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Chapter 10

Chapter 10. Inventory Management. Inventory. Stock of items held to meet future demand Inventory management answers two questions How much to order When to order. Types of Inventory. Raw materials Purchased parts and supplies Labor In-process (partially completed) products

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Chapter 10

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  1. Chapter 10 Inventory Management

  2. Inventory • Stock of items held to meet future demand • Inventory management answers two questions • How much to order • When to order

  3. Types of Inventory • Raw materials • Purchased parts and supplies • Labor • In-process (partially completed) products • Component parts • Working capital • Tools, machinery, and equipment

  4. Reasons to Hold Inventory • Meet unexpected demand • Smooth seasonal or cyclical demand • Meet variations in customer demand • Take advantage of price discounts • Hedge against price increases • Quantity discounts

  5. Two Forms of Demand • Dependent • Items used to produce final products • Independent • Items demanded by external customers

  6. 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

  7. 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

  8. PERCENTAGE PERCENTAGE CLASS OF UNITS OF DOLLARS A 5 - 15 70 - 80 B 30 15 C 50 - 60 5 - 10 ABC Classification System • Demand volume and value of items vary • Classify inventory into 3 categories, typically on the basis of the dollar value to the firm

  9. 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 20 120 ABC Classification Example 10.1

  10. TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE PART UNIT COST ANNUAL USAGE 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 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 ABC Classification Example 10.1

  11. TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE PART UNIT COST ANNUAL USAGE 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 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 ABC Classification A B C Example 10.1

  12. TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE PART UNIT COST ANNUAL USAGE 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 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 % OF TOTAL % OF TOTAL CLASS ITEMS VALUE QUANTITY B 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 C ABC Classification Example 10.1

  13. 100 – 80 – 60 – 40 – 20 – 0 – C B A % of Value | | | | | | 0 20 40 60 80 100 % of Quantity ABC Classification

  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 • The order quantity is received all at once

  15. Order quantity, Q Inventory Level Reorder point, R 0 Time The Inventory Order Cycle Figure 10.1

  16. Order quantity, Q Demand rate Inventory Level Reorder point, R 0 Time Lead time Lead time Order placed Order receipt Order placed Order receipt The Inventory Order Cycle Figure 10.1

  17. Annual ordering cost = CoD Q CoD Q Annual carrying cost = CcQ 2 CcQ 2 Total cost = + EOQ Cost Model Co - cost of placing order D - annual demand Cc - annual per-unit carrying cost Q - order quantity

  18. Deriving Qopt Proving equality of costs at optimal point CoD Q CcQ 2 TC = + CoD Q2 Annual ordering cost = Cc 2 TC Q = + = CoD Q CoD Q C0D Q2 Cc 2 Annual carrying cost = 0 = + 2CoD Cc CoD Q CcQ 2 CcQ 2 CcQ 2 Q2 = 2CoD Cc Qopt = 2CoD Cc Total cost = + Qopt = EOQ Cost Model Co - cost of placing order D - annual demand Cc - annual per-unit carrying cost Q - order quantity

  19. Annual cost ($) Order Quantity, Q EOQ Cost Model Figure 10.2

  20. Annual cost ($) CoD Q Ordering Cost = Order Quantity, Q EOQ Cost Model Figure 10.2

  21. Annual cost ($) Carrying Cost = CcQ 2 CoD Q Ordering Cost = Order Quantity, Q EOQ Cost Model Figure 10.2

  22. Annual cost ($) Total Cost Slope = 0 Carrying Cost = Minimum total cost CcQ 2 CoD Q Ordering Cost = Optimal order Qopt Order Quantity, Q EOQ Cost Model Figure 10.2

  23. CoD Q CcQ 2 TCmin = + Qopt = 2(150)(10,000) (0.75) (150)(10,000) 2,000 (0.75)(2,000) 2 Qopt = TCmin = + 2CoD Cc Qopt = 2,000 yards TCmin = $750 + $750 = $1,500 EOQ Example Cc = $0.75 per yard Co = $150 D = 10,000 yards Orders per year = D/Qopt = 10,000/2,000 = 5 orders/year Order cycle time = 311 days/(D/Qopt) = 311/5 = 62.2 store days Example 10.2

  24. Inventory level Maximum inventory level Q(1-d/p) Average inventory level Q 2 (1-d/p) 0 Time EOQ with Noninstantaneous Receipt Figure 10.3

  25. Inventory level Maximum inventory level Q(1-d/p) Average inventory level Q 2 (1-d/p) 0 Begin order receipt End order receipt Time Order receipt period EOQ with Noninstantaneous Receipt Figure 10.3

  26. 2CoD Cc1 - Q p Maximum inventory level = Q - d = Q 1 - Qopt = d p d p d p CoD Q CcQ 2 Q 2 d p Average inventory level = 1 - TC = + 1 - EOQ with Noninstantaneous Receipt p = production rate d = demand rate

  27. 2CoD Cc1 - Qopt = = = 2,256.8 yards d p Q p 2,256.8 150 CoD Q CcQ 2 d p 32.2 150 TC = + 1 - = $1,329 2(150)(10,000) 0.75 1 - Production run = = = 15.05 days per order Production Quantity Cc = $0.75 per yard Co = $150 D = 10,000 yards d = 10,000/311 = 32.2 yards per day p = 150 yards per day Example 10.3

  28. 2CoD Cc1 - Qopt = = = 2,256.8 yards d p D Q 10,000 2,256.8 Number of production runs = = = 4.43 runs/year Q p 2,256.8 150 CoD Q CcQ 2 d p 32.2 150 TC = + 1 - = $1,329 2(150)(10,000) 0.75 1 - d p 32.2 150 Maximum inventory level = Q 1 - = 2,256.8 1 - = 1,772 yards Production run = = = 15.05 days per order Production Quantity Cc = $0.75 per yard Co = $150 D = 10,000 yards d = 10,000/311 = 32.2 yards per day p = 150 yards per day Example 10.3

  29. CoD Q CcQ 2 TC = + + PD where P = per unit price of the item D = annual demand Quantity Discounts • Price per unit decreases as order quantity increases

  30. CoD Q CcQ 2 TC = + + PD ORDER SIZE PRICE 0 - 99 $10 100 - 199 8 (d1) 200+ 6 (d2) where P = per unit price of the item D = annual demand Quantity Discounts • Price per unit decreases as order quantity increases

  31. Inventory cost ($) Quantity Discount Model Figure 10.4

  32. TC = ($10 ) TC (d1 = $8 ) TC (d2 = $6 ) Inventory cost ($) Carrying cost Ordering cost Q(d1 ) = 100 Qopt Q(d2 ) = 200 Quantity Discount Model Figure 10.4

  33. TC = ($10 ) TC (d1 = $8 ) TC (d2 = $6 ) Inventory cost ($) Carrying cost Ordering cost Q(d1 ) = 100 Qopt Q(d2 ) = 200 Quantity Discount Model Figure 10.4

  34. QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 90+ 900 2CoD Cc 2(2500)(200) 190 Qopt = = = 72.5 PCs For Q = 72.5 CoD Qopt CcQopt 2 For Q = 90 CcQ 2 CoD Q TC = + + PD = $233,784 TC = + + PD = $194,105 Quantity Discount Co = $2,500 Cc = $190 per computer D = 200 Example 10.4

  35. When to Order Reorder Point is the level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

  36. 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 Example 10.5

  37. 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

  38. Q Inventory level Reorder point, R 0 Time Variable Demand with a Reorder Point Figure 10.5

  39. Q Inventory level Reorder point, R 0 LT LT Time Variable Demand with a Reorder Point Figure 10.5

  40. Q Inventory level Reorder point, R Safety Stock 0 LT LT Time Reorder Point with a Safety Stock Figure 10.6

  41. 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 Reorder Point With Variable Demand

  42. Probability of meeting demand during lead time = service level Probability of a stockout Safety stock zd L dL Demand R Reorder Point for a Service Level Figure 10.7

  43. 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 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 Example 10.6

  44. Q = d(tb + L) + zdtb + L - I where d = average demand rate tb = the fixed time between orders L = lead time sd = standard deviation of demand zdtb + L = safety stock I = inventory level Order Quantity for a Periodic Inventory System

  45. d = 6 bottles per day sd = 1.2 bottles tb = 60 days L = 5 days I = 8 bottles z = 1.65 (for a 95% service level) Q = d(tb + L) + zdtb + L - I = (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8 = 397.96 bottles Fixed-Period Model with Variable Demand

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