1. 1 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

2. 2 3. Process Flow Measures 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. 3 3. Process Flow Measures 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. 4 3. Process Flow Measures Assignment, Problem 2 Solution 2. A call center employs 1000 agents. Every month 50 employees leave the company and 50 new employees are hired. 1000 Agents 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

5. 5 3. Process Flow Measures 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 ?/month 2 years 1000 Agents 50/month 20 months

6. 6 3. Process Flow Measures 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. 7 3. Process Flow Measures 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. 8 3. Process Flow Measures 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

9. 9 3. Process Flow Measures New Process: The Same R, But smaller I Initial Review I IR =200 Subprocess A Review I A = 25 Subprocess B Review I B = 150 Accepted Rejected 1000/month 25% 50% 25% 70% 30% 90% 10% 800/month 200/month R = 1000 I = I IR + I A + I B = 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.

10. 10 3. Process Flow Measures Flow Time at Each Subprocess (or activity) Average Flow Time for Activity IR. Throughput R IR = 1,000 applications/month Average Inventory I IR = 200 applications T IR = 200/1,000 per month = 0.2 months or 6 days with the initial review team Average Flow Time for Activity A. Throughput R A = 250 applications/month Average Inventory I A = 25 applications T A = 25/250 months = 0.1 months or another 3 days in subprocess A. Average Flow Time for Activity B. Throughput R B = 250 applications/month Average Inventory I B = 150 applications T B = 150/250 months = 0.6 months or another 18 days in subproces B

11. 11 3. Process Flow Measures 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 T IR = 6 days T A = 3 days T B = 18 days We also need percentages of each of the five flow units

12. 12 3. Process Flow Measures New Process: Intermediate Probabilities Initial Review T = 6 Subprocess A Review T = 3 Subprocess B Review T = 18 Accepted Rejected 100% 25% 50% 25% 70% 30% 90% 10% 80% 20%

13. 13 3. Process Flow Measures New Process: Intermediate Probabilities Initial Review T = 6 Subprocess A Review T = 3 Subprocess B Review T = 18 Accepted Rejected 100% 25% 50% 25% 17.5% 7.5% 22.5% 2.5% 80% 20% 50%

14. 14 3. Process Flow Measures 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. fa09.som416.01-c@csun.edu

15. 15 3. Process Flow Measures 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

16. 16 3. Process Flow Measures A hospital emergency room (ER) is currently organized so that all patients register through an initial check-in process. At his or her turn, each patient is seen by a doctor and then exits the process, either with a prescription or with admission to the hospital. Currently 55 people per hour arrive at the ER, 10% of who are admitted to the hospital. On average, 7 people are waiting to be registered and 34 are registered and waiting to see a doctor. The registration process takes, on average, 2 minutes per patient. Among patients who receive prescriptions, average time spent with a doctor is 5 minutes. Among those admitted to the hospital, average time is 30 minutes. On average, how long does a patient spend in the ER? Assume the process to be stable; that is, average inflow rate equals average outflow rate. Problem 3.4 MBPF

17. 17 3. Process Flow Measures Directions o) Draw the flow process chart b) On average how long a patient spend in ER? c) On average how many patients are in ER? Hints: Compute flow time in buffer 1 Compute average activity time of Doctor Compute the average flow time in this process Compute average flow time for a simple prescription patient Compute average flow time for a potential admission patient Compute number of patients in Doctor activity Compute the average number of patients in the process.

18. 18 3. Process Flow Measures T PA = 7.6+2+37.1+30 = 76.7 7.6 7.5 37.1 54.2 T D =.9(5)+.1(30) = 7.5 T SP = 7.6+2+37.1+5 = 51.7 T P =.1(76.7)+.9(51.7) = 54.2 Flow Time

19. 19 3. Process Flow Measures 6.9 Inventory 1.8

20. 20 3. Process Flow Measures 49.7 I = 49.7, R = 55. Is our T= 54.2 correct? RT= I R = 55/60 = 0.916667 minutes RT = I  T=I/R = 49.7/0.916667 = 54.2 Recheck The Little’s Law