1. © 2007 Pearson Education Inventory Inventory Management Chapter 12

2. © 2007 Pearson Education Inventory Management  Inventory management is the planning and controlling of inventories in order to meet the competitive priorities of the organization.  Effective inventory management is essential for realizing the full potential of any value chain.  Inventory management requires information about expected demands, amounts on hand and amounts on order for every item stocked at all locations.  The appropriate timing and size of the reorder quantities must also be determined.

3. © 2007 Pearson Education Inventory Basics  An inventory manager’s job is to balance the advantages and disadvantages of both low and high inventories.  Both have associated cost characteristics.

4. © 2007 Pearson Education Pressures for Low Inventories  Inventory holding cost is the sum of the cost of capital and the variable costs of keeping items on hand, such as storage and handling, taxes, insurance, and shrinkage.  Cost of Capital is the opportunity cost of investing in an asset relative to the expected return on assets of similar risk.  Storage and Handling arise from moving in and out of a storage facility plus the rental cost and/or opportunity cost of that space.  Taxes, Insurance, and Shrinkage: More taxes are paid and insurance costs are higher if end-of-the-year inventories are high. Shrinkage comes from theft, obsolescence and deterioration.

5. © 2007 Pearson Education  Customer Service: Reduces the potential for stockouts and backorders.  Ordering Cost: The cost of preparing a purchase order for a supplier or a production order for the shop.  Setup Cost: The cost involved in changing over a machine to produce a different item.  Labor and Equipment: Creating more inventory can increase workforce productivity and facility utilization.  Transportation Costs: Costs can be reduced.  Quantity Discount: A drop in the price per unit when an order is sufficiently large. Pressures for High Inventories

6. © 2007 Pearson Education Types of Inventory  Cycle Inventory: The portion of total inventory that varies directly with lot size (Q). Average cycle inventory =  Lot Sizing: The determination of how frequently and in what quantity to order inventory.  Safety Stock Inventory: Surplus inventory that a company holds to protect against uncertainties in demand, lead time and supply changes. Q2Q2

7. © 2007 Pearson Education  Anticipation Inventory is used to absorb uneven rates of demand or supply, which businesses often face.  Pipeline Inventory: Inventory moving from point to point in the materials flow system. Types of Inventory Pipeline inventory = D L = dL D L is the average demand for the item per period (d) times the number of periods in the item’s lead time (L).

8. © 2007 Pearson Education Estimating Inventory Levels Example 12.1 A plant makes monthly shipments of electric drills to a wholesaler in average lot sizes of 280 drills. The wholesaler’s average demand is 70 drills a week. Lead time is 3 weeks. The wholesaler must pay for the inventory from the moment the plant makes a shipment. If the wholesaler is willing to increase its purchase quantity to 350 units, the plant will guarantee a lead time of 2 weeks. What is the effect on cycle and pipeline inventories? Average cycle inventory = = = 140 Q2Q2 280 2 Pipeline inventory = D L = dL = 70(3) = 210 Under new proposal, the average lot size becomes 350 and lead time of 2 weeks. Average demand remains at 70 drills a week. Q2Q2 Average cycle inventory = = = 175 350 2 Pipeline inventory = D L = dL = 70(2) = 140 drills

9. © 2007 Pearson Education Application 12.1

10. © 2007 Pearson Education Application 12.1 continued

11. © 2007 Pearson Education Inventory Reduction Tactics  Reducing:  Cycle Inventory  Safety stock inventory  Anticipation inventory  Pipeline inventory  The basic tactics (levers) for reducing inventory: 1.A primary lever is one that must be activated if inventory is to be reduced. 2.A secondary lever reduces the penalty costs of applying the primary lever and the need for having inventory in the first place.

12. © 2007 Pearson Education Reducing Cycle Inventory  The primary tactic (lever) for reducing cycle inventory is to reduce lot size.  This can be devastating if other changes are not made, so two secondary levers can be used: 1.Streamline the methods for placing orders and making setups in order to reduce ordering and setup costs and allow Q to be reduced. 2.Increase repeatability in order to eliminate the need for changeovers.  Repeatability is the degree to which the same work can be done again.

13. © 2007 Pearson Education  The primary lever to reduce safety stock inventory is to place orders closer to the time they must be received. However, this approach can lead to unacceptable customer service.  Four secondary levers can be used in this case: 1.Improve demand forecasts so that fewer surprises come from customers. 2.Cut the lead times of purchased or produced items to reduce demand uncertainty. 3.Reduce supply uncertainties. Share production plans with suppliers. Surprises from unexpected scrap or rework can be reduced by improving manufacturing processes. Preventive maintenance can minimize unexpected downtime caused by equipment failure. 4.Rely more on equipment and labor buffers, such as capacity cushions and cross-trained workers. Reducing Safety Stock Inventory

14. © 2007 Pearson Education  The primary lever to reduce anticipation inventory is simply to match demand rate with production rate.  Secondary levers can be used to even out customer demand in one of the following ways: 1.Add new products with different demand cycles so that a peak in the demand for one product compensates for the seasonal low for another. 2.Provide off-season promotional campaigns. 3.Offer seasonal pricing plans. Reducing Anticipation Inventory

15. © 2007 Pearson Education  The primary lever for reducing pipeline inventory is to reduce the lead time.  Two secondary levers can help managers cut lead times: 1.Find more responsive suppliers and select new carriers for shipments between stocking locations or improve materials handling within the plant. 2.Decrease lot size, Q, at least in those cases where the lead time depends on the lot size. Smaller jobs generally require less time to complete. Reducing Pipeline Inventory

16. © 2007 Pearson Education Placement of Inventories  The positioning of a firm’s inventories supports its competitive priorities.  Inventories can be held at the raw materials, work- in-process, and finished goods levels.  Managers make inventory placement decisions by designating an item as either a special or a standard.  Special: An item made to order. If purchased, it is bought to order.  Standard: An item that is made to stock or ordered to stock, and normally is available upon request.

17. © 2007 Pearson Education  Thousands of items are held in inventory by a typical organization, but only a small % of them deserves management’s closest attention and tightest control.  ABC analysis: The process of dividing items into three classes, according to their dollar usage, so that managers can focus on items that have the highest dollar value.  The goal of ABC analysis is to identify the inventory levels of class A items so management can control them tightly by using the levers Identifying Critical Inventory Items

18. © 2007 Pearson Education ABC Analysis 102030405060708090100 Percentage of items Percentage of dollar value 100 100 — 90 90 — 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 30 — 20 20 — 10 10 — 0 0 — Class C Class A Class B

19. © 2007 Pearson Education  Economic Order Quantity (EOQ) is the lot size that minimizes total annual inventory holding and ordering costs.  Assumptions of EOQ 1.The demand rate is constant and known with certainty. 2.There are no constraints on lot size. 3.The only relevant costs are holding costs and ordering/setup costs. 4.Decisions for items can be made independently of other items. 5.Lead time is constant and known with certainty. Economic Order Quantity

20. © 2007 Pearson Education Inventory depletion (demand rate) Receive order 1 cycle On-hand inventory (units) Time Q AveragecycleinventoryQ—2 Cycle-Inventory Levels

21. © 2007 Pearson Education Annual cost (dollars) Lot Size (Q) Total Annual Cycle-Inventory Costs Holding cost = (H) Q2 Ordering cost = (S) DQ Total cost = (H) + (S) DQQ2 Q = lot size; C = total annual cycle-inventory cost H = holding cost per unit; D = annual demand S = ordering or setup costs per lot

22. © 2007 Pearson Education Costing out a Lot Sizing Policy Example 12.2  Bird feeder sales are 18 units per week, and the supplier charges $60 per unit. The cost of placing an order (S) with the supplier is $45.  Annual holding cost (H) is 25% of a feeder’s value, based on operations 52 weeks per year.  Management chose a 390-unit lot size (Q) so that new orders could be placed less frequently.  What is the annual cycle-inventory cost (C) of the current policy of using a 390-unit lot size? Museum of Natural History Gift Shop:

23. © 2007 Pearson Education Costing out a Lot Sizing Policy Example 12.2  What is the annual cycle-inventory cost (C) of the current policy of using a 390-unit lot size? D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 C = $2925 + $108 = $3033 C = (H) + (S) = (15) + (45) Q2Q2 DQDQ 936 390 2 Museum of Natural History Gift Shop:

24. © 2007 Pearson Education Would a lot size of 468 be better? Lot Sizing at the Museum of Natural History Gift Shop D = 936 units; H = $15; S = $45; Q = 390 units; C = $3033 C = (H) + (S) = (15) + (45) Q2Q2 DQDQ 936 468 2 Q = 468 units; C = ? C = $3510 + $90 = $3600 Q = 468 is a more expensive option. The best lot size (EOQ) is the lowest point on the total annual cost curve!

25. © 2007 Pearson Education 3000 3000 — 2000 2000 — 1000 1000 — 0 0 — |||||||| 50100150200250300350400 Lot Size (Q) Annual cost (dollars) Total cost Holding cost Ordering cost Current cost Current Q Lowest cost Best Q (EOQ) Lot Sizing at the Museum of Natural History Gift Shop

26. © 2007 Pearson Education Computing the EOQ Example 12.3 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H D = annual demand S = ordering or setup costs per lot H = holding costs per unit D = 936 units H = $15 S = $45 EOQ = 2(936)45 15 = 74.94 or 75 units C = (15) + (45) 75 2 936 75 C = $1,124.10 Bird Feeders:

27. © 2007 Pearson Education Time Between Orders  Time between orders (TBO) is the average elapsed time between receiving (or placing) replenishment orders of Q units for a particular lot size. Example 12.3 continued :  For the birdfeeder example, using an EOQ of 75 units. TBO EOQ = EOQ D TBO EOQ = = 75/936 = 0.080 year EOQ D TBO EOQ = (75/936)(12) = 0.96 months TBO EOQ = (75/936)(52) = 4.17 weeks TBO EOQ = (75/936)(365) = 29.25 days

28. © 2007 Pearson Education Application 12.2

29. © 2007 Pearson Education Application 12.2 continued

30. © 2007 Pearson Education Understanding the Effect of Changes  A Change in the Demand Rate (D): When demand rises, the lot size also rises, but more slowly than actual demand.  A Change in the Setup Costs (S): Increasing S increases the EOQ and, consequently, the average cycle inventory.  A Change in the Holding Costs (H): EOQ declines when H increases.  Errors in Estimating D, H, and S: Total cost is fairly insensitive to errors, even when the estimates are wrong by a large margin. The reasons are that errors tend to cancel each other out and that the square root reduces the effect of the error.

31. © 2007 Pearson Education Inventory Control Systems  Inventory control systems tell us how much to order and when to place the order.  Independent demand items: Items for which demand is influenced by market conditions and is not related to the inventory decisions for any other item held in stock.  Dependent demand items are those required as components or inputs to a service or product  In this chapter, we focus on inventory control systems for independent demand items.  We will discuss and compare two inventory control systems:  (1) Continuous review system, called a Q systems, and  (2) Periodic review system, called a P system

32. © 2007 Pearson Education Inventory Control Systems  Continuous review (Q) systems (Reorder point systems ROP) are designed to track the remaining inventory of an item each time a withdrawal is made to determine whether it is time to reorder.  Periodic review (P) systems (Fixed Interval Reorder systems) in which an item’s inventory position is reviewed periodically rather than continuously.

33. © 2007 Pearson Education  Inventory position (IP) is the measurement of an item’s ability to satisfy future demand.  Inventory position = On-hand inventory +scheduled receipts - Backorders IP = OH + SR – BO  Scheduled receipts (SR) or Open orders are orders that have been placed but have not yet been received.  Reorder point (R) is the predetermined minimum level that an inventory position must reach before a fixed order quantity Q of the item is ordered. Continuous Review (Q) System

34. © 2007 Pearson Education Continuous Review (Q) System…  In a continuous review system, although the order quantity Q is fixed, the time between orders, TBO, can vary.  Q can be based on the  EOQ,  a price break quantity (the minimum lot size that qualifies for a quantity discount),  a container size (such as a truck load),  or some other quantity selected by management.

35. © 2007 Pearson Education Application 12.3

36. © 2007 Pearson Education Continuous Review Q systems when demand & lead time are constant and certain. Time On-hand inventory R TBO L TBO L TBO L Orderreceived Orderreceived Q OH OrderplacedIPOrderreceived Q OH Orderplaced IP Orderreceived OrderplacedIPQ OH

37. © 2007 Pearson Education  In this case,  the reorder point, R, equals the demand during lead time, with no added allowance for safety stocks.  The time between orders (TBO) is the same for each cycle.  The key point here is to compare IP, not OH, with R in deciding whether to reorder. Continuous Review Q systems when demand & lead time are constant and certain.

38. © 2007 Pearson Education Determining Whether to Place an Order Demand for chicken soup is always 25 cases a day and lead time is always 4 days. Chicken soup was just restocked, leaving an on-hand inventory of 10 cases. No backorders currently exist. There is an open order for 200 cases. What is the inventory position? Should a new order be placed? R = Average demand during lead time = (25)(4) = 100 cases IP = OH + SR – BO = 10 + 200 – 0 = 210 cases IP = Inventory Position OH = On-hand Inventory SR = Scheduled receipts BO = Back ordered Since IP exceeds R (210 > 100), do not reorder. An SR is pending. Example 12.4

39. © 2007 Pearson Education  In reality, demand and lead times are not always predictable.  Reorder point = average demand during lead time + safety stock. Continuous Review Q system when demand is uncertain.

40. © 2007 Pearson Education Time On-hand inventory TBO 1 TBO 2 TBO 3 L1L1L1L1 L2L2L2L2 L3L3L3L3 R Orderreceived Q Orderplaced Orderplaced OrderreceivedIPIP Q Orderplaced Q Orderreceived Orderreceived OH Continuous Review Q system when demand is uncertain.

41. © 2007 Pearson Education  The wavy downward-sloping line indicates that demand varies from day to day.  The changing demand rate means that the time between orders changes, so TBO 1 ≠TB 2 ≠TBO 3  Because of uncertain demand, sales during lead time are unpredictable, and safety stock is added to hedge against lost sales.  The greater the safety stock, and thus the higher point R, the less likely the stockout. Continuous Review Q system when demand is uncertain.

42. © 2007 Pearson Education Choosing an Appropriate Service-Level Policy  Deciding on a small or large safety stock is a trade off between customer service and inventory holding cost.  Service level (Cycle-service level): The desired probability of not running out of stock in any one ordering cycle, which begins at the time an order is placed and ends when it arrives.  Protection interval (lead time): The period over which safety stock must protect the user from running out.

43. © 2007 Pearson Education  Assume that the demand during lead time is normally distributed  Safety stock = z  L z = The number of standard deviations needed for a given cycle-service level.  L =  The standard deviation of demand during the lead time probability distribution.  Having no safety stock will be sufficient only 50 percent of the time. Choosing an Appropriate Service-Level Policy

44. © 2007 Pearson Education Finding Safety Stock With a normal Probability Distribution for an 85% Cycle-Service Level Average demand during lead time Cycle-service level = 85% Probability of stockout (1.0 – 0.85 = 0.15) zLzLzLzL R

45. © 2007 Pearson Education Finding Safety Stock and R Example 12.5 Records show that the demand for dishwasher detergent during the lead time is normally distributed, with an average of 250 boxes and  L = 22. What safety stock should be carried for a 99 percent cycle- service level? What is R? Safety stock= z  L = 2.33(22) = 51.3 = 51 boxes Reorder point = D L + SS = 250 + 51 = 301 boxes 2.33 is the number of standard deviations, z, to the right of average demand during the lead time that places 99% of the area under the curve to the left of that point.

46. © 2007 Pearson Education Application 12.4

47. © 2007 Pearson Education  Some times, records are not likely to be collected for a time interval that exactly the same as the lead time.  Suppose that the average demand, d, is known along with the standard deviation of demand, σ t, over some time interval t, where t does not equal the lead time  Also suppose identical d and σ t  Let L be the constant lead time, expressed as a multiple (or fraction) of t  d+ d +d +… = dL  σ t 2 + σ t 2 + σ t 2 + …= σ t 2 L  σ L = σ t L Development of Demand Distributions for the Lead Time

48. © 2007 Pearson Education Development of Demand Distributions for the Lead Time  t = 15 + 75 Demand for week 1  t = 26 225 Demand for 3-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15

49. © 2007 Pearson Education Calculating Total Q costs  Total costs = Annual cycle inventory holding cost + Annual ordering cost + Annual safety stock holding cost. Total cost = (H) + (S) Total cost = (H) + (S) + HzσL Total cost = (H) + (S) + Hz σLDQQ2

50. © 2007 Pearson Education Finding Safety Stock and R Example 12.6  L =  t L = 5 2 = 7.1 Safety stock = z  L = 1.28(7.1) = 9.1 or 9 units Reorder point = dL + safety stock = 2(18) + 9 = 45 units Suppose that the average demand for bird feeders is 18 units per week with a standard deviation of 5 units. The lead time is constant at 2 weeks. Determine the safety stock and reorder point for a 90 percent cycle-service level. What is the total cost of the Q system? (t = 1 week; d = 18 units per week; L = 2 weeks) C = ($15) + ($45) + 9($15) 75 2 936 75 C = $562.50 + $561.60 + $135 = $1259.10 Demand distribution for lead time must be developed:

51. © 2007 Pearson Education Application 12.5 Putting it all together for a Q System

52. © 2007 Pearson Education Application 12.5 Putting it all together for a Q System

53. © 2007 Pearson Education Application 12.5 Putting it all together for a Q System

54. © 2007 Pearson Education Periodic Review (P) System  Periodic review (P) system: A system in which an item’s inventory position is reviewed periodically rather than continuously.  Sometimes called a fixed interval reorder system or a periodic reorder system.  A new order is always placed at the end of each review, and the time between orders is fixed at P.  Demand is a variable, so total demand between reviews varies.  The lot size, Q, may change from one order to the next.

55. © 2007 Pearson Education Periodic Review (P) System PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH

56. © 2007 Pearson Education  When the predetermined time, P, has elapsed since the last review, an order is placed to bring the inventory position up to the target inventory level, T  Q t = T – IP t  P can be set to the average time between orders for the economic order quantity, or TBO EOQ P = ---- Periodic Review (P) System EOQ D

57. © 2007 Pearson Education Determining How Much to Order in a P system Example 12.7: A distribution center has a backorder for five 36” color TV sets. No inventory is currently on hand, and now is the time to review. How many should be reordered to achieve an inventory level of T = 400 if there are no scheduled receipts? T = 400 BO = 5 OH = 0 SR = 0 T = 400 BO = 5 OH = 0 SR = 0 IP = OH + SR – BO IP = 0 + 0 – 5 = –5 sets Q t = T – IP t Q = 400 – (–5) = 405 sets

58. © 2007 Pearson Education Application 12.6

59. © 2007 Pearson Education Selecting the target inventory level when demand is uncertain  Suppose that lead time is constant.  A protection interval of P+L is needed  In a P system, we must develop the distribution of demand for P+L time periods  The target inventory level T must equal the expected demand during the protection interval of P+L periods, plus enough safety stock to protect against demand uncertainty over the protection interval.

60. © 2007 Pearson Education  The average demand during the protection interval is d(P+L).  T= d(P+L)+ safety stock for the protection interval.  Safety stock = zσ P+L  σ P+L = σ t P+L  Because a P system requires safety stock to cover demand uncertainty over a longer time period than a Q system, a P system requires more safety stock (the overall inventory levels are higher than those for a Q system Selecting the target inventory level when demand is uncertain..

61. © 2007 Pearson Education Total P system Costs  The average order quantity will be the average consumption of inventory during the P periods between order.  Q = dP Total cost = (H) + (S) + Hzσ P+L Total cost = (H) + (S) + Hz σ P+LDdPdP2

62. © 2007 Pearson Education Calculating Total P System Costs Example 12.8 Bird feeder demand is normally distributed with a mean of 18 units per week and a standard deviation in weekly demand of 5 units, operating 52 weeks a year. Lead time (L) is 2 weeks and EOQ is 75 units with a safety stock of 9 units and a cycle-service level of 90%. Annual demand (D) is 936 units. What is the equivalent P system and total cost? P = (52) = (52) = 4.2 or 4 weeks EOQ D 75 936 Time between reviews =  P+L =    P + L = 5 6 = 12 units Standard deviation of demand over the protection period T= Average demand during the protection interval + Safety stock = d (P + L) + z  P + L = (18 units/week)(6 weeks) + 1.28(12 units) = 123 units z value for a 90% cycle-service level

63. © 2007 Pearson Education D = (18 units/week)(52 weeks) = 936 units Safety Stock during P = 15 Holding Costs = $15/unit Ordering Costs = $45  t = 18 units L = 2 weeks Cycle/service level = 90% EOQ = 75 units The time between reviews (P) = 4 weeks Average demand during P + Safety stock = T = 123 units C = ($15) + ($45) + 15($15) 4(18) 2 936 4(18) C = $540 + $585 + $225 = $1350 Example 12.8 continued The total P-system cost for the bird feeders is: The P system requires 15 units in safety stock, while the Q system only needs 9 units. If cost were the only criterion, the Q system would be the choice.

64. © 2007 Pearson Education Application 12.7 Putting it all together for a P System

65. © 2007 Pearson Education Application 12.7 Putting it all together for a P System

66. © 2007 Pearson Education Comparison of Q and P Systems P Systems  Convenient to administer  Orders for multiple items from the same supplier may be combined  Inventory Position (IP) only required at review  Systems in which inventory records are always current are called Perpetual Inventory Systems  Review frequencies can be tailored to each item  Possible quantity discounts  Lower, less-expensive safety stocks Q Systems

67. © 2007 Pearson Education Hybrid Systems  Optional replenishment system: A system used to review the inventory position at fixed time intervals and, if the position has dropped to (or below) a predetermined level, to place a variable-sized order to cover expected needs.  Base-stock system: An inventory control system that issues a replenishment order, Q, each time a withdrawal is made, for the same amount as the withdrawal.

68. © 2007 Pearson Education Approaches for Inventory Record Accuracy  Cycle counting, an inventory control method, whereby storeroom personnel physically count a small percentage of the total number of items each day, correcting errors that they find, is used to frequently check records against physical inventory.

69. © 2007 Pearson Education Solved Problem 1 A distribution center’s average weekly demand is 50 units for an item valued at $650 per unit. Shipments from the warehouse average 350 units. Average lead time (including ordering delays and transit time) is 2 weeks. The distribution center operates 52 weeks per year & carries a 1-week supply as safety stock and no anticipation inventory. What is the average aggregate inventory being held by the distribution center?

70. © 2007 Pearson Education Solved Problem 2 Booker’s Book Bindery divides inventory items into 3 classes, according to their dollar usage. Calculate the usage values of the following inventory items and determine which is most likely to be classified as an A item.

71. © 2007 Pearson Education Solved Problem 2 continued

72. © 2007 Pearson Education EOQ, is 75 units when annual demand, D, is 936 units/year, setup cost, S, is $45, and holding cost, H, is $15/unit/year. If we mistakenly estimate inventory holding cost to be $30/unit/year, what is the new order quantity, Q, if D = 936 units/year, S = $45, and H = $30/unit/year? What is the change in order quantity, expressed as a percentage of the EOQ (75 units)? The new order quantity is The change in percentage is Solved Problem 3

73. © 2007 Pearson Education Solved Problem 6 Comparison of P and Q Systems