Heuristics and Simulation Individual Coursework Assignment Solution

MN50753 Heuristics and Simulation Individual Coursework

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Assignment detail:-

  • Words : 2000 + Simulations work

You are going to simulate a small-scale call centre. There are two classes of customers calling: Premium and Standard. 6 premium and 8 standard customer calls arrive to the system in an hour based on historical data. There are two types of servers answering the calls: experienced and rookie servers. 40% of the premium customers are directed to experienced servers upon arrival and rest to the rookie servers. All of the standard customers are directed to rookie servers. However, premium customers have priority over standard customers, i.e. the rookie servers first answer the calls of premium customers and then standard ones. Premium customers calls take Triangular(5,7,10) amount of time in minutes while standard calls take expo(3) minutes.

Premium customers have a waiting tolerance that is normal distributed with mean 5 minutes and standard deviation 1 minute. Standard customers have a waiting tolerance that is normal distributed with mean 8 minutes and standard deviation 2 minutes. Please note that customer tolerance cannot be negative.

There is an operating policy of the call centre; the problems that cannot be solved in 10 minutes by a rookie server are considered as calls that need further assistance and directed to experienced servers (the calls that take more than 10 minutes with a rookie server is cut and sent to experienced servers). These calls with experienced servers take an additional time (additional to 10 minutes with the rookie server) which is uniform between (3,5) minutes. Moreover, these additional calls have priority over the premium calls in the experienced server queue.

There are 2 experienced and 3 rookie servers working in the centre. One of the experienced servers takes a lunch break between 12.00-13.00 while the other takes a break between

13.00 and 14.00. Rookie servers go to lunch break one by one in the following times: 12.30- 13.30, 13.30-14.30, 14.30-15.30.

At the end of the call, customers are asked if they want to answer a brief feedback questionnaire. There are 2 people, Alan and Mary, devoted to analysing these feedback and report back to management about results. They wait until 15 feedback are piled to analyse them.

You can assume that all customers fill the feedback questionnaire. You can use the data provided in Table 1 to estimate the time it takes to analyse 15 feedback surveys.

The call centre operates between 9.00 and 17.00 in a workday. Simulate the system until 500 customers are served and make 40 replications.

a. Find the following statistics:
Average waiting time in the rookie server queue

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Average waiting time in the experienced server queue Average utilization of the rookie servers
Average utilization of the experienced servers Average waiting time of a premium customer Average waiting time of standard customer
Average time spent in the system by a customer (independent of the type) Number of calls directed to experienced servers from rookie servers Number of premium/standard customers that balk
Average utilization of Alan and Mary

b. What can you say about the performance of the system? Can you suggest any changes/improvements to the system? Please state at least 3 of them, and implement one of them in Arena, report the results, and comment on the system performance.

c. Suppose that the call centre decided to change the way they direct the premium customers upon arrival. Instead of dividing them probabilistically, they started a system based on queue length. When a premium customer arrives, the queue lengths of experienced and rookie servers are checked, and the customer is directed to shortest queue. Change your model according to this procedure and simulate the system again. Report the required statistics and comment on the system performance. Has the system improved?

Table 1

6.161 7.746 6.270 5.918 7.186
8.891 6.727 6.298 5.562 8.178
8.138 7.007 8.318 6.029 5.537
5.891 7.073 7.165 8.903 5.462
6.264 7.600 7.832 6.920 8.161
6.215 6.640 5.759 6.174 6.717
6.636 7.422 5.926 8.680 6.174
9.117 5.884 5.686 8.497 5.586
8.722 9.457 7.570 6.923 7.469
9.203 7.380 6.810 8.027 6.096


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