Inventory management@ doms

1. Inventory Management

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. 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. 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

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. 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. 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. 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. 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

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. 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. 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. 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. Solution of EOQ Models With Excel 13- The optimal order size, Q , in cell D8

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. Solution of EOQ Models With OM Tools 13-

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. 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. 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. Quantity Discount Model With Excel 13- =(D4*D5/E10)+(D3*E10/2)+C10*D5 =IF(D10>B10,D10,B10)

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

36. Variable Demand With Reorder Point 13- Reorder point, R Q LT Time LT Inventory level 0

37. Reorder Point With Safety Stock 13- Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

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. 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. 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. Determining Reorder Point with Excel 13- The reorder point formula in cell E7

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. Periodic Inventory System 13-

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. Fixed-Period Model with Excel 13- Formula for order size, Q , in cell D10