This document summarizes key concepts in inventory management including inventory control systems, economic order quantity models, reorder points, safety stocks, and order quantities for periodic inventory systems. It discusses the costs of inventory like carrying costs and ordering costs. It also covers topics like ABC classification, quantity discounts, and production quantity models.

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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