Operation Management Hw3

Home Work set #2 1. Students arrive at the administrative services office at an average of one every 10 minutes and their request usually takes about 8 minutes to be processed. Only one clerk staffs the service counter. Assume that the arrival time and service time are random. a. What percentage of time is the server idle? b. How much time, on average, does a student spend waiting in line? c. How long is the queue? d. What’s the probability that an arriving student finds no one in the queue? e. Now assume that it takes on average 9 minutes for the clerk to serve each student. What would be your answers to part (b) and (c)? What is the percentage increase in wait time in the queue as we increase service time from 8 minutes to 9 minutes?

2. Assume that the service time and arrival times are deterministic, i.e., each student arrives exactly at 8, 8:10, 8:20, 8:30, …. In this case, please answer parts (a) to (d) of the previous question.

3. Sharp discount Wholesale club has two service desks, one at each entrance of the store. Customers arrive at each customer service desk at an average of one every six minutes. The service rate at each service desk is about 5 minutes per customer. a. How often is each service desk idle? b. What is the probability that both service desk clerks are busy? c. How much time does a customer spend at the service desk? d. How many customers are waiting in the line in front of each service desk, an average?

4. Sharp discount is considering consolidation of two queues. In that case customers need to wait in one line. Assume that instead of two servers serving one line of customers, we would have one server to serve these customers but the new server’s service time is just 2 minutes, on average. What would be your answers to parts (a) to (d) of question 3?

5. Now assume that you are the manager at Sharp discount and you need to decide whether you want to consolidate two queues or not. To answer this question you estimate that...