1. Beni Asllani University of Tennessee at Chattanooga Inventory Management Operations Management - 5 th Edition Chapter 12 Roberta Russell & Bernard W. Taylor, III

11. ABC Classification: Example 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. 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

15. 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

16. 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

17. 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

18. 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

19. 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

21. 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

22. 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

23. 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

24. 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

25. 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

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 )

27. 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

28. Reorder Point Level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

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 = (32.154)(10) = 321.54 yards

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

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

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

34. 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

35. 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

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 I = inventory level

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 = (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8 = 397.96 bottles

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