4. Flow-Time Analysis Problem 4.1 The Traffic Court of King James County operates 9 am-1 pm. Each...

4. Flow-Time Analysis

Problem 4.1

The Traffic Court of King James County operates 9 am-1 pm. Each morning, roughly at 9 p. m., 200 defendants show up for trial involving traffic violations. On a Monday, a sample of 10 defendants were selected at random. For each defendant, the actual time spent in discussion with the judge and the time paying the fine ( not including waiting) were recorded. Also recorded were the times the defendant arrived and left the court.

November 11, 2011 1Ardavan Asef-Vaziri


Problem 4.1

a) Estimate the flow time. (9:30-8:45) + (9:45-8:45) + …… + (12:55-9:00) + (9:20-

9:00) = 1200.Average Flow Time = 1200/10 = 120 min.

b) Estimate the theoretical flow time. Average time with judge = (1+1.5+…..+ 1+1.5)/10 =

1.55 min. The average time to pay fine = (5+2+…..+ 2+3)/10 =

2.4 min.Theoretical flow time: 1.55 + 2.4 = 3.95 min.

c) What is the flow- time efficiency?3.95/120 = 3.3% November 11, 2011 2Ardavan Asef-Vaziri


Problem 4.2

Wonder Shed Inc. ( Example 4.3) produces, in addition to the standard model, a deluxe version for the discriminating customer. The production process for the two models are identical and depicted in Figure 4.1. The activity times for deluxe models is listed below. All the times mentioned represent flow time at the various activities and include the effects of waiting.


Activity Activity Time (Work Content)

1 Separate 202 Punch the base 353 Punch the roof 454 Form the base 105 Form the roof 456 Subassemble the base 307 Assemble 258 Inspect 40


Problem 4.2

a) Compute the process flow time for producing a deluxe

shed.

Path 1 (roof) : = 20+ 45 +45 +25+ 40 = 175 min.

Path 2 (base): = 20+35+10 +30+ 25+ 40= 160 min.

The critical path is path 1, and the flow time is 175 min.

b) What is the impact on flow time of the process if the

flow time of Activity 2 is increased to 40 minutes?

Activity 2 is on path 2 ( not the critical path). Increasing

the time of this activity by 5 minutes does not make

path 2 critical. c) What is the impact on flow time of the process if the

flow time of Activity 3 is reduced to 40 minutes?The flow time will be reduced to 170 minutes. (170 still

>160)



Problem 4.3

When a guest calls room service, the room-service manager takes down the order. She submits an order ticket to the kitchen to begin preparing the food, and an order to the wine waiter to prepare alcoholic beverages . Finally, she assigns the order to a waiter. It takes 4 minutes to take down the order and to assign the work. It takes the kitchen 18 minutes to prepare the typical order, and the sommelier 6 minutes to prepare the drinks for the order. While the kitchen and the sommelier are doing their tasks, the waiter prepares the cart. This takes 10 minutes per order. Once the food, wine, and cart are ready, it takes the waiter 12 minutes to deliver the meal to the customer. It takes the waiter additional 4 minutes to return to the station and debit the guest’s account. All the times mentioned represent flow time at the various activities, and include the waiting times.



Problem 4.3

a) Draw a process map from receipt of order to delivery

of food

Activity 2 is not on the critical pathc. The lead time will be reduced to 170 minutes. 4.3. a.

b) What is the flow time of the process?

The critical path time is 4+18 + 12 +4 = 34 min


Order

Food

Alcohol BillDeliver

Cart

4

18

10

12 46


Problem 4.3

Activity 2 is not on the critical pathc. The lead time will be reduced to 170 minutes. 4.3. a.

c) What is the effect on the process flow time if the

waiter could prepare the cart in 8 minutes, instead of

10?

Cart preparation is not on the critical path.

d) What is the effect on the process flow time if the

waiter could deliver the order in 10 minutes, instead

of 12?

The critical path (flow time) is reduced by 2 min.



Problem 4.4

A home insurance application consists of two forms: F1 and F2 . On receipt, each application is processed and separated into F1 and F2; 10 min. F1 requires Activity A for 15 min and then Activity B for 10 min. F2 requires Activity C for 20 min. F1 and F2 are then combined and further processed by a loan officer for 15 min. All the times mentioned represent flow time at the various activities, and include the effects of waiting.a) Draw a process flowchart for the processes.


F1

F2

Process And Separate

Activity C

Loan Officer

Activity B

Activity

A

10

15

20

15

10


Problem 4.4

b) What is the flow time?

The flow time is 50 minutes. The critical path is the one

of F1.

c) What is the effect on flow time if 50% of F1 forms

must repeat Activity A one more time due to quality

problems?

Since 50% of F1 forms return to A, then 100% of F1

forms spend 15 minutes in A and the other 50% spend

15 more minutes at A. On average an F1 form spends

15+ 0.5(15) = 22.5.

Therefore activity A takes 7.5 minutes more.

Since activity A is on the critical path, the flow time will

increase 7.5 minutes, to 57.5 minutes.



Problem 4.5

A single security line in Vancouver International Airport comprising an X- ray scanner for carry on items and a screening station for passengers. Passengers first prepare themselves for the inspection by removing belts, coats and shoes, emptying their pockets, etc. and deposit all the bags in the trays on the scanner. They then proceed and pass through the screening station . They then retrieve their belongings. The X- ray scanner takes 40 seconds per tray, and the average passenger utilizes 1.5 trays. The personal screening station requires 30 seconds per person. Finally, retrieving of belongings and getting reorganized takes 60 seconds. All the times mentioned represent activity time at the various activities and do not include the effects of waiting. November 11, 2011 10Ardavan Asef-Vaziri


Problem 4.5

a) Draw a process map for the security check process.


b) What is theoretical flow time of the security check

process? The critical path is the one through the X-ray

scanner.

The flow time is 30 + 40*1.5 + 60 = 150 seconds.


Problem 4.5

c) A sample of 20 passengers were selected at random

and the time required for each to clear the security

check was recorded. The average of the individual times

was 530 seconds. What is the process flow-time

efficiency?

The flow time efficiency is 150/530 = 28%

d. What is the impact on theoretical flow time of the

process if the personal screening activity is expedited to

20 seconds?

The personal scanner is not on the critical path.November 11, 2011 12Ardavan Asef-Vaziri


A temp work service maintains an “inventory” of 200

computer specialists who are assigned to various

customers on a short term basis. The typical tour of

duty lasts for 7 weeks, and the period between

assignments typically lasts for 3 weeks. Assume 50

weeks per year.

a) On average, how many specialists start on a new

assignment each week?

Critical Path Example of Flow Time



Lets assume each job is composed of 7 weeks of activity

A (working on a job) and activity B (doing nothing).

Therefore we always have 200 of these jobs. Some

specialist are working on

The flow time of entire process is 3+7 = 10 weeks

Inventory is 200

RT = I R= I/T = 200/10 = 20 per week

Alternatively, each job takes 10 weeks. Each specialist

will be assigned 1/10 of a new job per week. There are

200 specialists, they will be assigned 200(1/10) = 20

new jobs per week. R = 20.




b) On average, how many specialists are idle (between

assignments)?

The flow time of “idle” is 3 weeks R=3

R = The throughput is 20 per week

RT = I 20(3) = 60

Alternative way % of idle time 3/10= 30%. Thus 30% of

staff will be idle on average, ( 30% of 200 = 60)




Practice: Draw the Network of Activities

Task Pred. Dur. Task Pred. Dur.

a -- 4 g c,d 1

b -- 3 h e 4

c a 3 i f 5

d a 2 j e,g 6

e b 6 k h,i 1

f b 4

For each task, compute ES, EF, LF, LS, slack



Practice: Compute the Theoretical Flow Time

Start Finish

a=4slack=

b=3slack=

c=3slack=

d=2slack=

e=6slack=

f=4slack=

g=1slack=

h=4slack=

i=5slack=

j=6slack=

k=1slack=

Task=durslack=xxx

LST LFT

EFTEST




Start Finish

a=4slack=

b=3slack=

c=3slack=

d=2slack=

e=6slack=

f=4slack=

g=1slack=

h=4slack=

i=5slack=

j=6slack=

k=1slack=

Task=durslack=xxx

LST LFT

EFTEST



EZS is a small fast food outlet serving mainly the corporate clientele. EZS’ main fare is a freshly prepared, customizable line of sandwiches. It is supplemented with an assortment of drinks, light salads, seasonal fruit and snacks. The restaurant is open 10:00AM to 10:00PM, but the peak demand is during lunch hours, 11:30 to 2:00PM. A customer joining the line makes a sandwich selection by consulting the billboard, marks her selection on a customized form, and hands the form to one of several assemblers who produce the sandwich. The customer does not wait for the sandwich to be assembled, but proceeds directly down the line to select additional items onto her tray. Next, the customer proceeds to pay at the cash register. Finally, (after the payment is completed) she collects her prepared sandwich at a designated location. Selecting the sandwich and marking the form takes 45 seconds. Assembling the sandwich requires 90 seconds. Selecting additional items takes 60 seconds. Paying at the cash register requires 40 seconds. Collecting the prepared sandwich requires 20 seconds. The restaurant employs 2 cash registers and 6 sandwich assemblers, and one person to disburse the prepared sandwiches.




a) Draw a process map



b) What is the theoretical flow time of the process?

The critical path is the top one, = 45 +60 + 40 +20 =

165 sec


Capacity and Buttleneck


c) What is the capacity of the process?

Assembly Capacity = 6*60/90 = 4 per min.

Cash register Capacity = 2*60/40 = 3 per min.

Disburse capacity = 1*60/20= 3 per min (assuming

time to collect = time to disburse).

d) During rush hour, demand exceeds capacity and long

lines form. Does it make sense to add a sandwich

assembler

No. Assembler is not a bottleneck


Honda's he "American Classic Edition" (ACE) motorcycle is assembled in the US from four

major subassemblies. The first subassembly produces the engine: (i) The left and right

part of the engine block come out of the automatic mold every 2 min. (ii) These parts are

welded together, requiring 1 min of welding machine. (iii) It takes the engine assembler 3

min to insert the two pistons and four valves. The second subassembly produces the

frame in two steps: (i) Heavy metal bars are bent in the 10K-pound press in 1 min. (ii) It

takes 3 min to weld the multiple bars together with the welding machine to produce the

frame. The third subassembly consists of the front and rear fenders, both of which are

formed using the same 10K-pound press for 1 min each. The fourth subassembly makes

the seat. It takes an assembler 7 min to cut the padding, pit it on a performed piece of

sheet metal and wrap the two with synthetic leather. In final assembly, first the four

subassemblies are put together. It takes 30 min to finish assembly of one motorcycle.

Currently, Honda ACE staffing is as follows there is 1 molding machine operator, 1 welder

1 press operator, 1 engine assembler, 2 seats assemblers, and 10 final assemblers.

a) Draw a process flowchart identifying resources, activity times, and any potential

storage buffers

Problem 4.4 from Second Edition. Four major subassemblies; Engine, Frame, Fenders, Seats.

4. Flow-Time AnalysisProblem 4.4 from Second Edition. Four major subassemblies; Engine, Frame, Fenders, Seats.

molding eng. ass.

seat ass.

stamping

welding

FA

aut. molding machine

1 molding operator

10K lbs press

1 press operator

welding machine

1 welder

2 seat assemblers

1 engine assembler

10 final assemblers

startend

2 min 1 min 3 min

1 min 3 min

2 min

7 min

30 minstamping welding



Problem 4.4 from Second Edition.

b) What is the theoretical flow time of the ACE

production process?

We have 4 paths, the critical path is the longest path =

37 minutes (going through seat assembly). Therefore,

the theoretical flow time = 37 minutes.

c) Knowing the benefits of flow-time reduction, Honda

would like to decrease the theoretical flow time of the

ACE process. Which specific action(s) do you

recommend?



Problem 4.4 from Second Edition.

We can decrease the theoretical flow time only by

decreasing the length of the critical path. Thus we

need to decrease the theoretical flow times of seat

assembly and/or final assembly: try to change the

design and process so that we can perform subtasks

parallel.

Easiest is to do final assembly of the first three

subassemblies first and seat assembly at the end.



Cross-traning

Cross training may not reduce flow time if the activities

cannot be subdivided into smaller activities that could

be done in parallel.


5

1

3 2

5

1

3 2

3

1

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4. Flow-Time Analysis Problem 4.1 The Traffic Court of King James County operates 9 am-1 pm. Each...

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