Operations Management MD021

1. Operations Management(MD021) Inventory Management

2. Agenda Inventory Definitions Processes for Inventory Management Economic Order Quantity Inventory Models Reorder Point/Reorder Quantity Inventory Models Single Period Inventory Models

3. Inventory Definitions

4. Inventory is a stock or store of goods

5. Each firm carries types of inventories relevant to its production demands Raw materials & purchased parts Partially completed goods – called work in process (WIP) Finished-goods inventories manufacturing firms Merchandise retail stores

6. Each firm carries types of inventories relevant to its production demands Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers

7. Example: My Wife’s Business (Goodies For Girls, Inc.) Business Line = direct-to-consumer retailing In-home parties for selling ladies romance enhancement products Inventories Products for sale (about 200 SKUs) Ordering sheets, post-cards, envelopes, plastic bags, credit card swiping machines Startup = $600 investment in inventories Maximum Inventory = $25,000 Great customer service, slow inventory turns, lots of cash tied up Present Inventory = $14,000 Reasonable customer service, much better inventory turns, less cash tied up

8. Inventory is carried for many different reasons across different industries To meet anticipated demand Meeting demand in a timely manner enhances customer satisfaction Smooth production requirements across seasons Produce one season, sell in next (or throughout year) To decouple successive operations and maintain continuity of production Protects against machine breakdowns To protect against stock-outs Vendors do not always deliver on time

9. Inventory is carried for many different reasons across different industries To take advantage of order cycles to minimize purchasing and inventory costs Minimum order size requirements, full truck loads To help hedge against price increases Buy now at low price, store goods for future use To permit operations to operate Operations require a certain amount of WIP inventory To take advantage of quantity discounts Vendors often give discounts when ordering large quantities

10. Operations Strategy Having too much inventory is not good Tends to hide problems Makes it easier to live with (i.e. ignore) problems than to eliminate them Costly to maintain large stocks of inventories Opportunity costs of potentially doing something else with the money tied up in inventory Wise objectives Reduce lot sizes Reduce safety stock Reduce ordering costs and holding costs These are difficult to calculate, and often underestimated, leading to higher order sizes

11. Objective of Inventory Control To achieve satisfactory levels of customer service while keeping inventory costs (costs of ordering and carrying inventory) within reasonable bounds

12. Processes for Inventory Management

13. An effective inventory management approach will have certain information A system to keep track of inventory on hand and on order A reliable forecast of demand Knowledge of order lead times and lead time variability Reasonable estimates of Holding costs Ordering costs Shortage costs A classification system for inventory items

14. Inventory Counting Systems Periodic System Physical count of items made at periodic intervals Walgreens (1987) – manager walked around weekly, ordered everything needed across whole store Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoringcurrent levels of each item 2005 – grocery store scanners (bar codes) 2005 – RFID-based systems

15. Perpetual inventory counting systems range from low-tech to high-tech Two-Bin System - Two containers of inventory; reorder when the first bin is empty 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) – Computer chip embedded in a label on side of package, cases, or pallets

16. Radio Frequency Identification (RFID) used in tags, chips, implants, and wristbands

17. RFID tags are activated by RFID reader devices

18. Lead time must be matched against expected demand Lead time: time interval between ordering and receiving the order If we expect that demand will occur on a certain day in the future, we will need to place an order several days earlier, and account for: Lead time Lead time variability

19. Managers must estimate several types of inventory-related costs Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year Annual cost of 20%-40% of value (unit price) of an item Ordering costs: costs of ordering and receiving inventory fixed dollar amount per order, regardless of order size Shortage costs: costs when demand exceeds supply difficult to calculate – often assumed

20. ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A - very important B - mod. important C - least important

21. Cycle Counting A physical count of items in inventory. Counts are conducted periodically. A items counted frequently B items counted less frequently C items counted least frequently Cycle counting management trades off inventory accuracy against costs of counting How much accuracy is needed? When should cycle counting be performed? Who should do it?

22. Example: My Wife’s Business (Goodies For Girls, Inc.) Inventory Tracking System Spreadsheets Peachtree Accounting System Demand Forecast None – highly random, very difficult to do Wife communicates frequently with party hostesses to determine potential demand Lead Times and Lead Time Variability 7 Days (+ variability due to UPS) UPS has shipment tracking – decreases uncertainty Costs of holding, ordering, shortage Holding = approx 20-30% of price; Ordering = cost of wife’s time; Shortage = shipping cost for mailing out product to customer Classification system In my wife’s head – she knows what the good sellers are Spreadsheet A/B/C classification of historical sales (high sellers)

23. Economic Order Quantity Inventory Models

24. Economic Order Quantity (EOQ) Models Economic order quantity (EOQ) model Economic production quantity (EPQ) model Quantity discount model

25. Assumptions of EOQ Model 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

26. The Inventory Cycle

27. Total Cost Under the Economic Order Quantity Assumptions

28. Cost Minimization Goal

29. Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

30. Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal.

31. Example: My Wife’s Business (Goodies For Girls, Inc.) Bottles of Soapy Water Yearly Demand (D) = 400 Unit Price = $11 Holding cost (H) = $3 Ordering cost (S) = $50 (cost of one hour of time + UPS shipping cost)

32. Economic Production Quantity (EPQ) Relevant when production is done in batches or lots Capacity to produce a part exceeds the part’s usage or demand rate Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

33. Economic Production Quantity (EPQ) Assumptions Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts

34. Economic Production Quantity (EPQ)

35. Economic Run Size

36. Quantity Discounts Volume (Per Unit) Discounts 1 to 49 = $10/unit 50 to 100 = $9/unit 100 and up = $8/unit Case Discounts Single units = $10/unit Case of 10 = $90 = $9/unit

37. Quantity DiscountingTotal Costs with Purchasing Cost

38. Taking the derivative with respect to Q doesn’t change the EOQ formula

39. Total Cost with Constant Carrying Costs

40. Example: My Wife’s Business (Goodies For Girls, Inc.) Shimmer Time Body Glitter Yearly Demand (D) = 200 Unit Price = $10 Holding cost (H) = $3 Ordering cost (S) = $10 Price is $8 for orders over 25; $7 for orders over 50

41. Reorder Point, Reorder Quantity Inventory Models

42. Reorder point models Goal is to place an order when the amount of inventory on hand is still sufficient to satisfy demand during the time it takes to receive that order (i.e., the lead time)

43. When to Reorder with EOQ Ordering 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.

44. The reorder point leaves you with lead time inventory plus safety stock

45. How do we determine the reorder point quantity? Calculation accounts for … The rate of demand The lead time Demand and/or lead time variability Stock-out risk (safety stock)

46. Assuming demand and lead time are constant (as in EOQ) Reorder Point Quantity ROP = d X LT d = demand rate (units per time) LT = lead time (in same units of time) Example Usage = 12 order forms/day Lead time = 7 days ROP = (12 forms/day)(7 days) = 84 order forms Reorder when 84 order forms are left

47. When lead times are random, reorder point (ROP) must be adjusted

48. When we have an estimate of standard deviation of demand during lead time Example Demand during lead time = 84 forms sdLT = 2 ROP = 84 forms + zsdLT = 84 + 1.96(2) = 88 forms Reorder when 88 order forms are left

49. When only demand is variable Example Usage = 12 order forms/day; sd = 3 Lead time = 7 days ROP = (12 forms/day)(7 days) + 1.96(7)0.5(3) = 84 + 15.5 = 90 Reorder when 90 order forms are left

50. When only lead time is variable Example Usage = 12 order forms/day Average Lead time = 7 days; sLT = 1 ROP = (12)(7) + 1.96(12)(1) = 84 + 24 = 108 Reorder when 108 order forms are left

51. When both demand and lead time are variable Example Average Usage = 12 order forms/day; sd = 3 Average Lead time = 7 days; sLT = 1 ROP = (12)(7) + 1.96[(7)(9) + (144)(1)] = 84 + 1.96(14.4) = 84 + 27.7 = 112 Reorder when 112 order forms are left

52. Single Period Inventory Model(“The Newsboy Problem”)

53. Single Period Inventory Model Single period model: model for ordering of perishables and other items with limited useful lives how many newspapers should a newsboy on a street corner stock for a specific day? magazines fresh fruits fresh vegetables seafood cut flowers commemorative t-shirts and souvenirs spare parts

54. Single period model balances costs of a shortage against excess costs Shortage cost: generally the unrealized profits per unit (plus loss of customer goodwill) Cshortage = 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 Cexcess = Ce = original cost/unit – salvage value/unit

55. Single Period Model Continuous stocking levels Demand can be approximated using a continuous distribution Identifies optimal stocking levels Optimal stocking level balances unit shortage and excess cost Discrete stocking levels Demand can be approximated using a discrete distribution Service levels are discrete rather than continuous Desired service level is equaled or exceeded

56. Continuous stocking level assuming a uniform demand distribution Service level represents the probability that demand will not exceed the stocking level

57. Continuous stocking level assuming a uniform demand distribution Example: The movie “Gigli 2” will be released soon. A (somewhat crazy) retailer wants to determine the number of commemorative t-shirts to stock. Based on the rousingly successful “Gigli”, we have: Demand = uniform(1, 10) Cost/unit = $5 per t-shirt Revenue = $10 per t-shirt Salvage value = $1 per t-shirt Cs = revenue/unit – cost/unit = $10 - $5 = $5 Ce = cost/unit – salvage value/unit = $5 - $1 = $4 Service Level = Cs/(Cs+Ce) = ($5)/($5 + $4) = 0.555 The optimal stocking level must satisfy demand 55% of the time Soptimal = 1 + 0.55(10-1) = 1 + 5 = 6 t-shirts

58. Discrete stocking levels involve inverse transform from service level to order units