1. Inventory Management McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

2. You should be able to: 1. Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management 2. Discuss the nature and importance of service inventories 3. Explain periodic and perpetual review systems 4. Explain the objectives of inventory management 5. Describe the A-B-C approach and explain how it is useful 6. Describe the basic EOQ model and its assumptions and solve typical problems 7. Describe the economic production quantity model and solve typical problems 8. Describe the quantity discount model and solve typical problems 9. Describe reorder point models and solve typical problems 10. Describe situations in which the single-period model would be appropriate, and solve typical problems Instructor Slides 13-2

3. Inventory A stock or store of goods Independent demand items Items that are ready to be sold or used Inventories are a vital part of business: (1) necessary for operations and (2) contribute to customer satisfaction A “typical” firm has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory Instructor Slides 13-3

4. Raw materials and purchased parts Work-in-process (WIP) Finished goods inventories or merchandise Tools and supplies Maintenance and repairs (MRO) inventory Goods-in-transit to warehouses or customers (pipeline inventory) Instructor Slides 13-4

5. 12-5 Independent Demand A B(4) C(2) D(2)E(1) D(3) F(2) Dependent Demand Independent demand is uncertain. Dependent demand is certain. Inventory: a stock or store of goods

6. Inventory management has two main concerns: 1. Level of customer service Having the right goods available in the right quantity in the right place at the right time 2. Costs of ordering and carrying inventories The overall objective of inventory management is to achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds 1. Measures of performance 2. Customer satisfaction Number and quantity of backorders Customer complaints 3. Inventory turnover Instructor Slides 13-6

7. Management has two basic functions concerning inventory: 1. Establish a system for tracking items in inventory 2. Make decisions about When to order How much to order Instructor Slides 13-7

8. Requires: 1. A system keep track of inventory 2. A reliable forecast of demand 3. Knowledge of lead time and lead time variability 4. Reasonable estimates of holding costs ordering costs shortage costs 5. A classification system for inventory items Instructor Slides 13-8

9. Periodic System Physical count of items in inventory made at periodic intervals Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item An order is placed when inventory drops to a predetermined minimum level Two-bin system Two containers of inventory; reorder when the first is empty Instructor Slides 13-9

10. Forecasts Inventories are necessary to satisfy customer demands, so it is important to have a reliable estimates of the amount and timing of demand Point-of-sale (POS) systems A system that electronically records actual sales Such demand information is very useful for enhancing forecasting and inventory management Lead time Time interval between ordering and receiving the order Instructor Slides 13-10

11. Purchase cost The amount paid to buy the inventory Holding (carrying) costs Cost to carry an item in inventory for a length of time, usually a year Ordering costs Costs of ordering and receiving inventory Setup costs The costs involved in preparing equipment for a job Analogous to ordering costs Shortage costs Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit Instructor Slides 13-11

12. A-B-C approach Classifying inventory according to some measure of importance, and allocating control efforts accordingly A items (very important) 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value B items (moderately important) C items (least important) 50 to 60 percent of the number of items in inventory but only about 10 to 15 percent of the annual dollar value Instructor Slides 13-12

13. Cycle counting A physical count of items in inventory Cycle counting management How much accuracy is needed? A items: ± 0.2 percent B items: ± 1 percent C items: ± 5 percent When should cycle counting be performed? Who should do it? Instructor Slides 13-13

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15. Economic order quantity models identify the optimal order quantity by minimizing the sum of annual costs that vary with order size and frequency 1. The basic economic order quantity model 2. The economic production quantity model 3. The quantity discount model Instructor Slides 13-15

16. The basic EOQ model is used to find a fixed order quantity that will minimize total annual inventory costs Assumptions: 1. Only one product is involved 2. Annual demand requirements are known 3. Demand is even throughout the year 4. Lead time does not vary 5. Each order is received in a single delivery 6. There are no quantity discounts Instructor Slides 13-16

17. 12-17 H: Holding cost S: Ordering cost Q: Quantity TC: Total Inventory Costs = Ordering Costs + Holding Costs

18. Profile of Inventory Level Over Time Quantity on hand Q Receive order Place order Receive order Place order Receive order Lead time Reorder point Usage rate Time Instructor Slides 13-18

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22. Instructor Slides 13-22

23. Order Quantity (Q) The Total-Cost Curve is U-Shaped Ordering Costs QOQO Annual Cost ( optimal order quantity) Holding Costs Instructor Slides 13-23

24. 12-24 The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q 2 H D Q S = TC = 2 (Q/2)H = 2 (D/Q)S

25. Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal. Instructor Slides 13-25

26. 12-26 Annual Demand: D = 9,600 tires Carrying Cost: H = $16/unit/year Ordering Cost: S = $75/order Annual Number of Business days: 288 Q: What is EOQ? A:

27. 12-27 Q: What is the number of orders per year? A: Q: What is the length of an order cycle? A:

28. 12-28 Q: What is the total minimum inventory costs? A:

29. The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate) Assumptions 1. Only one item is involved 2. Annual demand requirements are known 3. Usage rate is constant 4. Usage occurs continually, but production occurs periodically 5. The production rate is constant 6. Lead time does not vary 7. There are no quantity discounts Instructor Slides 13-29

30. Q QpQp I max Production and usage Production and usage Production and usage Usage only Usage only Cumulative production Amount on hand Time Instructor Slides 13-30

31. 12-31 Given: D = 1,000,000 units per year p = 8,000 units per day u = 4,000 units per day H = $2/unit/year S = $200 per setup Q = 20,000 units

32. 12-32 Q: At what rate the inventory is built up? A: p – u = 8000 – 4000 = 4000 per day Q: What is the Run Time? This is the production phase of the cycle (the length of the production time per cycle) A: 20,000/8000 = 2.5 days = Q/p Q: What is the maximum inventory? A: (4000 units per day) X (2.5 days) = 10,000 units = I max = (p – u)(Q/p)

33. Instructor Slides 13-33

34. 12-34 Given: D = 1,000,000 units per year p = 8,000 units per day u = 4,000 units per day H = $2/unit/year S = $200 per setup Q = 20,000 units

35. 12-35 Q: What is the number of runs per year? 1,000,000/20,000 = 50 = D/Q Q: What is the annual setup cost? (50 setups) X ($200 per setup) = $10,000 =(D/Q)S Q: What is the cycle time? 20,000/4,000 = 5 days = Q/u

36. Instructor Slides 13-36

37. Quantity discount Price reduction for larger orders offered to customers to induce them to buy in large quantities Instructor Slides 13-37

38. 12-38 Given: D = 48,000 units per year p = 800 units per day u = 200 units per day H = $1/unit/year S = $45 per setup

39. 12-39 Optimal run size (Q) is:

40. 12-40 Total minimum cost: TC = ((2400)/(2x800))(800-200)x1 + (48000/2400)x45 = $900 + $900 = $1,800

41. Adding PD does not change EOQ Instructor Slides 13-41

42. 12-42 When price reduction for large orders is offered the economic order quantity may change. Example: Order QuantityUnit Price ($) 0 – 399 2.2 400 – 699 2.0 700+ 1.8 D = 10,000 units S = $5.5 per order H =.2P or 20% of price EOQ Model

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44. 12-44 Annual carrying cost Purchasing cost TC =+ Q 2 H D Q S + + Annual ordering cost PD +

45. 12-45 Cost EOQ TC with PD TC without PD PD 0 Quantity Adding Purchasing cost doesn’t change EOQ 552.8 Lowest cost order 700

46. 12-46 Cost EOQ TC with PD TC without PD PD 0 Quantity Adding Purchasing cost doesn’t change EOQ 524.4 Lowest cost order 524.4

47. 12-47 Cost EOQ TC with PD TC without PD PD 0 Quantity Adding Purchasing cost doesn’t change EOQ 500 Lowest cost order 399

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49. 12-49 The lowest cost is obtained with an order size of 700 units

50. 12-50 Beginning with the lowest price, determine the EOQ for each price range until a feasible EOQ is found. If the feasible EOQ is for the lowest price range it is the optimal order quantity. If the feasible EOQ is not for the lowest price, compare the total cost (TC) of the feasible EOQ to the total cost of the lowest price breaks. The order quantity with the minimum TC is optimal.

51. 12-51 1. Price $1.8/unit: EOQ = 552.8 < 700 units (infeasible) 2. Price $2.0/unit: EOQ = 524.4 (feasible) 3. TC 1.8 = $18,204.57 4. TC 2.0 = $20,209.76 5. Optimum Q = 700

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54. 12-54 Cost EOQ TC with PD TC without PD PD 0 Quantity Adding Purchasing cost doesn’t change EOQ Figure 12.7

55. 12-55 OC EOQ Quantity Total Cost TC a TC c TC b Decreasing Price CC a,b,c Figure 12.9

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59. 12-59 OC EOQ Quantity Total Cost TC a TC c TC b Decreasing Price CC a,b,c Figure 13-9

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63. 12-63 Compute the common minimum point (EOQ). Identify the quantity range which contains the minimum point. Only one of the unit prices will have the minimum point in its feasible range. If the feasible minimum point is on the lowest price range, that is the optimum order quantity. If the feasible EOQ is not for the lowest price, compare the total cost (TC) of the feasible minimum point to the total cost of the lowest price breaks. The order quantity with the minimum TC is optimal

64. 12-64 Example: Order QuantityUnit Price ($) 0 – 399 2.2 400 – 699 2.0 700+ 1.8 D = 10,000 units S = $5.5 per order H = $.4 per unit/year EOQ Model

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67. The total-cost curve with quantity discounts is composed of a portion of the total-cost curve for each price Instructor Slides 13-67

68. Reorder point When the quantity on hand of an item drops to this amount, the item is reordered. Determinants of the reorder point 1. The rate of demand 2. The lead time 3. The extent of demand and/or lead time variability 4. The degree of stockout risk acceptable to management Instructor Slides 13-68

69. 12-69 Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time. Service Level - Probability that demand will not exceed supply during lead time.

70. 12-70 Demand rate (d) Length of lead time (LT) Variability and uncertainty of demand and lead time The degree of stock-out risk acceptable to management ROP = Demand During Lead Time + Safety Stock

71. Instructor Slides 13-71

72. 12-72 Demand rate (d) : constant Lead Time (LT) : constant ROP = (d)(LT) (no safety stock) Example: A Order for 81/2”X11” letter size paper is delivered 7 days after the order is placed. The usage rate is 10,00 sheets per day. The reorder point is: ROP = (1,000)(7) = 7,000 sheets

73. Demand or lead time uncertainty creates the possibility that demand will be greater than available supply To reduce the likelihood of a stockout, it becomes necessary to carry safety stock Safety stock Stock that is held in excess of expected demand due to variable demand and/or lead time Instructor Slides 13-73

74. 12-74 ROP Risk of a stockout Service level Probability of no stockout Expected demand Safety stock 0z Quantity z-scale Figure 12.13 The ROP based on a normal Distribution of lead time demand

75. Instructor Slides 13-75

76. As the amount of safety stock carried increases, the risk of stockout decreases. This improves customer service level Service level The probability that demand will not exceed supply during lead time Service level = 100% - Stockout risk Instructor Slides 13-76

77. The amount of safety stock that is appropriate for a given situation depends upon: 1. The average demand rate and average lead time 2. Demand and lead time variability 3. The desired service level Instructor Slides 13-77

78. 12-78 Z is determined by stockout risk or service level (SL) SL = 1 – Stockout Risk For example 95% service level implies that the probability that demand will not exceed supply during lead time is 95%. There is a 5% chance that demand will exceed supply during the lead time.

79. Note: If only demand is variable, then Instructor Slides 13-79

80. 12-80 Assume that the demand rate for a product is normally distributed with a mean of 10 tons and the standard deviation of 2 tons. Lead time is 4 days. Q: What is the expected demand during lead time?

81. 12-81 Q: For a service level of 97%, what is the safety stock: Z = 1.88 (from the standard normal table) ss = = (1.88)(2)(2) = 7.52

82. Note: If only lead time is variable, then Instructor Slides 13-82 Example: Page 598, Solved Problem 5

83. 12-83 Demand Rate: Random Variable Lead Time: Random Variable

84. 12-84 Example: Solved problem 6, page 598 (text)

85. Single-period model Model for ordering of perishables and other items with limited useful lives Shortage cost Generally, the unrealized profit per unit C shortage = C s = Revenue per unit – Cost per unit Excess cost Different between purchase cost and salvage value of items left over at the end of the period C excess = C e = Cost per unit – Salvage value per unit Instructor Slides 13-85

86. The goal of the single-period model is to identify the order quantity that will minimize the long-run excess and shortage costs Two categories of problem: Demand can be characterized by a continuous distribution Demand can be characterized by a discrete distribution Instructor Slides 13-86

87. Service level S o Balance Point Quantity CsCs CeCe S o =Optimum Stocking Quantity Instructor Slides 13-87

88. 12-88 Single period model: model for ordering of perishables and other items with limited useful lives Shortage cost: generally the unrealized profits per unit Cs = Revenue per unit – Cost per unit Excess cost: difference between purchase cost and salvage value of items left over at the end of a period Ce = Original cost per unit – Salvage value per unit

89. 12-89 Continuous stocking levels Identifies optimal stocking levels Optimal stocking level balances unit shortage and excess cost Examples 15 & 16; pages 589, 590 Discrete stocking levels Service levels are discrete rather than continuous Desired service level is equaled or exceeded Examples 17 & 18; pages 591 & 592

90. 12-90 Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) =.6/(.6+.2) Service level =.75 Service Level = 75% Quantity CeCs Stockout risk = 1.00 – 0.75 = 0.25

91. Improving inventory processes can offer significant cost reduction and customer satisfaction benefits Areas that may lead to improvement: Record keeping Records and data must be accurate and up-to-date Variation reduction Lead variation Forecast errors Lean operations Supply chain management Instructor Slides 13-91