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

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


1November 11, 2011 2Ardavan Asef-Vaziri


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).



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



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.



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


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



Schematic Representation of the Flow Dynamics


Rp< Ra =5/minRp = 4/min

Ra -Rp=1/minRp -Ra=2/min

8:00 10:00 12:007:15

120

9:00


a) How many customers are in the waiting line at 10

AM?

Dynamics of Inventory and Waiting Time


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




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.


d) Rachel does not want to wait more than 15 minutes.

When should she show up (in terms of time)?



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


Average Inventory


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


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



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



Average Flow Time


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.




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



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


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



End

Wondershed Inc. : Schematic Representation

StartSeparate

Sheet

Punch base

Punch roof

Form base

Form roof

Sub assemble base

InspectAssemble

StartActivity

AActivity

BActivity

CEnd



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



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


Sequential Activities

Sequential Activities

Parallel Activities

How many Paths?





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


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



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



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


Industry Process Average 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%



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


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?



Critical Path Example of Flow Time


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?


Critical Path Example of Flow Time


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.


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?





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


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.



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.



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.


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


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.



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


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.



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



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.


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.




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?



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



Forward Path; Earliest Starts


10

3020

Max = 30

5

35

35

35


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



30

3030

Min = 35

5

35

45

30

Backward Path; Latest Starts


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



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


Documents

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