1 3. process flow measures assignment, problem 1 solution 1. bank xyz receives 20 loan requests per...

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3. Process Flow Measures

Assignment , Problem 1 Solution

1. Bank XYZ receives 20 loan requests per hour on average. Each loan request goes through an initial processing stage, after which an “accept or reject” decision is made. Approximately 80% of the loans are accepted, and these require additional processing. Rejected loans require no additional processing. Suppose that on average 5 loans are in the initial processing stage, and 25 (accepted) loans are in the additional processing stage.

5

Reject

Accept 80%

20%

20 25

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a) What is the average processing time required for a loan request?

R = 20 loans/hour

I = 5+25 = 30 loans

Average processing time = Throughput Time

RT= I T = I/R = 30/20 = 1.5 hours

b) What is the average processing time required for a rejected loan?

R = 20 loans/hour

I = 5 loans

Average processing time = Throughput Time

RT= I T = I/R = 5/20 = 0.25 hours

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c) What is the average processing time required for an accepted loan (including the initial processing stage)?

Initial Stage: As computed for rejected applications the time for the initial process is

T = I/R = 5/20 = 0.25 hours

Additional Processing Stage:

R = 20 × 0.8 = 16 loans/hour, I = 25 loans

T = I/R = 25/16 = 1.5625

Average Total Processing Time =

= 0.25 + 1.5625 = 1.8125 hours

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2. A call center employs 1000 agents. Every month 50 employees leave the company and 50 new employees are hired.

1000 Agents

50/month 50/month

a) How long on average does an agent work for this call center?

R = 50 people/month

I = 1000 people

Average working time = Throughput Time

= I/R = 1000/50 = 20 months or 20/12 = 1.67 years

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Suppose the cost of hiring and training a new agent is $1000. The manager of this call center believes that increasing agents’ salary would keep them working longer term in the company. The manager wants to increase the average time that an agent works for the call center to 24 months, or 2 years.

b) If an agent works for the call center for 24 months on average, how much can the company save on hiring and training costs over a year? Hint: first determine the current annual cost for hiring and training, then determine the new annual cost for hiring and training.

1000 Agents

?/month ?/month

2 years

1000 Agents

50/month 50/month

20 months

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Current annual cost for hiring and training:

Throughput Rate = 50 people/month

= 600 people/year

Annual hiring and training cost is 600 (1000) = $600,000

New annual cost for hiring and training:

Average working time = Throughput Time = 24 months = 2 years

Throughput Rate R= I/T = 1000 people / 2 years = 500 people/year 41.7 per month

Annual hiring and training cost is 500 (1000) = $500,000

Annual saving on hiring and training cost is $600,000-$500,000 = $100,000

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c) How much the monthly salary of each agent can be increased?

Average # of employees = 1000

Annual saving on hiring and training cost = $100,000

Monthly saving = $8,333.33

8333.33/1,000 = $8.33 per employee/month

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Little’s Law: Auto-Moto Financial Services

Auto-Moto receives 1,000 applications per month (30 working days). In the old process, each application is handled individually, with 20% of applications being approved. 500 were in the process at any time. Average flow time T = ?

The firm recently implemented a new loan application process. In the new process, applicants go through an initial review and are divided into three categories

Average flow time T = I/R = 500/1,000 months = 0.5 month or 15 days.

ProcessIp=500

1000/month200/month

800/month

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Practice; New Process, R, I, and T

Initial Review

Subprocess A Review

Subprocess B Review

Accepted

Rejected

1000/month

25%

50%

25%

70%

30%

90%

10%

800/month

200/month

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New Process: The Same R, But smaller I

Initial ReviewIIR=200

Subprocess A ReviewIA = 25

Subprocess B ReviewIB = 150

Accepted

Rejected

1000/month

25%

50%

25%

70%

30%

90%

10%

800/month

200/month

R = 1000I = IIR + IA + IB = 200 + 25 + 150 = 375Inventory reduced to 375 from 500 in the old process. Since R is constant, therefore T has reducedT = I/R = 375/1000 = 0.375 month or 0.375(30) = 11.25 daysThe new process has decreased the processing time from 15 days to 11.25 days.

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Flow Time at Each Subprocess (or activity)

Average Flow Time for Activity IR. Throughput RIR = 1,000 applications/month Average Inventory IIR = 200 applications TIR = 200/1,000 per month = 0.2 months or 6 days with the initial

review team

Average Flow Time for Activity A.

Throughput RA = 250 applications/month

Average Inventory IA = 25 applications

TA = 25/250 months = 0.1 months or another 3 days in subprocess A.

Average Flow Time for Activity B.

Throughput RB = 250 applications/month

Average Inventory IB = 150 applications

TB = 150/250 months = 0.6 months or another 18 days in subproces B

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Routing, Flow Time, and Percentage of Each Flow units

One flow unit at very macro level: Application1000 flow units/month at very micro level: Each specific applicationTwo flow units: Accepted and rejectedFive flow units: Accepted-A, accepted-B, rejected-IR,

rejected-A, rejected-B

Accepted-A: IR, AAccepted-B: IR, BRejected-IR: IRRejected-A: IR, ARejected-B: IR, B

TIR = 6 daysTA = 3 daysTB = 18 days

We also need percentages of each of the five flow units

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New Process: Intermediate Probabilities

Initial ReviewT = 6

Subprocess A ReviewT = 3

Subprocess B ReviewT = 18

Accepted

Rejected

100%

25%

50%

25%

70%

30%

90%

10%

80%

20%

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New Process: Intermediate Probabilities

Initial ReviewT = 6

Subprocess A ReviewT = 3

Subprocess B ReviewT = 18

Accepted

Rejected

100%

25%

50%

25%

17.5%

7.5%

22.5%

2.5%

80%

20%

50%

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Flow Time of the Accepted Applications

Under the Original Process – the average time spent by an application in the process is 15 days (approved or rejected)

In the new process: On average, how long does it take to approve an applicant? On average, how long does it take to reject an applicant?

Accepted-A: IR, A Accepted-A(T) = 6 + 3 = 9 Accepted-A(%) = 17.5 Accepted-B: IR, B Accepted-B(T) = 6 + 18 = 24 Accepted-A(%) = 2.5

Average Flow time of an accepted application =[0.175(9)+0.025(24)]/(0.175+.025) = 10.875

In the new process, the average flow time has been reduced from 15 to 11.25.

In addition, the flow time of accepted applications has been reduced to 10.875. That is what the firm really cares about, the flow time of the accepted applications.

[email protected] [email protected]

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Flow Time of Rejected Applications

Rejected-IR: IR Rejected-IR(T) = 6 Rejected-IR(%) = 50% Rejected-A: IR, A Rejected-A(T) = 6+3 = 9 Rejected-A(%) = 7.5%Rejected-B: IR, B Rejected-B(T) = 6+18 = 24 Rejected-B(%) = 22.5%

Average Flow time of a rejected application =[0.5(6)+0.075(9)+0.225(24)]/0.8 = 11.343

Check our computations:Average flow time of an application0.8(11.343)+0.2(10.875) = 11.25

1 3. process flow measures assignment, problem 1 solution 1. bank xyz receives 20 loan requests per...

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