Exercise 7.11 Calculate the cycle time, cycle time efficiency, and cost of the university admission process described in Exercise 1.1 (page 5), assuming that: 

• The process starts when an online application is submitted. 

• It takes on average 2 weeks (after the online application is submitted) for the documents to arrive to the student’s service by post. 

• The check for completeness of documents takes about 10 min. In 20% of the cases, the completeness check reveals that some documents are missing. In this case, an email is sent to the student automatically by the university admission management system based on the input provided by the international student’s officer during the completeness check. 

• A student services officer spends on average 10 min to put the degrees and transcripts in an envelope and to send them to the academic recognition agency. The time it takes to send the degrees and transcripts to the academic recognition agency and to receive back a response is 2 weeks on average. 

• About 10% of applications are rejected after the academic recognition assessment. 

• The university pays a fee of e 5 each time it requests the academic recognition agency to accept an application. 

• Checking the English language test results takes 1 day on average, but the officer who performs the check only spends 10 min on average per check. This language test check is free. 

• About 10% of applications are rejected after the English language test. 

• It takes on average 2 weeks between the time students service sends the copy of an application to the committee members and the moment the committee makes a decision (accept or reject). On average, the committee spends 1 h examining each application. 

• It takes on average 2 days (after the decision is made by the academic committee) for the student’s service to record the academic committee’s decision in the university admission management system. Recording a decision takes on average 2 min. Once a decision is recorded, a notification is automatically sent to the student. 

• The hourly cost of the officers at the international student’s office is e 50. 

• The hourly cost of the academic committee (as a whole) is e 200.

Exercise 7.18 Consider the process model in Figure 7.17. 

This model captures a simplified process for handling mortgage applications. There are two checks involved. CT1 deals with a check of the financial coverage of the mortgage application. The second check CT2 concerns the verification of the property that is to be mortgaged. If the result of both checks is positive, the application is accepted (task AC). On average, after the execution of task CT1, 20% of all applications are rejected. Meanwhile, task CT2 leads to 30% of further rejections. If either of the checks has an unsatisfactory result, the application is rejected (task AW). The arrival process is Poisson with an average arrival of 5 cases per hour during business hours. For each task, exactly one dedicated resource is available. The processing time of every task follows an exponential distribution. The mean processing times for tasks CT1, CT2, AC, and AW are respectively 5, 4, 3, and 3 min. The wage of each resource is e 20 per hour. Business hours are from Monday to Friday from 9 a.m. to 5 p.m. Resources are only available during these hours. 

a. Determine the resource utilization of each resource. 

Resource utilization of each resource:

From the question, we have λ = 5 cases per hour. Now, we need to find μ, which is the theoretical capacity per resource, or the number of cases a task can handle in each business unit. 

b. Determine the average cycle time of the process. 

c. Determine the cycle time efficiency of the process. 

d. Determine the average number of mortgage applications that are being handled at any given point in time. 

Hint For this exercise, it might be convenient to use a combination of process simulation, Little’s law, and flow analysis.