4. flow-time analysis flow time and theoretical flow time 1: flow time 2: paths on a network of...
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4. Flow-Time Analysis
Flow Time and Theoretical Flow Time
1: Flow Time
2: Paths on a Network of Activities and the Critical Path
3: Flow Time Levers
4. Critical Path Method and Slacks
November 11, 2011 1Ardavan Asef-Vaziri
4. Flow-Time Analysis
1November 11, 2011 2Ardavan Asef-Vaziri
4. Flow-Time Analysis
Competitive Advantages of a shorter flow time
Shorter response time (both in production and product design).
Delayed differentiation (Postponement). Moving from the
extreme of MTS towards MTO.
Lower inventory costs (due to Little’s Law).
November 11, 2011 3Ardavan Asef-Vaziri
4. Flow-Time Analysis
Inventory adversely affects all competing edges (P/Q/V/T) Has cost:
Physical carrying costs Financial costs
Causes obsolescence: Due to market changes Due to technology changes
Leads to poor quality: Feedback loop is long
Hides problems: Unreliable suppliers. High defect rate. Long tools changeover times. Frequent machine breakdowns.
Causes long flow time
Lean Operations: The Real Cost of Inventory
November 11, 2011 4Ardavan Asef-Vaziri
4. Flow-Time Analysis
Direct Methods of Measuring Flow Time
Randomly sample flow units over an extended period of time.
Measure the flow time for each flow unit from entry to exit.
Compute the average of flow times.
During a given month, a sample of 50 applications was taken The average flow time = 20.85 working days.
November 11, 2011 5Ardavan Asef-Vaziri
4. Flow-Time Analysis
Indirect Methods of Measuring Flow Time
Count the number of units produced over an extended period of time.
R = number of units produced / duration of time period .
Count the number of units of inventory at random points during the time period. Compute the average inventory (I).
Compute flow time T =I/R
200 applications processed during 20 days; average throughput of R=200/20 = 10 applications per day. The number of applications were counted at 4 random points during these days, the average inventory (I) was 860/4 =215.
T = I/R T = 215/10 flow time is 21.5 daysNovember 11, 2011 6Ardavan Asef-Vaziri
4. Flow-Time Analysis
The “Steal a Deal” gift shop specializes in heavily discounted merchandise for the holiday season. The store prices are so appealing that lines of people queue up in the early AM hours in front of the store doors in order to secure a place in the line. On the morning after Thanksgiving, one of the most busy days of the year, the store opened its doors at 8:00AM. From 7:45 to 8:00, 120 customers arrive and are already waiting in line. From 8:00AM to 10:00AM, new customers arrive at the rate of 5 per minute. After 10:00AM, the rate reduces to 2 per minute. The store admits customers at the rate of 4 per minute.
Flow Time Example
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4. Flow-Time Analysis
Schematic Representation of the Flow Dynamics
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Rp< Ra =5/minRp = 4/min
Ra -Rp=1/minRp -Ra=2/min
8:00 10:00 12:007:15
120
9:00
4. Flow-Time Analysis
a) How many customers are in the waiting line at 10
AM?
Dynamics of Inventory and Waiting Time
November 11, 2011 9Ardavan Asef-Vaziri
120 at 8:00
Buffer increases at rate of
1/min.
At 10:00 thee are 120+1(120) =
240b) Jacob plans to arrive to the store at 9:00AM. How
long should he expect to wait?
120 at 8:00
Buffer increases at rate of
1/min.
At 9:00 thee are 120+1(60) =
180
4. Flow-Time Analysis
Dynamics of Inventory and Waiting Time
November 11, 2011 10Ardavan Asef-Vaziri
Buffer is served at rate of 4/min
180/4 = 45 min.
It takes Jacob 45 min to get in
9:00 + 45 min = 9:45
c) Rachel does not want to wait more than 15 minutes.
When should she show up (in terms of the number of
customers in the waiting line)?
Buffer is served at rate of 4/min
In 15 min they can serve 15(4) = 60. When there are 60
customers in line.
4. Flow-Time Analysis
d) Rachel does not want to wait more than 15 minutes.
When should she show up (in terms of time)?
Dynamics of Inventory and Waiting Time
November 11, 2011 11Ardavan Asef-Vaziri
At 10:00 there are 240 customers in the waiting line.
Rachel should arrive when there are no more than 60
customers in line because those in front of her are
served at rate of 4/ min.
2 new customers per minutes arrive after 10:00 AM.
Customers are reduced at rate of (4-2) = 2/min
(240-60)/2 = 90 min
10:00 + 90 min = 11:30
4. Flow-Time Analysis
Average Inventory
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e) Compute the average inventory from 7:45AM to
12:00PM.
Inventory starts from 0, goes up to 120 in 15 min.
Therefore during 0.25 hour the average inventory is
(0+120)/2 = 60.
Inventory then starts from 120, goes up to 240 in 2
hours. Therefore, during 2 hour the average inventory is
(120+240)/2 = 180.
Then inventory goes down from 240 to 0 in 240/2 = 120
min = 2 hour; at 12:00. Therefore during 2 hours the
average inventory is (240+0)/2 = 120.
The average inventory 0.25(60) + 2(180) + 2(120) =
615
4. Flow-Time Analysis
We should divide this by the sum of the relative
weights;
0.25 + 2 + 2 = 4.25
The average inventory (customers in the line) =
615/4.25 = 144.7
Average inventory is the same, regardless the unit of
time used (for hours, minutes and in this case, 4.25
hours).
Average Inventory
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4. Flow-Time Analysis
f) Compute the average throughput from 7:45AM to
12:00PM.
From 7:45 to 8:00; 0.25 hours 120 customers arrive
From 8:00 to 10:00; 2 hours (2×60)(5) = 600 customers
arrive
From 10:00 to 12:00; 2 hours (2×60)(2) = 240
customers arrive
A total of 120+5(60×2)+2(120) = 960 arrive over the
time interval of 7:45 to 12:00PM, that is 4 hours and 15
min. or in 4.25 hours. R is 960 customers per 4.25
hours.
R = 960/4.25 = 225.882 per hour.
R = 225.882/60 = 3.76 per min.
Average Throughput
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4. Flow-Time Analysis
Average Flow Time
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g) Compute the average flow time from 7:45AM to
12:00PM.
RT = I, R = 3.76 per min, I = 144.7
T = 144.7/3.76 = 38.44 min.
4. Flow-Time Analysis
2November 11, 2011 16Ardavan Asef-Vaziri
4. Flow-Time Analysis
Process : Network of activities performed by resources
1. Flow unit: The unit of analysis– Level of detail
2-3. Network of Activities & Storage/Buffers
- Define Process Boundaries
- Activities with activity times
- Buffers with waiting flow times
- Routes: precedence relationships (solid lines) with throughputs
4. Resources & Allocation
- Who does what?
5. Information Structure & flow (dashed lines)
Key for capacity analysis
Process Flow Chart
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4. Flow-Time Analysis
Flowcharting
ActivityBuffer
Physical flowEvent
Information flow
See the total process; a systems view Define flow units and process boundaries Include only the key steps Clarify the level of detail needed. Processes can be
broken down into sub-activities. On the other hand, cascading allows several activities to be combined in a single sub-process
Depicts resources required to carry out activities Identify the processes that need attention (weak
points)
Decision
4. Flow-Time Analysis
Wondershed Inc: Narrative Representation
1. Separate the roof and the base sheets
2. Punch the base
3. Punch the roof
4. Form the base
5. Form the roof
6. Sub-assemble the base
7. Assemble
8. Inspect
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4. Flow-Time Analysis
End
Wondershed Inc. : Schematic Representation
StartSeparate
Sheet
Punch base
Punch roof
Form base
Form roof
Sub assemble base
InspectAssemble
StartActivity
AActivity
BActivity
CEnd
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4. Flow-Time Analysis
Theoretical Flow Time
Theoretical Flow Time: The minimum time for processing a flow
unit.
Activity Time: The time required to complete an activity.
An activity cannot be broken down into smaller activities that can be
executed in parallel. What does that mean???
Entry Buffer Activity Exit
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4. Flow-Time Analysis
Critical Path
Theoretical flow time of each path in the process flowchart = sum of the activity times of all activities on that pathCritical Path: the longest path Critical Activities: activities that lie on the critical pathTheoretical flow time of the process = Time of the theoretical
critical path
Activity Time 2Activity Time 1 Activity Time 3
Activity Time 5Activity Time 4 Activity Time 6
Sequential Activities
Sequential Activities
Parallel Activities
How many Paths?
Activity Time 2Activity Time 1 Activity Time 3
Activity Time 2Activity Time 1 Activity Time 3
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4. Flow-Time Analysis
Wondershed Inc. Theoretical Flow Time
Path 1 (roof) Start 1 3 5 7 8 End 10 +20 +10 +10+30 = 80 minPath 2 (base) Start 1 2 4 6 7 8 End 10 +25+5 + 10 +10+30 = 90 minTheoretical Flow Time = 90 min
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Activity Activity Time (Work Content)
1 Separate 102 Punch the base 253 Punch the roof 204 Form the base 55 Form the roof 106 Subassemble the base 107 Assemble 108 Inspect 30
4. Flow-Time Analysis
Theoretical Flow Time
Theoretical Flow Time: The minimum amount of time required for
processing a typical flow unit without any waiting.
Activity Time: The time required by a typical flow unit to complete
the activity. Unless stated otherwise, we assume that an activity
cannot be broken down into smaller activities that can be executed in
parallel. What does that mean???
Entry Buffer Activity Exit
November 11, 2011 24Ardavan Asef-Vaziri
4. Flow-Time Analysis
Wondershed Inc. Flow Time
Path 1 (roof) Start 1 3 5 7 8 End 30 + 110 + 85 + 55 + 105 = 385 minPath 2 (base) Start 1 2 4 6 7 8 End 30 + 70 + 40 + 70 + 55+ 105 = 370 minFlow Time = 385 minNovember 11, 2011 25Ardavan Asef-Vaziri
Activity Activity Time (Work Content)
Waiting Time Flow Time
1Separate 10 20 302Punch the base 25 45 703Punch the roof 20 90 1104Form the base 5 35 405Form the roof 10 75 856Subassemble the base 10 60 707Assemble 10 45 558Inspect 30 75 105
4. Flow-Time Analysis
Industry Process Average Flow Time
Theoretical Flow Time
Flow Time Efficiency
Life Insurance New Policy Application
72 hrs. 7 min. 0.16%
Consumer Packaging
New Graphic Design
18 days 2 hrs. 0.14%
Commercial Bank
Consumer Loan
24 hrs. 34 min. 2.36%
Hospital Patient Billing
10 days 3 hrs. 3.75%
Automobile Manufacture
Financial Closing
11 days 5 hrs 5.60%
Flow Time Efficiencies in White Collar Processes
Flow Time Efficiency = Theoretical Flow Time / Flow
Time
Flow Time Efficiency = 90/385 = 23.4%
November 11, 2011 26Ardavan Asef-Vaziri
4. Flow-Time Analysis
Flow Time Example: Activity Times
A1 A3
A4 A6
A5A2
4
3
6
4
2
3
E
S
What is the Theoretical Flow Time November 11, 2011 27Ardavan Asef-Vaziri
4. Flow-Time Analysis
Critical Path Method: Paths
A1 A3
A4 A6
A5A2
4
3
6
4
2
3
E
S
10
Critical Path is the longest Path
11 8
How many paths?
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4. Flow-Time Analysis
Critical Path Example of Flow Time
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a) The Critical Path is A1-A4-
A6. The theoretical flow time
of the process is 4+4+3= 11.
b) What will happen if
activity A5 is increased from
2 to 4?
A5 is not on critical path. Increasing its time by 2
increases the length of the path A2-A5-A6 from 8 to 10.
It does not become a critical path. The flow time is still
11.
c) What will happen if activity A5 is increased from 2 to
5?
4. Flow-Time Analysis
Critical Path Example of Flow Time
November 11, 2011 30Ardavan Asef-Vaziri
Increasing A5 time by 3
increases the length of the path
A2-A5-A6 from 8 to 11. Now
both paths of A1-A4-A6 and A2-
A5-A6 are critical path. The
flow time is still 11.
d) What will happen if activity A1 is increased from 4 to
5?
Path A1-A4-A6 is still critical and the flow time increases
to 12.
e) What will happen if activity A3 is increased from 4 to
8?
Now path A1-A3 becomes critical and the flow time
increases to 4+8 =12.
4. Flow-Time Analysis
Theoretical Critical Path vs. Critical Path
A1 A3
A4 A6
A5A2
4
3
6
4
2
3
E
S
W1
W2
W4
W3
W6
W7
W5
W9
W8
The time of the critical path differs from the time of the theoretical critical path. Why?
The critical path itself also may differ from the theoretical critical path. Why?
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4. Flow-Time Analysis
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4. Flow-Time Analysis
Levers for Managing Flow Time
To reduce the flow time we must shorten the length
of every critical path. Flow time is the sum of two components—Waiting
time and Activity time. These two components have different natures and the levers available for managing each are distinct. The main levers for reducing waiting times are
Managing congestion (Utilization and Variability) – Ch3 and Ch8.
Reducing Batch sizes and Safety stock – Ch6 and Ch7.
Synchronization – Ch10. November 11, 2011 33Ardavan Asef-Vaziri
4. Flow-Time Analysis
Reducing Theoretical Flow Time: Shorten the Length of Every Critical Path
Re-Structure - Moving work off the critical path- Move work off the critical path to a noncritical activity- Move work off the critical path to the outer loop (pre-processing or post-
processing).
Eliminate - Reducing the work content of critical activities- Work smarter. Reduce non-value-adding part of the activity; Business Process
Re-engineering.- Work Faster. Increase the speed of the activity. Better Methods, Training,
Advanced Technology, Better Management.- Reduce the amount of extra work. Work right the first time; implement a robust
quality management system.
Modify the product sequencing- Priority to the product that requires less processing time - Given market condition.
November 11, 2011 34Ardavan Asef-Vaziri
4. Flow-Time Analysis
Reducing Theoretical Flow Time: Shorten the Length of Every Critical Path
Whatever approach we take, it must be directed towards the critical path. Reducing the work content of noncritical activities does not reduce the theoretical flow time. Such reduction may still be useful for decreasing total processing costs, increasing process capacity, and reducing the potential for errors and defects.
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4. Flow-Time Analysis
1. Restructure the Critical Path
Move work off the critical path to a noncritical activity. So that critical activities are performed in parallel rather than sequentially.
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Moving activities to the outer loop: perform them before or after the process. Instead of assembling a complete hamburger in MTO (make to order), shift towards MTS (made to stock), precook beef patties and keep them ready.
A :5 days B:5 days C:5 days
A 1:3 days C:5 daysA 2:2 days
B:5 day
4. Flow-Time Analysis
2. Work Smarter; Reduce Non-Value-Adding Activities
Value-adding activities increase the economic value of a flow unit from the perspective of the customer. Performing surgery, flying airplane, serving meals, manufacturing products, and dispensing loans are value-adding.
Non-value-adding activities do not directly increase the value of a flow unit. Moving work or workers, setting up machines, scheduling activities or personnel, sorting, storing, counting, filling out forms, participating in meetings, obtaining approvals or maintaining equipment are non- value -adding.
November 11, 2011 37Ardavan Asef-Vaziri
4. Flow-Time Analysis
2. Reduce Non-Value-Adding Activities
Non value adding activities come in two types; necessary or non-necessary. The second type should be eliminated outright. The first type activities can also be eliminated . A process with high fraction of defectives may require a sorting station to separate the defective from the good units. If the process capability is increased so that no defectives are produced, the sorting activity could be eliminated. The primary value-adding activity the accounts-payable (A/P) process is paying the bills in an accurate and timely fashion. The A/P department spends much of its time reconciling contradictory information, verifying, matching documents, and investigating discrepancies. Such activities do not add value but are still necessary. They can be eliminated if the process is modified. November 11, 2011 38Ardavan Asef-Vaziri
4. Flow-Time Analysis
3. Work Faster; Increase the Speed of Operations
Increase the speed of operation - work faster. Technology, Method, Training, Incentive. The speed of a manual checkout counter can be increased by using bar codes with a scanner, adding a second worker to bag products, or proper incentives, coupled with training and better equipment so that checkout personnel work faster without increasing error rates or jeopardizing service quality.
November 11, 2011 39Ardavan Asef-Vaziri
4. Flow-Time Analysis
4. Do It Right in the First Time; Reduce the Amount of Rework
Decreasing the amount of repeat work can often be achieved by process-improvement techniques such as statistical process control, method improvement and training. In data-processing, the goal is to input each piece of data just once; to avoid additional time (as well as cost and errors).
Work content = Activity time × Average number of visitsActivity time 10 min, rework 10% number of visits 1.1Work content = 1.1(10) = 11 min.
Theoretical flow time is computed based on work content not based on Activity time
November 11, 2011 40Ardavan Asef-Vaziri
4. Flow-Time Analysis
5. Modifying the Product Sequencing
Modify the product sequencing - do the quickest thing first. Most processes involve a mix of products, characterized by different flow times for the various units of flow. If we give priority to flows unit that move through the process faster, the overall flow time of the process will decrease.
November 11, 2011 41Ardavan Asef-Vaziri
Of course, product mix is often dictated by the market, and even when the organization has some control over it, there may be other relevant factors, such as profitability, resource-utilization issues, and market considerations.
(2+3)/2 = 2.5
(1+3)/2 = 2.0
Product Blue needs two days, Product Red needs one day.
4. Flow-Time Analysis
4November 11, 2011 42Ardavan Asef-Vaziri
4. Flow-Time Analysis
Critical Path Method: Paths
A1 A3
A4 A6
A5A2
4
3
6
4
2
3
E
S
10
Critical Path is the longest Path
11 8
How many paths?
November 11, 2011 43Ardavan Asef-Vaziri
4. Flow-Time Analysis
Critical Path Methos: Forward Path; Earliest Starts
A1 A3
A4 A6
A5A2
4
3
6
4
2
3
E
S0
0
0
0
0
0
4
3
3
4
4
3
4
4
3
4
4 10
8
5
5
5
8 8
10
10
8 11
11
11
11
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4. Flow-Time Analysis
Forward Path; Earliest Starts
November 11, 2011 45Ardavan Asef-Vaziri
10
3020
Max = 30
5
35
35
35
4. Flow-Time Analysis
Backward Path; Latest Starts
A1 A3
A4 A6
A5A2
4
3
6
4
2
3
E
S0
0
0
0
0
0
4
3
3
4
4
3
4
4
3
4
4 10
8
5
5
5
8 8
10
10
8 11
11
11
111
111
11
11
11
555
88
8
8
8
8
8
4
6
4
4
66
633
3
40
0
0 11
11
November 11, 2011 46Ardavan Asef-Vaziri
4. Flow-Time Analysis
30
3030
Min = 35
5
35
45
30
Backward Path; Latest Starts
4. Flow-Time Analysis
Activity Slack
Slack, or float: The amount of time a noncritical
task can be delayed without delaying the project
Slack—LFT – EFT or LST – EST
EST—Earliest Start Time; Largest EFT of all predecessors
EFT—Earliest Finish Time; EST + duration for this
task
LFT—Latest Finish Time; Smallest LST of following tasks
LST—Latest Start Time; LFT – duration for this task
November 11, 2011 48Ardavan Asef-Vaziri
4. Flow-Time Analysis
Critical Path, Slacks
A1 A3
A4 A6
A5A2
4
3
6
4
2
3
E
S
0
0
4
3 3
4
4 10
8
5
8 11
11
11
11
5
88
8
4
663
40
11
November 11, 2011 49Ardavan Asef-Vaziri