D10

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