2013 HiMCM B题特等奖学生论文下载4342

2013 HiMCM B题特等奖学生论文下载4342

 

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论文摘要如下：

The problem we are presented with involves determining minimal changes to the teller system of a bank to achieve the goals set by the manager, namely to minimize the length of the waiting line and the time customers spend waiting. Although the context of our problem is narrow, the models we developed can be applied to any situation involving queues and improving operational efficiency.

 

In this project, we wanted to make the smallest change to the bank’s teller system while satisfying management goals of having the average queue lengths be 2 people or fewer and the average wait time in queue be 2 minutes or less. To achieve these goals, we constructed a system of probabilistic differential equations that related the related the average arrival and departure rates to find the likelihood that our bank will be serving a given number of people at any time. From these probabilities, we determined the expected number of customers we will see waiting in line and the average time they will spend waiting. Using our model we determined that hiring an extra teller would decrease average queue lengths from 2.79 to 0.28 people and wait time from 6.84 to 0.69 minutes. We also accounted for factors such as bank peak hours where we would see an increased arrival rate by adding piecewise components with respect to time to our system of differential equations. Again, hiring an extra teller to serve during those peak hours decreased average queue length from 2.32 to 0.98 people and wait time from 5.68 to 2.4 minutes.

 

We also created a computational model of the system using stochastic processes. This computational model allows for the analysis of more complex scenarios and results in more accurate numerical data than the mathematical model. The computational model agreed with the mathematical model in that the current system does not achieve the manager’s goals for queue length and wait time, and that improvements are necessary. Multiple improvements were modeled and tested, including adding a full-time and a part-time additional teller and installing an ATM. All of these changes brought the queue length and wait time within the manager’s specifications, so we performed a cost/benefit analysis to choose the optimal change. We found that, although hiring a part-time teller to work peak hours only costs $8,300/year, installing an ATM will be a cheaper and better solution in the long run, with a payback period of only 3 years. Therefore, we state this solution achieves the objectives while having minimal costs.

 

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