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Assignment , Problem 1 Solution

Assignment , Problem 1 Solution .

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Assignment , Problem 1 Solution

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  1. 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. Accept 80% 25 20 5 Reject 20%

  2. Assignment , Problem 1 Solution 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

  3. Assignment , Problem 1 Solution 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

  4. 1000 Agents 50/month 50/month Assignment , Problem 2 Solution • 2. A call center employs 1000 agents. Every month 50 employees leave the company and 50 new employees are hired. 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

  5. Assignment , Problem 2 Solution 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 1000 Agents ?/month 50/month ?/month 50/month 20 months 2 years

  6. Assignment , Problem 2 Solution 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

  7. Assignment , Problem 2 Solution 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

  8. 200/month Process Ip=500 1000/month 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 = ? 800/month Average flow time T = I/R = 500/1,000 months = 0.5 month or 15 days. 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

  9. Practice; New Process, R, I, and T Subprocess A Review 70% 200/month Accepted 30% 25% 10% Subprocess B Review Initial Review 1000/month 25% 90% 50% 800/month Rejected

  10. New Process: The Same R, But smaller I Subprocess A Review IA = 25 70% 200/month Accepted 30% 25% 10% Subprocess B Review IB = 150 Initial Review IIR=200 1000/month 25% 90% 50% 800/month Rejected R = 1000 I = IIR + IA + IB = 200 + 25 + 150 = 375 Inventory reduced to 375 from 500 in the old process. Since R is constant, therefore T has reduced T = I/R = 375/1000 = 0.375 month or 0.375(30) = 11.25 days The new process has decreased the processing time from 15 days to 11.25 days.

  11. 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

  12. Routing, Flow Time, and Percentage of Each Flow units One flow unit at very macro level: Application 1000 flow units/month at very micro level: Each specific application Two flow units: Accepted and rejected Five flow units: Accepted-A, accepted-B, rejected-IR, rejected-A, rejected-B Accepted-A: IR, A Accepted-B: IR, B Rejected-IR: IR Rejected-A: IR, A Rejected-B: IR, B TIR = 6 days TA = 3 days TB = 18 days We also need percentages of each of the five flow units

  13. New Process: Intermediate Probabilities Subprocess A Review T = 3 70% 20% Accepted 30% 25% 10% Subprocess B Review T = 18 Initial Review T = 6 100% 25% 90% 50% 80% Rejected

  14. New Process: Intermediate Probabilities Subprocess A Review T = 3 17.5% 20% Accepted 7.5% 25% 2.5% Subprocess B Review T = 18 Initial Review T = 6 100% 25% 22.5% 50% 80% 50% Rejected

  15. fa09.som416.01-c@csun.edu fa09.som416.01-c@csun.edu 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.

  16. 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 application 0.8(11.343)+0.2(10.875) = 11.25

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