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1. OPERATIONS ANALYTICS By Dr. Rajesh Chouksey Monday, November 6, 2023 1

2. Inventory Management

3. Amazon.com started as a “ virtual ” retailer No inventory No warehouses No overhead – just computers taking orders to be filled by others Growth has forced Amazon.com to become a world leader in warehousing and inventory management Inventory Management at Amazon.com

4. Each order is assigned by computer to the closest distribution center that has the product(s) A “ flow meister ” at each distribution center assigns work crews Technology helps workers pick the correct items from the shelves with almost no errors Items are placed in crates on a conveyor, bar code scanners scan each item 15 times to virtually eliminate errors Inventory Management at Amazon.com

5. Crates arrive at central point where items are boxed and labeled with new bar code Gift wrapping is done by hand at 30 packages per hour Completed boxes are packed, taped, weighed and labeled before leaving warehouse in a truck Order arrives at customer within 1 - 2 days Inventory Management at Amazon.com

6. The objective of inventory management is to strike a balance between inventory investment and customer service Inventory Management

7. Inventory can be visualized as stacks of money sitting on forklifts, on shelves, and in trucks and planes while in transit. Inventory can be difficult to convert back into cash. It is a good idea to try to get your inventory down as far as possible. Inventory

8. For many businesses, inventory is the largest asset on the balance sheet at any given time. A “typical” firm has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory and as much as 50% of total invested capital Less inventory lowers costs but increases chances of running out More inventory raises costs but always keeps customers happy Inventory

9. Inventory A stock or store of goods Independent demand items Items that are ready to be sold or used Inventory

10. Raw material Purchased but not processed Work-in-process (WIP) Undergone some change but not completed A function of cycle time for a product Maintenance/repair/operating (MRO) Necessary to keep machinery and processes productive Tools and supplies Finished goods Completed product awaiting shipment Pipeline Goods-in-transit to warehouses or customers Types of Inventory

11. Seasonal Inventory : Seasonality in demand is absorbed using inventory Decoupling Inventory : Complexity of production control is reduced by splitting manufacturing into stages and maintaining inventory between these stages Cyclic Inventory : Periodic replenishment causes cyclic inventory Pipeline Inventory : Exists due to lead time Safety Stock : Used to absorb fluctuations in demand due to uncertainty Types of Inventory

12. Independent versus Dependent Demand The source of demand determines its type Independent – Customer demand that is not directly influenced by the actions of the firm (e.g. customer orders) Dependent – Demand that is driven by the plans and activities of the firm (e.g. components, warehouse demand)

13. Demand Type

14. Demand Management and MPC Environment DM must conform to the strategy of the firm, capabilities of manufacturing, and needs of customers These define the MPC environment MPC environment is defined by customer order decoupling point The point where demand changes from independent to dependent Alternatively, order penetration point

15. Make-to-Stock Customer demand is filled from finished goods inventory (cosmetics, grocery items) Key focus of demand management is maintenance of finished goods inventories Physical distribution is a key concern

16. Assemble-to-Order Customer requirements are met by a combination of standard options (personal computers, fast food) Primary task of demand management is to define the customer’s order in terms of components and options (configuration management)

17. Make-to-Order Items built to customer specifications, starting with raw materials (airplanes) Primary task of demand management is gathering information about customer needs and coordinating with manufacturing

18. Engineer-to-Order Firm works with the customer to design the product, then produces the product, starting with raw materials (ships, bridges) Primary task of demand management is gathering information about customer needs and coordinating with engineering and manufacturing

19. MPC Environments Suppliers Raw materials Work-in-process Finished goods Make-to-Stock Assemble-to-Order Make-to-Order Engineer-to-Order Independent Dependent Independent Dependent Independent Dependent Independent Dependent Decoupling Points MPC Environment Inventory Location

20. Independent Demand Finished goods and spare parts typically belong to independent demand items in manufacturing organizations Two attributes characterize and distinguish independent demand items: Timing of demand : Independent demand items have a continuous demand Uncertainty of demand : There is considerable element of uncertainty in the demand in the case of independent demand items Inventory planning of independent demand items must address the following two key questions: How much? When?

21. Managing Inventory

22. 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 Inventory Counting Systems

23. Universal product code (UPC) Bar code printed on a label that has information about the item to which it is attached Radio frequency identification (RFID) tags A technology that uses radio waves to identify objects, such as goods, in supply chains Inventory Counting Technologies

24. Selective Control of Inventories Alternative Classification Schemes ABC Classification (on the basis of consumption value) XYZ Classification (on the basis of unit cost of the item) High Unit cost (X Class item) Medium Unit cost (Y Class item) Low unit cost (Z Class item) FSN Classification (on the basis of movement of inventory) Fast Moving Slow Moving Non-moving VED Classification (on the basis of criticality of items) Vital Essential Desirable On the basis of sources of supply Imported Indigenous (National Suppliers) Indigenous (Local Suppliers)

25. ABC Classification 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

26. 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 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 value ABC Classification System

27. ABC ANALYSIS A Items B Items | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100 Percentage of annual dollar usage 80 – 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Percentage of inventory items C Items

28. ABC Classification A graphical illustration

29. DAT, Inc., produces digital audiotapes to be used in the consumer audio division. DAT lacks sufficient personnel in its inventory supply section to closely control each item stocked, so it has asked you to determine an ABC classification. Here is a sample from the inventory records: Develop an ABC classification for these 10 items. Problem Item Average Monthly Demand Price per Unit Item 1 700 6 2 200 4 3 2,000 12 4 1,100 20 5 4,000 21 6 100 10 7 3,000 2 8 2,500 1 9 500 10 10 1,000 2

30. Classify the items as A, B, or C. Problem Item Annual Demand Unit Price H4-010 20,000 2.5 H5-201 60,200 4 P6-400 9,800 28.5 P6-401 14,500 12 P7-100 6,250 9 P9-103 7,500 22 TS-300 21,000 45 TS-400 45,000 40 TS-041 800 20 V1-001 33,100 4

31. Boreki Enterprises has the following 10 items in inventory. Theodore Boreki asks you, a recent OM graduate, to divide these items into ABC classifications. a) Develop an ABC classification system for the 10 items. b) How can Boreki use this information? c) Boreki reviews the classification and then places item A2 into the A category. Why might he do so?

32. ITEM ANNUAL DEMAND COST/UNIT A2 3000 50 B8 4000 12 C7 1500 45 D1 6000 10 E9 1000 20 F3 500 500 G2 300 1500 H2 600 20 I5 1750 10 J8 2500 5 DATA

33. L. Houts Plastics is a large manufacturer of injection-molded plastics in North Carolina. An investigation of the company’s manufacturing facility in Charlotte yields the information presented in the table below. How would the plant classify these items according to an ABC classification system?

34. ITEM CODE # AVERAGE INVENTORY (UNITS) V7ALUE ($/UNIT) A 400 3.75 B 300 4.00 C 120 2.50 D 75 1.50 E 60 1.75 F 30 2.00 G 20 1.15 H 12 2.05 I 8 1.80 J 7 2.00 K 6 3.00 L. Houts Plastics’ Charlotte Inventory Levels

35. Inventory MODEL IDEPENDENT DEMAND - EOQ Model

36. Inventory Models for Independent Demand Basic economic order quantity (EOQ) model Production order quantity model Quantity discount model

37. Basic EOQ Model Demand is known, constant, and independent Lead time is known and constant Receipt of inventory is instantaneous and complete Quantity discounts are not possible Only variable costs are setup (or ordering) and holding Stockouts can be completely avoided Important assumptions

38. Economic order quantity models identify the optimal order quantity by minimizing the sum of annual costs that vary with order size and frequency The basic economic order quantity model The economic production quantity model The quantity discount model How Much to Order: EOQ Models

39. Robust Model The EOQ model is robust It works even if all parameters and assumptions are not met The total cost curve is relatively flat in the area of the EOQ

40. Total Annual Cost Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order) Annual demand Number of units in each order Setup or order cost per order =

41. Inventory Usage Over Time Order quantity = Q (maximum inventory level) Usage rate Average inventory on hand Q 2 Minimum inventory Inventory level Time Total order received

42. Total Annual Cost Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity 2 (Holding cost per unit per year) =

43. Total Annual Cost Q* = Optimal number of units per order (EOQ)   Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order)

44. Minimizing Cost : Monday, November 6, 2023 44 Total cost of carrying Total cost of ordering Sum of the two costs Minimum Cost Economic Order Qty. Level of Inventory Cost of Inventory Objective is to minimize total costs

45. Goal: Total Cost Minimization Order Quantity (Q) The Total-Cost Curve is U-Shaped Ordering Costs Q O Annual Cost ( optimal order quantity) Holding Costs

46. Minimizing Costs Optimal order quantity is found when annual setup cost equals annual holding cost Solving for Q * Q = Number of pieces per order Q * = Optimal number of pieces per order (EOQ) D = Annual demand in units for the inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year

47. The basic EOQ model is used to find a fixed order quantity that will minimize total annual inventory costs Assumptions: Only one product is involved Annual demand requirements are known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts Basic EOQ Model

48. Quantity Time Safety stock Cyclic Stock Pipeline inventory L Cyclic inventory, pipeline inventory and safety stocks are critically linked to “how much” and “when” decisions in inventory planning The Inventory Cycle

49. The Inventory Cycle 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

50. 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. Deriving EOQ  

51. An EOQ Example = N = = Expected number of orders Demand Order quantity Total annual cost = Setup cost + Holding cost = T = Expected time between orders Number of working days per year Expected number of orders ROP = Demand per day * Lead time for a new order in days ROP = d * L The demand per day, d , is found by dividing the annual demand, D , by the number of working days in a year: d = D / Number of working days in a year

52. Illustration A toy manufacturer uses approximately 32,000 silicon chips annually. The chips are used at a steady rate during the 240 days a year that the plant operates. Annual holding cost is $3 per chip, and ordering cost is $120. Determine a. The optimal order quantity. b. The number of workdays in an order cycle. Given Data D = 32,000 chips per year S = $120 H = $3 per unit per year Monday, November 6, 2023 52

53. Illustration Given Data D = 32,000 chips per year, S = $120, H = $3 per unit per year a. Monday, November 6, 2023 53     1600 chips  

54. Illustration Given Data D = 32,000 chips per year, S = $120, H = $3 per unit per year b. Q*/ D = 1600 chips / 32,000 chips/ yrs = 1/20 year = 1/20*240 days = 12 days Monday, November 6, 2023 54 12 days  

55. Illustration William Beville’s computer training school, in Richmond, stock workbooks with the following characteristics: Demand D = 19,500 units / year Ordering cost S = $ 25 /order Holding cost H = $ 4 /unit/year a) Calculate the EOQ for the workbooks. b) What are the annual holding costs for the workbooks? c) What are the annual ordering costs? Monday, November 6, 2023 55

56. Illustration If D-5 8,000 per month, S-5 $45 per order, and H-5 $2 per unit per month, a) What is the economic order quantity? b) How does your answer change if the holding cost doubles? c) What if the holding cost drops in half? Monday, November 6, 2023 56

57. Illustration The Warren W. Fisher Computer Corporation purchases 8,000 transistors each year as components in minicomputers. The unit cost of each transistor is $10, and the cost of carrying one transistor in inventory for a year is $3. Ordering cost is $30 per order. What are the optimal order quantity, the expected number of orders placed each year, and the expected time between orders? Assume that Fisher operates on a 200-day working year. Monday, November 6, 2023 57

58. Illustration Given Data D = 32,000 chips per year, S = $120, H = $3 per unit per year a. Monday, November 6, 2023 58     1600 chips  

59. An EOQ Example Determine optimal number of needles to order D = 1,000 units S = Rs 10 per order H = Rs .50 per unit per year

60. An EOQ Example Determine optimal number of needles to order D = 1,000 units S = Rs 10 per order H = Rs .50 per unit per year

61. An EOQ Example Determine expected number of orders D = 1,000 units Q * = 200 units S = Rs 10 per order H = Rs .50 per unit per year N = = 5 orders per year 1,000 200 = N = = Expected number of orders Demand Order quantity

62. An EOQ Example Determine optimal time between orders D = 1,000 units Q * = 200 units S = Rs 10 per order N = 5 orders/year H = Rs .50 per unit per year T = = 50 days between orders 250 5 = T = Expected time between orders Number of working days per year Expected number of orders

63. An EOQ Example Determine the total annual cost D = 1,000 units Q * = 200 units S = Rs 10 per order N = 5 orders/year H = Rs .50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost

64. Numerical William Beville’s computer training school, in Richmond, stocks workbooks with the following characteristics: Demand D = 19,500 units / year Ordering cost = S = Rs 25 / order Holding Cost = H = Rs 4 per unit per year Calculate the EOQ for the workbooks. What are the annual holding costs for the workbooks? What are the annual ordering costs?

65. Solution (b) Annual holdings costs = [ Q /2] H = [494/2](4) = Rs 988 Annual ordering costs = [ D/Q ] S = [19500/494](25) = Rs 987   (a) 

66. Numerical If D = 8000 per month, S = Rs 45 per order, and H = Rs 2 per unit per month, What is the economic order quantity? How does your answer change if the holding cost doubled? What if the holding cost drops in half?

67. Solution ( a ) ( b ) If H doubles, from Rs 2 to Rs 4/unit/month , ( c ) If H drops in half, from Rs 2 to Rs 1/unit/month ,

68. Numerical Henry Crouch’s law office has traditionally ordered ink refills 60 units at a time. The firm estimates that carrying cost is 40% of the Rs 10 unit cost and that annual demand is about 240 units per year. The assumptions of the basic EOQ model are thought to apply. For what value of ordering cost would its action be optimal? If the true ordering cost turns out to be much greater than your answer to (a), what is the impact on the firm’s ordering policy?

69. Solution (a)   This problem reverses the unknown of a standard EOQ problem to solve for S . S = Rs 30 If S were Rs 30, then the EOQ would be 60. If the true ordering cost turns out to be much greater than RS 30, then the firm’s order policy is ordering too little at a time .

70. Solution An Apple store has a demand (D) for 8,000 iPhones per year. The firm operates a 250-day working year. On average, delivery of an order takes 3 working days, but has been known to take as long as 4 days. The store wants to calculate the reorder point without a safety stock and then with a one-day safety stock. d = D / Number of working days in a year = 8,000 / 250 = 32 units ROP = Reorder point = d * L = 32 units per day * 3 days = 96 units

71. Thank You! Monday, November 6, 2023 71