Chapter 10

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