Heizer 12
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The document discusses inventory management and the economic order quantity (EOQ) model. It explains that the EOQ model aims to minimize total inventory costs by balancing setup costs from ordering too frequently and holding costs from ordering too infrequently. The model assumes known, constant demand and costs. It describes how the optimal order quantity is calculated based on annual demand, setup cost per order, and holding cost per unit.
![Production Order Quantity
Model
Q= Number of pieces per order p = Daily production rate
H= Holding cost per unit per year d = Daily demand/usage rate
D= Annual demand
Setup cost = (D/Q)S
1
Holding cost = 2 HQ[1 - (d/p)]
1
(D/Q)S = 2 HQ[1 - (d/p)]
2DS
Q =
2
H[1 - (d/p)]
2DS
Q* =
p H[1 - (d/p)]
© 2008 Prentice Hall, Inc. 12 – 51](https://image.slidesharecdn.com/heizer12-121111104803-phpapp01/85/Heizer-12-51-320.jpg)
![Production Order Quantity
Example
D = 1,000 units p = 8 units per day
S = $10 d = 4 units per day
H = $0.50 per unit per year
2DS
Q* =
H[1 - (d/p)]
2(1,000)(10)
Q* = = 80,000
0.50[1 - (4/8)]
= 282.8 or 283 hubcaps
© 2008 Prentice Hall, Inc. 12 – 52](https://image.slidesharecdn.com/heizer12-121111104803-phpapp01/85/Heizer-12-52-320.jpg)
Heizer 12
- 1. Operations Management Chapter 12 – Inventory Management PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 7e Operations Management, 9e © 2008 Prentice Hall, Inc. 12 – 1
- 2. Outline Global Company Profile: Amazon.com Functions of Inventory Types of Inventory Inventory Management ABC Analysis Record Accuracy Cycle Counting Control of Service Inventories © 2008 Prentice Hall, Inc. 12 – 2
- 3. Outline – Continued Inventory Models Independent vs. Dependent Demand Holding, Ordering, and Setup Costs © 2008 Prentice Hall, Inc. 12 – 3
- 4. Outline – Continued Inventory Models for Independent Demand The Basic Economic Order Quantity (EOQ) Model Minimizing Costs Reorder Points Production Order Quantity Model Quantity Discount Models © 2008 Prentice Hall, Inc. 12 – 4
- 5. Outline – Continued Probabilistic Models and Safety Stock Other Probabilistic Models Fixed-Period (P) Systems © 2008 Prentice Hall, Inc. 12 – 5
- 6. Learning Objectives When you complete this chapter you should be able to: 1. Conduct an ABC analysis 2. Explain and use cycle counting 3. Explain and use the EOQ model for independent inventory demand 4. Compute a reorder point and safety stock © 2008 Prentice Hall, Inc. 12 – 6
- 7. Learning Objectives When you complete this chapter you should be able to: 5. Apply the production order quantity model 6. Explain and use the quantity discount model 7. Understand service levels and probabilistic inventory models © 2008 Prentice Hall, Inc. 12 – 7
- 8. Amazon.com 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 © 2008 Prentice Hall, Inc. 12 – 8
- 9. Amazon.com 1. Each order is assigned by computer to the closest distribution center that has the product(s) 2. A “flow meister” at each distribution center assigns work crews 3. Lights indicate products that are to be picked and the light is reset 4. Items are placed in crates on a conveyor. Bar code scanners scan each item 15 times to virtually eliminate errors. © 2008 Prentice Hall, Inc. 12 – 9
- 10. Amazon.com 5. Crates arrive at central point where items are boxed and labeled with new bar code 6. Gift wrapping is done by hand at 30 packages per hour 7. Completed boxes are packed, taped, weighed and labeled before leaving warehouse in a truck 8. Order arrives at customer within a week © 2008 Prentice Hall, Inc. 12 – 10
- 11. Inventory One of the most expensive assets of many companies representing as much as 50% of total invested capital Operations managers must balance inventory investment and customer service © 2008 Prentice Hall, Inc. 12 – 11
- 12. Functions of Inventory 1. To decouple or separate various parts of the production process 2. To decouple the firm from fluctuations in demand and provide a stock of goods that will provide a selection for customers 3. To take advantage of quantity discounts 4. To hedge against inflation © 2008 Prentice Hall, Inc. 12 – 12
- 13. Types of Inventory Raw material Purchased but not processed Work-in-process 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 Finished goods Completed product awaiting shipment © 2008 Prentice Hall, Inc. 12 – 13
- 14. The Material Flow Cycle Cycle time 95% 5% Input Wait for Wait to Move Wait in queue Setup Run Output inspection be moved time for operator time time Figure 12.1 © 2008 Prentice Hall, Inc. 12 – 14
- 15. Inventory Management How inventory items can be classified How accurate inventory records can be maintained © 2008 Prentice Hall, Inc. 12 – 15
- 16. ABC Analysis Divides inventory into three classes based on annual dollar volume Class A - high annual dollar volume Class B - medium annual dollar volume Class C - low annual dollar volume Used to establish policies that focus on the few critical parts and not the many trivial ones © 2008 Prentice Hall, Inc. 12 – 16
- 17. ABC Analysis Percent of Percent of Item Number of Annual Annual Annual Stock Items Volume Unit Dollar Dollar Number Stocked (units) x Cost = Volume Volume Class #10286 20% 1,000 $ 90.00 $ 90,000 38.8% A 72% #11526 500 154.00 77,000 33.2% A #12760 1,550 17.00 26,350 11.3% B #10867 30% 350 42.86 15,001 6.4% 23% B #10500 1,000 12.50 12,500 5.4% B © 2008 Prentice Hall, Inc. 12 – 17
- 18. ABC Analysis Percent of Percent of Item Number of Annual Annual Annual Stock Items Volume Unit Dollar Dollar Number Stocked (units) x Cost = Volume Volume Class #12572 600 $ 14.17 $ 8,502 3.7% C #14075 2,000 .60 1,200 .5% C #01036 50% 100 8.50 850 .4% 5% C #01307 1,200 .42 504 .2% C #10572 250 .60 150 .1% C 8,550 $232,057 100.0% © 2008 Prentice Hall, Inc. 12 – 18
- 19. Percent of annual dollar usage ABC Analysis A Items 80 – 70 – 60 – 50 – 40 – 30 – 20 – B Items 10 – C Items 0 – | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100 Percent of inventory items Figure 12.2 © 2008 Prentice Hall, Inc. 12 – 19
- 20. ABC Analysis Other criteria than annual dollar volume may be used Anticipated engineering changes Delivery problems Quality problems High unit cost © 2008 Prentice Hall, Inc. 12 – 20
- 21. ABC Analysis Policies employed may include More emphasis on supplier development for A items Tighter physical inventory control for A items More care in forecasting A items © 2008 Prentice Hall, Inc. 12 – 21
- 22. Record Accuracy Accurate records are a critical ingredient in production and inventory systems Allows organization to focus on what is needed Necessary to make precise decisions about ordering, scheduling, and shipping Incoming and outgoing record keeping must be accurate Stockrooms should be secure © 2008 Prentice Hall, Inc. 12 – 22
- 23. Cycle Counting Items are counted and records updated on a periodic basis Often used with ABC analysis to determine cycle Has several advantages Eliminates shutdowns and interruptions Eliminates annual inventory adjustment Trained personnel audit inventory accuracy Allows causes of errors to be identified and corrected Maintains accurate inventory records © 2008 Prentice Hall, Inc. 12 – 23
- 24. Cycle Counting Example 5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days) Item Number of Items Class Quantity Cycle Counting Policy Counted per Day A 500 Each month 500/20 = 25/day B 1,750 Each quarter 1,750/60 = 29/day C 2,750 Every 6 months 2,750/120 = 23/day 77/day © 2008 Prentice Hall, Inc. 12 – 24
- 25. Control of Service Inventories Can be a critical component of profitability Losses may come from shrinkage or pilferage Applicable techniques include 1. Good personnel selection, training, and discipline 2. Tight control on incoming shipments 3. Effective control on all goods leaving facility © 2008 Prentice Hall, Inc. 12 – 25
- 26. Independent Versus Dependent Demand Independent demand - the demand for item is independent of the demand for any other item in inventory Dependent demand - the demand for item is dependent upon the demand for some other item in the inventory © 2008 Prentice Hall, Inc. 12 – 26
- 27. Holding, Ordering, and Setup Costs Holding costs - the costs of holding or “carrying” inventory over time Ordering costs - the costs of placing an order and receiving goods Setup costs - cost to prepare a machine or process for manufacturing an order © 2008 Prentice Hall, Inc. 12 – 27
- 28. Holding Costs Cost (and range) as a Percent of Category Inventory Value Housing costs (building rent or 6% (3 - 10%) depreciation, operating costs, taxes, insurance) Material handling costs (equipment lease or 3% (1 - 3.5%) depreciation, power, operating cost) Labor cost 3% (3 - 5%) Investment costs (borrowing costs, taxes, 11% (6 - 24%) and insurance on inventory) Pilferage, space, and obsolescence 3% (2 - 5%) Overall carrying cost 26% Table 12.1 © 2008 Prentice Hall, Inc. 12 – 28
- 29. Holding Costs Cost (and range) as a Percent of Category Inventory Value ng Housing costs (building ry considera bly dependi -s. va rent or 6% (3e 10%) depreciation, operating costs, taxes,and interest ra t Ho lding costs , location, ech insurance) e business on t h % , some high t ater than 15 leasetorr tha3%50%.3.5%) Material nerally gre (equipment grea e n (1 - Ge handling costs ing costs depreciation, power,old h operating cost) items have Labor cost 3% (3 - 5%) Investment costs (borrowing costs, taxes, 11% (6 - 24%) and insurance on inventory) Pilferage, space, and obsolescence 3% (2 - 5%) Overall carrying cost 26% Table 12.1 © 2008 Prentice Hall, Inc. 12 – 29
- 30. Inventory Models for Independent Demand Need to determine when and how much to order Basic economic order quantity Production order quantity Quantity discount model © 2008 Prentice Hall, Inc. 12 – 30
- 31. Basic EOQ Model Important assumptions 1. Demand is known, constant, and independent 2. Lead time is known and constant 3. Receipt of inventory is instantaneous and complete 4. Quantity discounts are not possible 5. Only variable costs are setup and holding 6. Stockouts can be completely avoided © 2008 Prentice Hall, Inc. 12 – 31
- 32. Inventory Usage Over Time Usage rate Average Order inventory quantity = Q Inventory level on hand (maximum Q inventory level) 2 Minimum inventory 0 Time Figure 12.3 © 2008 Prentice Hall, Inc. 12 – 32
- 33. Minimizing Costs Objective is to minimize total costs Curve for total cost of holding and setup Minimum total cost Annual cost Holding cost curve Setup (or order) cost curve Optimal order Order quantity Table 11.5 quantity (Q*) © 2008 Prentice Hall, Inc. 12 – 33
- 34. The EOQ Model setup cost = Q S Annual D 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 Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order) Annual demand Setup or order = Number of units in each order cost per order D = (S) Q © 2008 Prentice Hall, Inc. 12 – 34
- 35. The EOQ Model setup cost = Q S Annual D Q Annual holding cost = H Q = Number of pieces per order 2 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 Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity = (Holding cost per unit per year) 2 Q = ( H) 2 © 2008 Prentice Hall, Inc. 12 – 35
- 36. The EOQ Model setup cost = Q S Annual D Q Annual holding cost = H Q = Number of pieces per order 2 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 Optimal order quantity is found when annual setup cost equals annual holding cost D Q S = H Q 2 Solving for Q* 2DS = Q2H Q2 = 2DS/H Q* = 2DS/H © 2008 Prentice Hall, Inc. 12 – 36
- 37. An EOQ Example Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year 2DS Q* = H 2(1,000)(10) Q* = = 40,000 = 200 units 0.50 © 2008 Prentice Hall, Inc. 12 – 37
- 38. An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order H = $.50 per unit per year Expected Demand D number of = N = = orders Order quantity Q* 1,000 N= = 5 orders per year 200 © 2008 Prentice Hall, Inc. 12 – 38
- 39. An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year Number of working Expected days per year time between = T = orders N 250 T= = 50 days between orders 5 © 2008 Prentice Hall, Inc. 12 – 39
- 40. An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost D Q TC = S + H Q 2 1,000 200 TC = ($10) + ($.50) 200 2 TC = (5)($10) + (100)($.50) = $50 + $50 = $100 © 2008 Prentice Hall, Inc. 12 – 40
- 41. 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 © 2008 Prentice Hall, Inc. 12 – 41
- 42. An EOQ Example Management underestimated demand by 50% D = 1,000 units 1,500 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days D Q TC = S + H Q 2 1,500 200 TC = ($10) + ($.50) = $75 + $50 = $125 200 2 Total annual cost increases by only 25% © 2008 Prentice Hall, Inc. 12 – 42
- 43. An EOQ Example Actual EOQ for new demand is 244.9 units D = 1,000 units 1,500 units Q* = 244.9 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days D Q TC = S + H Q 2 Only 2% less 1,500 244.9 than the total TC = ($10) + ($.50) cost of $125 244.9 2 when the TC = $61.24 + $61.24 = $122.48 order quantity was 200 © 2008 Prentice Hall, Inc. 12 – 43
- 44. Reorder Points EOQ answers the “how much” question The reorder point (ROP) tells when to order Demand Lead time for a ROP = per day new order in days =dxL D d = Number of working days in a year © 2008 Prentice Hall, Inc. 12 – 44
- 45. Reorder Point Curve Q* Inventory level (units) Slope = units/day = d ROP (units) Time (days) Figure 12.5 Lead time = L © 2008 Prentice Hall, Inc. 12 – 45
- 46. Reorder Point Example Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days D d= Number of working days in a year = 8,000/250 = 32 units ROP = d x L = 32 units per day x 3 days = 96 units © 2008 Prentice Hall, Inc. 12 – 46
- 47. Production Order Quantity Model Used when inventory builds up over a period of time after an order is placed Used when units are produced and sold simultaneously © 2008 Prentice Hall, Inc. 12 – 47
- 48. Production Order Quantity Model Part of inventory cycle during which production (and usage) is taking place Inventory level Demand part of cycle with no production Maximum inventory t Time Figure 12.6 © 2008 Prentice Hall, Inc. 12 – 48
- 49. Production Order Quantity Model Q= Number of pieces per order p = Daily production rate H= Holding cost per unit per year d = Daily demand/usage rate t= Length of the production run in days Annual inventory Holding cost = (Average inventory level) x per unit per year holding cost Annual inventory = (Maximum inventory level)/2 level Maximum Total produced during Total used during = – inventory level the production run the production run = pt – dt © 2008 Prentice Hall, Inc. 12 – 49
- 50. Production Order Quantity Model Q= Number of pieces per order p = Daily production rate H= Holding cost per unit per year d = Daily demand/usage rate t= Length of the production run in days Maximum Total produced during Total used during = – inventory level the production run the production run = pt – dt However, Q = total produced = pt ; thus t = Q/p Maximum Q Q d inventory level =p –d =Q 1– p p p Maximum inventory level Q d Holding cost = ( H) = 1– H 2 2 p © 2008 Prentice Hall, Inc. 12 – 50
- 51. Production Order Quantity Model Q= Number of pieces per order p = Daily production rate H= Holding cost per unit per year d = Daily demand/usage rate D= Annual demand Setup cost = (D/Q)S 1 Holding cost = 2 HQ[1 - (d/p)] 1 (D/Q)S = 2 HQ[1 - (d/p)] 2DS Q = 2 H[1 - (d/p)] 2DS Q* = p H[1 - (d/p)] © 2008 Prentice Hall, Inc. 12 – 51
- 52. Production Order Quantity Example D = 1,000 units p = 8 units per day S = $10 d = 4 units per day H = $0.50 per unit per year 2DS Q* = H[1 - (d/p)] 2(1,000)(10) Q* = = 80,000 0.50[1 - (4/8)] = 282.8 or 283 hubcaps © 2008 Prentice Hall, Inc. 12 – 52
- 53. Production Order Quantity Model Note: D 1,000 d=4= = Number of days the plant is in operation 250 When annual data are used the equation becomes 2DS Q* = annual demand rate H 1– annual production rate © 2008 Prentice Hall, Inc. 12 – 53
- 54. Quantity Discount Models Reduced prices are often available when larger quantities are purchased Trade-off is between reduced product cost and increased holding cost Total cost = Setup cost + Holding cost + Product cost D Q TC = S+ H + PD Q 2 © 2008 Prentice Hall, Inc. 12 – 54
- 55. Quantity Discount Models A typical quantity discount schedule Discount Discount Number Discount Quantity Discount (%) Price (P) 1 0 to 999 no discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75 Table 12.2 © 2008 Prentice Hall, Inc. 12 – 55
- 56. Quantity Discount Models Steps in analyzing a quantity discount 1. For each discount, calculate Q* 2. If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount 3. Compute the total cost for each Q* or adjusted value from Step 2 4. Select the Q* that gives the lowest total cost © 2008 Prentice Hall, Inc. 12 – 56
- 57. Quantity Discount Models Total cost curve for discount 2 Total cost curve for discount 1 Total cost $ Total cost curve for discount 3 b a Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b 1st price 2nd price break break 0 1,000 2,000 Figure 12.7 Order quantity © 2008 Prentice Hall, Inc. 12 – 57
- 58. Quantity Discount Example Calculate Q* for every discount 2DS Q* = IP 2(5,000)(49) Q1* = = 700 cars/order (.2)(5.00) 2(5,000)(49) Q2* = = 714 cars/order (.2)(4.80) 2(5,000)(49) Q3* = = 718 cars/order (.2)(4.75) © 2008 Prentice Hall, Inc. 12 – 58
- 59. Quantity Discount Example Calculate Q* for every discount 2DS Q* = IP 2(5,000)(49) Q1* = = 700 cars/order (.2)(5.00) 2(5,000)(49) Q2* = = 714 cars/order (.2)(4.80) 1,000 — adjusted 2(5,000)(49) Q3* = = 718 cars/order (.2)(4.75) 2,000 — adjusted © 2008 Prentice Hall, Inc. 12 – 59
- 60. Quantity Discount Example Annual Annual Annual Discount Unit Order Product Ordering Holding Number Price Quantity Cost Cost Cost Total 1 $5.00 700 $25,000 $350 $350 $25,700 2 $4.80 1,000 $24,000 $245 $480 $24,725 3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50 Table 12.3 Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit © 2008 Prentice Hall, Inc. 12 – 60
- 61. Probabilistic Models and Safety Stock Used when demand is not constant or certain Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit x the number of orders per year © 2008 Prentice Hall, Inc. 12 – 61
- 62. Safety Stock Example ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Number of Units Probability 30 .2 40 .2 ROP 50 .3 60 .2 70 .1 1.0 © 2008 Prentice Hall, Inc. 12 – 62
- 63. Safety Stock Example ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Safety Additional Total Stock Holding Cost Stockout Cost Cost 20 (20)($5) = $100 $0 $100 10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290 0 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960 A safety stock of 20 frames gives the lowest total cost ROP = 50 + 20 = 70 frames © 2008 Prentice Hall, Inc. 12 – 63
- 64. Probabilistic Demand Minimum demand during lead time Inventory level Maximum demand during lead time Mean demand during lead time ROP = 350 + safety stock of 16.5 = 366.5 ROP Normal distribution probability of demand during lead time Expected demand during lead time (350 kits) Safety stock 16.5 units 0 Lead time Time Figure 12.8 Place Receive order order © 2008 Prentice Hall, Inc. 12 – 64
- 65. Probabilistic Demand Probability of Risk of a stockout no stockout (5% of area of 95% of the time normal curve) Mean ROP = ? kits Quantity demand 350 Safety stock 0 z Number of standard deviations © 2008 Prentice Hall, Inc. 12 – 65
- 66. Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + Zσ dLT where Z = number of standard deviations σ dLT = standard deviation of demand during lead time © 2008 Prentice Hall, Inc. 12 – 66
- 67. Probabilistic Example Average demand = µ = 350 kits Standard deviation of demand during lead time = σ dLT = 10 kits 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = Zσ dLT = 1.65(10) = 16.5 kits Reorder point = expected demand during lead time + safety stock = 350 kits + 16.5 kits of safety stock © 2008 Prentice Hall, Inc. = 366.5 or 367 kits 12 – 67
- 68. Other Probabilistic Models When data on demand during lead time is not available, there are other models available 1. When demand is variable and lead time is constant 2. When lead time is variable and demand is constant 3. When both demand and lead time are variable © 2008 Prentice Hall, Inc. 12 – 68
- 69. Other Probabilistic Models Demand is variable and lead time is constant ROP = (average daily demand x lead time in days) + Zσ dLT where σ d = standard deviation of demand per day σ dLT = σ d lead time © 2008 Prentice Hall, Inc. 12 – 69
- 70. Probabilistic Example Average daily demand (normally distributed) = 15 Standard deviation = 5 Lead time is constant at 2 days Z for 90% = 1.28 90% service level desired From Appendix I ROP = (15 units x 2 days) + Zσ dlt = 30 + 1.28(5)( 2) = 30 + 9.02 = 39.02 ≈ 39 Safety stock is about 9 iPods © 2008 Prentice Hall, Inc. 12 – 70
- 71. Other Probabilistic Models Lead time is variable and demand is constant ROP = (daily demand x average lead time in days) = Z x (daily demand) x σ LT where σ LT = standard deviation of lead time in days © 2008 Prentice Hall, Inc. 12 – 71
- 72. Probabilistic Example Z for 98% = 2.055 Daily demand (constant) = 10 From Appendix I Average lead time = 6 days Standard deviation of lead time = σ LT = 3 98% service level desired ROP = (10 units x 6 days) + 2.055(10 units)(3) = 60 + 61.65 = 121.65 Reorder point is about 122 cameras © 2008 Prentice Hall, Inc. 12 – 72
- 73. Other Probabilistic Models Both demand and lead time are variable ROP = (average daily demand x average lead time) + Zσ dLT σd = standard deviation of demand per day σ LT = standard deviation of lead time in days σ dLT = (average lead time x σ d2) + (average daily demand)2 x σ LT2 © 2008 Prentice Hall, Inc. 12 – 73
- 74. Probabilistic Example Average daily demand (normally distributed) = 150 Standard deviation = σ d = 16 Average lead time 5 days (normally distributed) Standard deviation = σ LT = 1 day 95% service level desired Z for 95% = 1.65 From Appendix I ROP = (150 packs x 5 days) + 1.65σ dLT = (150 x 5) + 1.65 (5 days x 162) + (1502 x 12) = 750 + 1.65(154) = 1,004 packs © 2008 Prentice Hall, Inc. 12 – 74
- 75. Fixed-Period (P) Systems Orders placed at the end of a fixed period Inventory counted only at end of period Order brings inventory up to target level Only relevant costs are ordering and holding Lead times are known and constant Items are independent from one another © 2008 Prentice Hall, Inc. 12 – 75
- 76. Fixed-Period (P) Systems Target quantity (T) Q4 Q2 On-hand inventory Q1 P Q3 P P Time Figure 12.9 © 2008 Prentice Hall, Inc. 12 – 76
- 77. Fixed-Period (P) Example 3 jackets are back ordered No jackets are in stock It is time to place an order Target value = 50 Order amount (Q) = Target (T) - On- hand inventory - Earlier orders not yet received + Back orders Q = 50 - 0 - 0 + 3 = 53 jackets © 2008 Prentice Hall, Inc. 12 – 77
- 78. Fixed-Period Systems Inventory is only counted at each review period May be scheduled at convenient times Appropriate in routine situations May result in stockouts between periods May require increased safety stock © 2008 Prentice Hall, Inc. 12 – 78