1. Topic 3 Operations Management (2) Inventory Models
Prof. Upendra Kachru

2. WHY STUDY INVENTORY? All organizations have inventory
Can be a sizable organizational asset
Influences sales (revenue generation and customer relations)
Influences production/ operations costs
Large amounts reduces ROI
Costs of having inventory
Frequently the largest single expenditure
Excesses can result in losses
Prof. Upendra Kachru

3. WHAT IS
INVENTORY?
Inventory is the stock of any item or resource used in an organization.
Prof. Upendra Kachru

4. Inventory Categories Working Stock Safety Stock Anticipation Stock
Pipeline Stock
Decoupling Stock
Psychic Stock
Prof. Upendra Kachru 4

5. Functions of Inventory
To protect against variations (fluctuations) in demand and supply
To take advantage of batches and longer production runs
To provide flexibility to allow changes in production plans in view of changes in demand etc.
To facilitate intermittent production
To take advantage of price discounts by bulk purchases
To meet anticipated and current demand
Prof. Upendra Kachru

6. Functions of Inventory
Excess Demand from Inventory
J F M A M J J A S O N D
Demand
Capacity Requirement without Inventory
Capacity Requirement with Inventory
Excess Production to Inventory
 To smooth production requirements from seasonality

7. Functions of Inventory
Department 1
Department 2
Department 3
Department 4
Interstage
Inventory D1
Interstage
Inventory D2
Interstage
Inventory D3
 To decouple different components of the internal inventory-distribution system.

8. Raw Materials & Supplies
(Purchasing)
Supply
INVENTORY
FUNCTIONS
Safety Stock
In-Process Goods
(Production)
Decoupling Stock
Finished Goods
(Production)
Anticipation Stock
 To meet anticipated demand
(Marketing)
Demand
Psychic Stock
Prof. Upendra Kachru 8

9. Significance of Inventory
Functional
Area
Functional Responsibility
Inventory Goal
Inventory
Inclination
Marketing
Sell the Product
Maximize customer service
High
Production
Make the Product
Efficient lot sizes
Purchasing
Buy required materials
Low cost per unit
Finance
Provide working capital
Efficient use of capital
Low
Engineering
Design the product
Avoid obsolescence
Prof. Upendra Kachru

10. Typical Response Area Marketing / Sales Production Purchasing Finance
revenue generation
customer relations
Typical Response
I can’t sell without adequate stocks. I can’t keep our customers if we continue to stockout and there is not sufficient product variety
If I can produce larger lot sizes, I can reduce per unit cost and function efficiency.
I can reduce our per unit cost if I buy large quantities in bulk.
Where am I going to get the funds to pay for the inventory? The levels should be lower.
I am out of space. I can’t fit anything else in the building.
Area
Marketing / Sales
Production
Purchasing
Finance
Warehousing
Production
efficiency
cost of operations cost of operations
Finance
liquidity
return on investment
Logistics
Handling Capacity
Space
Prof. Upendra Kachru

11. Inventory Objectives Balancing Objectives 1. Provide customer service
2. Support plant efficiency
3. Minimize inventory investment
Maximize
Customer
Service
Minimize
Inventory
Investment
Operating
Efficiency
Prof. Upendra Kachru 11

12. Inventory – PLANNING & CONTROL
CONSTRAINTS
Mgt. policies
Working capital
Space
Plant capacity
INPUTS
OUTPUTS
OPERATIONS PLANNING
Forecasts
Demand rates
Production rates
Stock-on-hand
Backorders
Lead times
Product structures
DECISION RULES
1. What to order?
2. When to order?
3. How much?
4. From whom?
INVENTORY
PLANNING
AND CONTROL
Purchase
Order / Set-up
Holding
Stockout
COSTS
Prof. Upendra Kachru

13. Inventory Costs
Inventory Costs are additive
Prof. Upendra Kachru

14. Inventory Costs Holding (or carrying) costs
Ordering Costs/ Setup (or production change) costs
Shortage or Stock-out Costs
Inventory Costs
Prof. Upendra Kachru

15. Stock-out Costs External Shortage
1. Present Profit Loss (potential sales)
2. Backorder Costs
3. Future Profit Loss (goodwill erosion)
Internal Shortage
1. Lost Production (idle people / machines)
2. Substitute Cost (alternate)
3. Overtime / Extra Shift Cost
4. Delay Project Completion Date
Prof. Upendra Kachru

16. Inventory Metrics
Average Inventory Investment: The rupee value of a company’s average level of inventory is one of the most common measures of inventory.
Inventory Turnover Ratio: It is a ratio that measures how many times during a year the inventory turns around.
Inventory turnover = annual cost of goods sold/average inventory investment
Prof. Upendra Kachru

17. Inventory Metrics
Days of Inventory: This measure is an indication of approximately how many days of sales can be supplied solely from inventory.
Days of inventory = avg. inventory investment/ (annual cost of gods sold/days per year)
Days of inventory = days per year/ inventory turnover rate
Prof. Upendra Kachru

18. Inventory Control by Classification Systems
The inventory of a medium sized business organization would comprise thousands of items, each item with different usage, price, lead time and specifications. There could be different procurement and technical problems associated with different items.
In order to escape this quagmire many selective inventory management techniques are used.
Prof. Upendra Kachru

19. Vilfredo Pareto’s 80-20 rule.
The ABC classification is based on focusing efforts where the payoff is highest; i.e. high-value, high-usage items must be tracked carefully and continuously.
Typically only 20 percent of all the items account for 80 percent of the total rupee usage, while the remaining 80 percent of the items typically account for remaining 20 percent of the rupee value.
The large value items constitute only 20 percent, the ABC analysis makes the task relatively easier.
Prof. Upendra Kachru

20. TYPICAL ABC INVENTORY ANALYSIS20 40 60 80
100
120 C B A
PERCENT OF TOTAL DOLLAR USAGE
PERCENT OF TOTAL ITEMS
A = HIGH VALUE ITEMS
B = MEDIUM VALUE ITEMS
C = LOW VALUE ITEMS
Prof. Upendra Kachru

21. TYPICAL ABC INVENTORY ANALYSIS80
PERCENT OF
RUPEE VALUE 60 40 B 20 C 20
PERCENT OF
ITEMS 40 60
Prof. Upendra Kachru

22. RELATIVE ANALYSIS OF ABC CLASSIFICATIONS
Item
Degree of
Type of Records
Lot Sizes
Frequency of
Size of Safety
Control
Review
Stocks A
Tight
Accurate / Complete
Low
Continuous
Small B
Moderate
Good
Medium
Occasional
Moderate C
Loose
Simple
Large
Infrequent
Large
Prof. Upendra Kachru

23. ABC EXCEPTIONS 1. Difficult Procurement Items 2. Short Shelf Life
3. Large Storage Space Requirements
4. Item’s Operational Criticality
5. Likelihood of Theft
6. Difficult Forecast Items
Prof. Upendra Kachru

24. Other Classification Systems
Title
Basis
Main Uses
ABC (Level of Usage)
Value of consumption
raw material components and work-in progress inventories
HML (High, medium, low usage)
Unit price of the material
Mainly to control purchase.
FSND (Fast, Slow moving, Non moving, Dead )
Consumption pattern of the component
Control obsolescence.
SDE (Scarce, difficult, easy to obtain items)
Problems faced in procurement
Lead time analysis and purchasing strategies
GOLF (Government, Ordinary, Local, Foreign)
Source of the material
Procurement strategies
VED (Vital, Essential, (Desirable)
Criticality of the component
To determine the stocking levels of spare parts.
SOS (Seasonal, Off-seasonal)
Nature of suppliers
Seasonal items like agriculture products
XYZ ( Value of Stock)
Value of items in storage
To review the inventories and their use scheduled intervals.
Prof. Upendra Kachru

25. INVENTORY
MODELS
E(1)
Independent Demand
Dependent Demand
subassemblies,
raw materials, etc)
Finished
product
Component parts
Inventory systems are predicated on whether demand is derived from an end item or is related to the item itself.
There are two types of models that are used in the case of independent demand:
Single Period Models, and
Multiple Period Models.
Prof. Upendra Kachru

26. SINGLE PERIOD MODELS
Prof. Upendra Kachru

27. Single-Period Inventory Model
Single-Period Inventory Models are a special case of periodic inventory systems.
One time purchasing decision (Example: vendor selling food at Siababa temple)
Seeks to balance the costs of inventory overstock and under stock
It is used for a wide variety of service and manufacturing applications
Prof. Upendra Kachru 7 27

28. Problem and Solution F(0.9)= ŷ+1.282σ f(z) z z*
After prayers at the Siababa temple on Thursdays, people go to a vendor to eat food. The vendor has collected data over a few months that show, on an average, 100 meals were sold with a standard deviation of 10 meals. If our vendor wants to be 90 percent sure of not running out of food each Thursday, how many meals should he prepare?
If we assume that the distribution is normal and the vendor prepared food for exactly 100 persons, the risk of food running out would be 50 percent. The demand would be expected to be less than 100 meals 50 percent of the time, and greater than 100 the other 50 percent.
To be 90 percent sure of not falling short, he needs to prepare more food.
From the “standard normal distribution“, we can find out that he needs to have additional food to cover standard deviations.
In order to ensure that he is 90 percent sure having sufficient food:
The number extra food required would be x 100 = 128.2, or 129 meals.
Prof. Upendra Kachru

29. Single-Period Inventory Model
If Co = Cost per unit of demand overage, Cu = Cost per unit of demand underage, The probability that the unit will be sold is ‘P’;
Here (1-P) is the probability of the service/ product not being sold.
The expected marginal cost equation can be represented as:
P * Co < (1-P) * Cu
Solving for P, we obtain
P < [Cu / (Co +Cu)]
Prof. Upendra Kachru

30. The Classical Newsvendor’s Problem
A newspaper vendor is faced with the problem of deciding how many newspapers to order daily so as to maximize the daily profit.
Daily demand (d) for newspapers is a random variable.
No reordering is possible during a day,
If the newsvendor orders fewer papers than customers demand he or she will lose the opportunity to sell some papers.
If supply exceeds demand, the vendor will be stuck with papers which cannot be sold.
Prof. Upendra Kachru

31. Demand Data
Based on observations over several weeks, the vendor has established the following probability distribution of daily demand:
The vendor purchases daily papers at Rs.2 and sells them at Rs. 5 apiece. Leftover papers are valueless and are discarded (i.e. no salvage value).
Demand d
Probability
P(d)
Cumulative Prob.
F(d) = P(D  d)
35 or less 36 37 38 39 40 41 42 43 44 45
46 or more
0.00
0.05
0.07
0.08
0.15
0.20
0.10
0.03
0.02
0.12
0.35
0.50
0.70
0.85
0.95
0.98
1.00
Prof. Upendra Kachru

32. The vendor identifies two penalty costs which he/she will incur, regardless of his/her decision: Cost of Overage CO = Purchase Price - Salvage Value = c - s For each paper overstocked the newsvendor incurs a penalty cost of: CO = Rs – Rs.0.00 = Rs Cost of Underage CU = Selling Price - Purchase Price = p - c For each paper understocked the newsvendor incurs a penalty (opportunity) cost of: CU = Rs – Rs = Rs. 3.00
Prof. Upendra Kachru

33. Consider the decisions:
Assume that there is already a policy in place to order a certain number of papers daily, say 38.
Consider the decisions:
D1 : Continue the present policy: Stock 38 papers.
D2 : Order one more paper: Stock 39 papers.
The possible events are:
E1 : The 39th paper sells (i.e. demand  39 = demand > 38).
E2 : The 39th paper does not sell (i.e. demand  39 = demand  38).
Prof. Upendra Kachru

34. To Stock or Not to Stock! The expected payoff is:
Item 39 will not sell on a given day only if demand on that day is for 38 or fewer items:
P(D  38) = F(38) = 0.20.
The probability that an item will not sell is the cumulative probability associated with the previous item. Item 39 will sell on a given day only if demand on that day is for 39 or more items:
P(D  39) = 1 - P(D  38) = 1 - F(38) = = 0.80.
The expected payoff is:
Rs. 3(0.8) + (- Rs. 2)(0.2) = Rs. 2.
This implies an increase in profit of Rs as compared to the alternative decision which has a payoff of Rs He should stock the 39th paper.
Prof. Upendra Kachru

35. Inventory Management Game
Product
Price
Sell
Don’t Sell (Overage)
Stockout (Underage)
Burger
18.00
7.00
9.00
11.00
Pizza
23.00
12.00
17.00
Patties
8.00
4.00
6.00
Samosa
2.00
3.00
Sandwich
10.00
5.00
Pastry
3.50
Hotdog
Prof. Upendra Kachru

36. MULTI PERIOD INVENTORY MODELS
Prof. Upendra Kachru

37. Multi-Period Inventory Models
Fixed-Order Quantity Models: Event triggered (Example: running out of stock)
Fixed-Time Period Models: Time triggered (Example: Monthly sales call by sales representative)
Time T1 T2
Inventory Level ‘Q’
Prof. Upendra Kachru
Prof. Upendra Kachru

38. Fixed order Quantity and Fixed-Time Period Differences
Feature
Fixed-order quantity Model
Fixed-Time Period Model
Order quantity
The same amount ordered each time
Quantity varies each time order is placed
When to place order
Reorder point when inventory position dips to a predetermined level
Reorder when the review period arrives
Record keeping
Each time a withdrawal or addition is made
Counted only at review period.
Size of inventory
Less than fixed-time period model
Larger than fixed-order quantity model
Time to maintain
Higher due to perpetual record keeping
Type of items
Higher-priced, critical, or important items.
Prof. Upendra Kachru

39. Fixed Order Quantity Models
Economic Order Quantity (EOQ) models, due to simplicity and versatility, are fixed order quantity models used for material planning.
When independent demand is the most important issue, the EOQ model provides a solution to the problem.
Prof. Upendra Kachru

40. The Inventory Cycle Q Usage rate Lead time
The inventory cycle determines when an order should be placed and how much should be ordered so as to minimize average annual variable costs.
Profile of Inventory Level Over Time Q
Usage
rate
Quantity
on hand
Reorder
point
Place
order
Lead time
Receive
order
Time
Receive
order
Prof. Upendra Kachru

41. The EOQ Model The basic assumptions in the EOQ Model are as follows:
The rate of demand for the item is deterministic and is a constant ‘D’ units per annum independent of time.
Lead time is zero or constant and it is independent of both demand as well as the quantity ordered.
Price per unit of product is constant
Inventory holding cost is based on average inventory
Ordering or setup costs are constant 41
Prof. Upendra Kachru
Prof. Upendra Kachru

42. COST MINIMIZATION GOAL
By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs
average inventory level:
The holding cost per unit:
The setup cost per unit:
The production cost per unit:
Total Cost C O S T
Holding
Costs
QOPT
Annual Cost of
Items (DC)
Ordering Costs
Order Quantity (Q) 42
Prof. Upendra Kachru 11 42

43. BASIC FIXED-ORDER QUANTITY (EOQ) MODEL FORMULA
TC=Total annual cost
D =Demand
P =Cost per unit
Q =Order quantity
A =Cost of placing an order or setup cost
R =Reorder point
L =Lead time
H = v*r =Annual holding and storage cost per unit of inventory
Total
Annual =
Cost
Annual
Purchase
Cost
Annual
Ordering
Cost
Annual
Holding
Cost + +
TC = P*D + D*A / Q + Q*v*r / 2
Prof. Upendra Kachru 12 43

44. The EOQ We also need a reorder point to tell us when to place an order
Prof. Upendra Kachru 13 44

45. EOQ Model Problem
A company, for one of its class ‘A’ items, placed 8 orders each for a lot of 150 numbers, in a year. Given that the ordering cost is Rs. 5,400.00, the inventory holding cost is 40 percent, and the cost per unit is Rs Find out if the company is making a loss in not using the EOQ Model for order quantity policies.
What are your recommendations for ordering the item in the future? And what should be the reorder level, if the lead time to deliver the item is 6 months?
‘D’ = Annual demand = 8*150 = 1200 units
‘v’ = Unit purchase cost = Rs
‘A’ = Ordering Cost = Rs
‘r’ = Holding Cost = 40%
Prof. Upendra Kachru

46. QEOQ = √ (2*A*D /r*v) = 900 units.
TC= = √ 2*5400*1200*0.40*40
Using the Economic Order Equation:
QEOQ = √ (2*A*D /r*v) = 900 units.
Minimum Total Annual Cost (TC) = √ 2*A*D*r*v = Rs. 14,400.00
The Total annual Cost under the present system = Rs. 45,000.00
The loss to the company = Rs. 45,000 – Rs. 14,400 = Rs. 30,600.00
Reorder Level = Ro = L*D = (6/12)* 1200 = 600 units
The company should place orders for economic lot sizes of 900 units in each order.
It should have a reorder level at 600 units.
= Rs. (1200*5400/ *40*150/2) = Rs. (43, )
Prof. Upendra Kachru

47. Total Costs with Purchasing Cost
EOQ
TC with Purchasing Cost
TC without Purchasing Cost
Purchasing Cost
Quantity
Adding Purchasing cost doesn’t change EOQ
Prof. Upendra Kachru

48. Total Cost with Constant Carrying CostsOC
EOQ
Quantity
Total Cost
TCa
TCc
TCb
Decreasing
Price
CC a,b,c
Prof. Upendra Kachru

49. Problem
Novelty Ltd carries a wide assortment of items for its customers. One item, Gaylook, is very popular. Desirous of keeping its inventory under control, a decision is taken to order only the optimal economic quantity, for this item, each time. You have the following information. Make your recommendations:
Annual demand : 1,60,000 units
Price per unit : Rs.20
Carrying cost : Re.1 per unit or 5 per cent
Cost per order : Rs. 50
Determine the optimal economic quantity.
Prof. Upendra Kachru

50. Solution
Order per year
Size
Average inventory
Carrying cost (Re.1)
Ordering cost (Rs.50 per order)
Total cost per year 1
1,60,000
80,000 50 10
16,000
8,000
500
8,500 40
4,000
1,000
5,000 80
2,000
100
1,600
800
5,800
The optimum economic quantity (lot size) for this item is 4,000 numbers.
Prof. Upendra Kachru

51. What-if
Show that changing the order quantity by a small amount has very little effect on the cost.
Prof. Upendra Kachru

52. Quantity Discounts
Quantity discounts, which are price incentives to purchase large quantities, create pressure to maintain a large inventory.
For any per-unit price level, P, the total cost is:
Total annual cost = Annual holding cost + Annual ordering or setup cost + Annual cost of materials
C = (H) (A) + PD Q 2 D
Prof. Upendra Kachru

53. Total cost curves with purchased materials added
Quantity Discounts
C for P = Rs.4.00
C for P = Rs.3.50
C for P = Rs.3.00
PD for
P = Rs.4.00
P = Rs.3.50
P = Rs.3.00
EOQ 4.00
EOQ 3.50
EOQ 3.00
First price break
Second price break
Total cost (Rupees)
Purchase quantity (Q)
Total cost curves with purchased materials added
EOQs and price break quantities
Prof. Upendra Kachru

54. Finding Q with Quantity Discounts
Step 1. Beginning with the lowest price, calculate the EOQ for each price level until a feasible EOQ is found.
It is feasible if it lies in the range corresponding to its price.
Step 2. If the first feasible EOQ found is for the lowest price level, this quantity is the best lot size.
Otherwise, calculate the total cost for the first feasible EOQ and for the larger price break quantity at each lower price level. The quantity with the lowest total cost is optimal.
Prof. Upendra Kachru

55. Problem
A supplier for Apollo Hospital has introduced quantity discounts to encourage larger order quantities of a special catheter. The price schedule is:
Order Quantity Price per Unit
0 – 299 Rs
300 – 499 Rs
500 or more Rs
Annual demand (D) = 936 units
Ordering cost (A) = Rs. 45
Holding cost (H) = rv = 25% of unit price
Prof. Upendra Kachru

56. Step 1: Start with lowest price level:
EOQ =
2DS H
2(936)(45)
0.25(57.00) =
= 77 units
Not feasible
EOQ =
2DS H
2(936)(45)
0.25(58.80) =
= 76 units
Not feasible
EOQ =
2DS H
2(936)(45)
0.25(60.00) =
= 75 units
Feasible
This quantity is feasible because it lies in the range corresponding to its price.
Prof. Upendra Kachru

57. Step 2: The first feasible EOQ of 75 does not correspond to the lowest price level. Hence, we must compare its total cost with the price break quantities (300 and 500 units) at the lower price levels (Rs and Rs.57.00):
C = (rv) (A) + PD Q 2 D
C75 = [(0.25)(Rs )] (Rs. 45) + Rs (936) 75 2
936
C75 = Rs. 57,284
C300 = [(0.25)(Rs )] (Rs. 45) + Rs (936)
300 2
936
= Rs. 57,382
C500 = [(0.25)(Rs.57.00)] (Rs.45) + Rs (936)
500 2
936
The best purchase quantity is 500 units, which qualifies for the deepest discount.
= Rs. 56,999
Prof. Upendra Kachru

58. © 2007 Pearson Education
Decision Point:
If the price per unit for the range of 300 to 499 units is reduced to Rs , the best decision is to order 300 catheters.
Annual Demand 936
Ordering Cost Rs
Holding Cost 25%
Price
EOQ
Inventory Cost
Order Cost
Purchase Cost
Total Cost Rs 75 Rs
Rs. 56,160
Rs. 57,284 Rs
300
Rs. 2175 Rs
Rs. 54,288
Rs. 56,603 Rs
500
Rs. 3563 Rs
Rs. 53,352
Rs. 56,999
This shows that the decision is sensitive to the price schedule. A reduction of slightly more than 1 percent is enough to make the difference in this example.
Prof. Upendra Kachru

59. QUANTITY DISCOUNTS Advantages Disadvantages
Lower unit cost Higher holding costs
Lower ordering costs Larger inventory investment
Fewer stockouts Older stock
Price increase hedge Slow inventory turnover

60. Fixed-Time Period Models
In many retail merchandising systems, a fixed- time period system is used. Sales people make routine visits to customers and take orders. Inventory, therefore, is counted only at particular times.  
Fixed-time period models generate order quantities that vary from period to period, depending on the usage rates.
Prof. Upendra Kachru

61. Fixed Period Model
Prof. Upendra Kachru

62. T = Time between orders I = Existing Inventory L = Lead Time
Q = Order Size
Total Annual Cost = Purchase Cost + Ordering Cost + Holding Cost

63. Prof. Upendra Kachru

64. Accounting for Safety Stock:
Order Quantity = Average demand over the vulnerable period + safety stock - Inventory currently on hand
Accounting for Safety Stock:
Where
z = Number of standard deviations for a specified service probability
σT + L= Standard deviation of demand over the review and lead time
Prof. Upendra Kachru

65. Fixed Time Period System - Advantages
Fewer orders are placed
Purchase discounts more likely
Lower shipping and freight costs
Prof. Upendra Kachru

66. Requires storage space Incurs taxes Requires insurance
Consumes capital
Requires storage space
Incurs taxes
Requires insurance
Can become lost, stolen, damaged, outdated, or obsolete
Must be counted, sorted, verified, stored, retrieved, moved, issued, and protected
Prof. Upendra Kachru 66

67. Classical Inventory Prblems
Ever - increasing storage space needs
Slow-moving materials
Disposition of scrap, obsolete, & surplus materials
Transaction recording errors
Misplaced materials
Prof. Upendra Kachru

68. RAW MATERIALS INVENTORY PROFILE
Excess Stock
Surplus / Idle
Working Stock
Safety Stock
Outputs
Inputs
Nonproductive
Productive
Prof. Upendra Kachru

69. IN-PROCESS INVENTORY PROFILE
Unreleased Orders
Orders in Transit
Orders in Temporary Storage
Orders Waiting to be Worked
Orders Being Inspected
Orders Being Worked
Backlog
Nonproductive
Productive
Outputs
Inputs
Finished Goods
In-Process
Inventory
Prof. Upendra Kachru

70. Inventory System Improvement
1. Standardize Stock Items 2. Reduce Lead Times 3. Reduce Cycle Times 4. Use Fewer Suppliers 5. Inform Suppliers of Expected Demand 6. Contract for Minimum Annual Purchases 7. Buy on Consignment 8. Consider Transportation Costs 9. Order Economical Quantities 10. Control Access to Storage Areas 11. Obtain Better Forecasts
Prof. Upendra Kachru

71. Inventory System Improvement
12. Dispose of Excess Stock 13. Improve Record Accuracy (cycle count) 14. Improve Capacity Planning 15. Minimize Setup Times 16. Simplify Product Structures 17. Multishift operations 18. Continuous Improvement
Prof. Upendra Kachru

72. Click to edit company slogan .
Operations
Management (2)
Thank You !
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