Question 2 South Beach University is conducting an online exam. There are 1,200 students taking this...

 

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Question 2 South Beach University is conducting an online exam. There are 1,200 students taking this exam. Students are required to download the exam questions from the university's learning management system (LMS), solve the questions, type their workings and answers in a computer word processing application, and submit the files back to the LMS. It is estimated that the LMS takes an average of 30 seconds to process a submission. For example, if a student submits his files at time T and the LMS is able to start processing his submitted files right away, it is estimated that the LMS accepts the submission at T + 30 seconds. The cut-off time of the exam is 12pm on the exam day, that is, if a submission cannot be accepted by the LMS by 12pm, it is considered late submission. Due to the capacity of the LMS servers, a maximum of 150 submissions can be processed at any point of time. Submissions are processed on a first-come-first-serve basis. If the number of submissions exceeds the capacity, some submissions would be put on hold. Use Little's Law to analyse and answer the following questions. (a) (b) Is it wise for a student to submit his file at 11:58am on the exam day? Why or why not? You should explain assumption (if any) and show calculation steps using Little's Law. (10 marks) Estimate the percentage of late submissions if all students submit their files in the last three (3) minutes. (4 marks) The university administration wants to ensure that all 1,200 students are able to submit their files in the last two (2) minutes without late submission. Based on the analysis from Little's Law, what kind of specific suggestions you can propose to the university? (10 marks) (c) Explain Little's Law and its three (3) parameters. Link the three parameters to various quantities of interest in this question. (6 marks) (d) Hilltop Restaurant is located in Dempsey Hill. The restaurant has a capacity of 35 tables to serve customers. When doing its capacity planning and evaluating operational performance, the restaurant adopts the concept of "customer group" and uses it as unit of measurement to measure the workload in the service process. A customer group is a group of one or more people who arrive, get seated at a table, eat and depart. On average, a customer group takes 70 minutes to eat dinner, and then another 25 minutes to eat dessert. On average, a customer group generates a profit of $100 on dinner, and $30 on dessert. (a) Assume that all customer groups eat both dinner and dessert. Estimate the maximum number of customer groups per hour the restaurant can serve (capacity rate) by applying Little's Law. At what rate (dollars per hour) is profit generated by the restaurant if it operates at capacity rate? (12 marks) Now assume that Hilltop leases new space to open a "dessert bar" next door, and has opened up the wall between the two units to allow inside access from the restaurant to the dessert bar. The dessert bar can accommodate 15 tables. With this change, a customer group arrives and is seated at a table in Hilltop restaurant as usual. However, when the customer group finishes eating dinner, the waiter would ask them if they would like to move to the dessert bar for dessert. Assume that all customer groups eat both dinner and dessert and agree to move to dessert bar after dinner. (b) Apply Little's Law to the following questions: what is the capacity rate (customer groups per hour) of the total system (restaurant and dessert bar)? At what rate (dollars per hour) is profit generated by the system if it is operating at capacity rate? (13 marks) Question 2 South Beach University is conducting an online exam. There are 1,200 students taking this exam. Students are required to download the exam questions from the university's learning management system (LMS), solve the questions, type their workings and answers in a computer word processing application, and submit the files back to the LMS. It is estimated that the LMS takes an average of 30 seconds to process a submission. For example, if a student submits his files at time T and the LMS is able to start processing his submitted files right away, it is estimated that the LMS accepts the submission at T + 30 seconds. The cut-off time of the exam is 12pm on the exam day, that is, if a submission cannot be accepted by the LMS by 12pm, it is considered late submission. Due to the capacity of the LMS servers, a maximum of 150 submissions can be processed at any point of time. Submissions are processed on a first-come-first-serve basis. If the number of submissions exceeds the capacity, some submissions would be put on hold. Use Little's Law to analyse and answer the following questions. (a) (b) Is it wise for a student to submit his file at 11:58am on the exam day? Why or why not? You should explain assumption (if any) and show calculation steps using Little's Law. (10 marks) Estimate the percentage of late submissions if all students submit their files in the last three (3) minutes. (4 marks) The university administration wants to ensure that all 1,200 students are able to submit their files in the last two (2) minutes without late submission. Based on the analysis from Little's Law, what kind of specific suggestions you can propose to the university? (10 marks) (c) Explain Little's Law and its three (3) parameters. Link the three parameters to various quantities of interest in this question. (6 marks) (d) Hilltop Restaurant is located in Dempsey Hill. The restaurant has a capacity of 35 tables to serve customers. When doing its capacity planning and evaluating operational performance, the restaurant adopts the concept of "customer group" and uses it as unit of measurement to measure the workload in the service process. A customer group is a group of one or more people who arrive, get seated at a table, eat and depart. On average, a customer group takes 70 minutes to eat dinner, and then another 25 minutes to eat dessert. On average, a customer group generates a profit of $100 on dinner, and $30 on dessert. (a) Assume that all customer groups eat both dinner and dessert. Estimate the maximum number of customer groups per hour the restaurant can serve (capacity rate) by applying Little's Law. At what rate (dollars per hour) is profit generated by the restaurant if it operates at capacity rate? (12 marks) Now assume that Hilltop leases new space to open a "dessert bar" next door, and has opened up the wall between the two units to allow inside access from the restaurant to the dessert bar. The dessert bar can accommodate 15 tables. With this change, a customer group arrives and is seated at a table in Hilltop restaurant as usual. However, when the customer group finishes eating dinner, the waiter would ask them if they would like to move to the dessert bar for dessert. Assume that all customer groups eat both dinner and dessert and agree to move to dessert bar after dinner. (b) Apply Little's Law to the following questions: what is the capacity rate (customer groups per hour) of the total system (restaurant and dessert bar)? At what rate (dollars per hour) is profit generated by the system if it is operating at capacity rate? (13 marks)

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Littles Law states that the average number of items in a system L is equal to the average arrival ra... View the full answer