2013 HiMCM B题特等奖学生论文下载4100

2013 HiMCM B题特等奖学生论文下载4100

 

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论文摘要如下：

Businesses are always looking for ways to improve customer satisfaction so that they can attract new customers and retain old ones. In order to accomplish this, a specific bank manager would like to reduce the average time customers spend waiting for services to less than 2 minutes and the average length of the waiting line to less than 2 people. We developed a two part model capable of determining the minimal changes necessary to meet the manager’s requirements.

 

The first part of our model was a purely theoretical approach. We derived a discrete-time equivalent of Lindley’s equation, which is typically used to simulate continuous time queues, and created a recurrence relation that allowed us to find the probability distribution of wait times for any given customer. We then used these distributions to provide an exact value for the average waiting time for customers. This approach, however, is not capable of testing data with multiple servers and also does not directly yield the average queue length.

 

The second part of our model was a computational approach, which we used to test more complex scenarios and find the average queue length. We created an algorithm to simulate the bank’s day-to-day operations and then tested our simulation by running multiple trials and comparing the resulting frequency distributions with the theoretical probability distributions. We found that the average waiting times derived from the two approaches agreed to within 0.164 percent. This indicated that our computer simulation could approximate the theoretical values with high accuracy, allowing us to extend our simulation to test the impact of adding new servers, as well as the addition of “emergency” servers who only serve customers when the queue length exceeds a predetermined limit.

 

Using our model, we determined that the bank’s current system limits the average queue size to a relatively small 1.8 customers, but the average customer waits about 5 minutes for service, and some customers wait as long as 8 minutes. We tested two ways to reduce the mean wait time, choosing to also measure server idle time, the amount of time a server spends not helping a customer, in order to determine which method would be more efficient. By modifying the bank’s system to use two servers simultaneously, we were able to decrease the average wait time to about 6 seconds and reduce the average queue length to 0.04 customers, but we also greatly increased the time servers spent doing nothing from 37 minutes to 430 minutes (more than 7 hours). By adding an emergency server who would only begin serving customers when the queue reached 3 customers, however, we were able to reduce the wait time to 1.46 minutes and the queue length to 0.55 customers while keeping the idle time to a more reasonable 62 minutes. Furthermore, this change would only require the emergency server to work for about 40 minutes each day, a relatively minimal change. Our model shows that adding a second “emergency” server is the most efficient method to reduce average customer wait times and average queue length to within the requirements.

 

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