* Management optimization of bank’s queuing system *
Abstract
Nowadays the queue phenomenon in the bank offices is a common and troublesome issue that nearly occurs everyday in the banks of China. The rapid tempo of life makes people pay much attention to the time management, they don’t willing to spend much time on queuing and gradually lose confidence in banks. In order to improve the efficiency and the satisfy degree of customers and finally increase the profit of banks, the banks have to do something about their current queuing system. This proposal aims at analyzing the current queuing system of the China banks, finding out existing problems and carrying out some effective measures based on the previous researches, the principle of queuing and statistic method. Under the premise of less increasing the operation cost of the banks to improve the service efficiency in order to realize the win-win result of customers satisfaction and banks profit.

Background
Every person no matter he is young or old may have some painful experiences waiting in the banks of China. Customers still have to wait for a period of time even when they avoid the busy hours of the banks. Not alone the busy operation time or the peak period of the banks people have to wait for ages. I also had the similar experiences when I was an undergraduate student. As a student we need to pay our tuition fee through a certain bank such as Bank of China before a semester begins. However so many students also need to pay through the same banks at that time. Then you can imagine how long the queue is and how terrible the atmosphere is. So from then on I have a bad feeling about the banks near my university and whenever I enter a bank of China I may have a low impression of that bank because I still have to wait for a certain time and the efficiency of the bank is relatively low. Then I suppose the queuing system of the banks should be improve in order to meet the current increasing demand of the customers.

The queuing phenomenon in the bank offices is a common issue now especially when we join in the WTO. The banks of China pay much attention to the intensive operation and management. Some bank offices have been closed down because of the low operation profit or some other reasons such as merger. Then people have to go to the intensive offices to transact business instead of the previous one that have been shut down which result in the problem of queuing in the banks becoming more and more outstanding. People have to wait for a long time once they enter the banks and some customers are not wiling to transact business in the banks if not necessary. Therefore the fame of banks of China has been somewhat damaged and finally the profit of China banks could be influenced by this problem. Based on a survey on Sep. 2007, only 10% of residents are satisfied with the Chinese banks, the overall evaluation on the service of the Chinese banks are 69.6% of the customers regard their service as ordinary, 20.3% are not satisfied with their service. When focusing on the evaluation of waiting time, only 5.7% are content with them while 57.9% are not satisfied. Therefore we can clearly see that waiting time in any banks of China has become a big issue among Chinese residents. Which means the manager of banks should pay more attention to this problem and try their best to find some solutions to improve the queuing system of the banks. May be after some effective methods are taken into practice the bad impression of the service of the banks can be improve and the profit can be increase at that time.

For our country the research on queuing problems is on the primary stage. The appearance of the queuing products started from the using of those products by Foreign Affairs Office. The concept of the queuing system is introduced within recent ten years. However after we joint in the WTO, the traditional internal standard has gradually changed into the international standard especially the service industry. Many youths go abroad to learn the advanced technology and concept and back to China with adequate knowledge and apply them to the relative field. Queuing system is also a branch of knowledge. Although our China does not have so much experience on queuing system, our development of the queuing system of the banks is more rapid than some developed countries. In terms of the technology and the function our country is now beyond some developed countries. Our queuing industry began in 2001 and developed rapidly from 2003. Customers gradually recognized accepted and adapted to the new concept. Though our queuing industry develops rapidly, many aspects should be improved or modified completely when focus on the certain field such as the queuing system in a particular bank of China. So we still have a lot of work to do on the queuing system.

This proposal is based on the research and survey of the current outcome on the queuing industry, combined with my knowledge on the queuing system to find out some new idea and methods to optimize the queuing problems in the banks of China. This proposal should first focus on the problems that cause the queuing of banks becoming longer and longer. Then focusing on these problems carry out some solutions. Hoping these methods can really solve some of the problems that already exist in the queuing system of the banks. And eventually the stress of banks’ queuing can be reduced and the customers may regain confidence to the banks of China. Therefore not only the efficiency but also the profit and fame of the banks can be significantly improved. And the residents would not feel quit boring and troublesome waiting in the banks because they don’t need waiting in the lines for a lot of time, instead they will transact their business within a short time. Customer will have more leisure time to do something they prefer to do and they will then show some confidence in the banks.

Problem Statement
The operational process of the banks should be re-checked and analyzed if the banks waiting line is always quit long in a period of time. Banks have common characteristics that result in people waiting for a long time. The operation time of a bank is usually from 9am to 5pm. It is always the same as or a little earlier than customers’ working time. The banks are also closed in the weekends or holidays. So people have to transact business when they get off work at noon. Therefore it becomes the business peak period of the banks and the queue is quit long at noon. However banks do not increase the service windows at noon, sometimes even close some windows than the waiting time is quit long at this period for the customers due to the low working efficiency of the counters or the proportion of the public-private windows are unreasonable. For example there are 13 windows in a bank, only 4 windows open for private. What’s more, most banks don’t operate on weekends, only some offices operate for certain period on Saturday. On the other hand, the outlet of the bank offices is not reasonable to some extent. Based on the survey the Banking Association found out that larger volume of business is majorly concentrated in economic development hotpot, downtown business distracts, large residential and inadequate facilities distract. These distracts are either service radius is too large to arrange or the banks offices are relatively inadequate. The effect of this fact can be conclude as the supply of the financial service can not meet the demand of the residents. Then the queuing problems are outstanding in these distracts.

The utilization of the self-service devices of the banks is relatively low. Although the ATM, mobile banking and other e-banking of the banks are quit familiar now some people especially the elders still go to the service windows to transact business, even the deposit and withdrawal service that can easily finish from the ATM. Because the traditional habit of the customers when they transact and the propaganda of the banks is not enough they believe the service windows are more convenient and do not cause some mistakes that may happen in the ATM. They do not trust or rely on these electrical devices that cause the utilization of the e-banking service inadequate, hard to relief the stress of the current courters of the banks. On the other hand, some businesses have to be finished in the banks because the self-service banking does not contain those functions in that region. For example the interface of the ATM and the e-booking system are not unified with the Traffic violation fines and other third-party systems, constraining the development of the intermediate business on the self-service devices.

The queuing system of the banks is not quit reasonable since it do not distinguish the purpose of the customer. Some people may have emergency to deal with and need to transact in a early time. However the banks only have general service windows and VIP counter and not everyone can become the VIP of the banks. In addition, because of the constant introduction of the individual financial product and the financial derivatives, not only the population of the customers is larger than before but also the individual service demanding is much more extensive than before which is another factor that result in delaying on the basis of the supply of the banks remaining. For example, customers may need 2mins to finish a transaction before while they can spend 10mins for consulting the new service. Controlling the banks risk can be another that cause queuing. Since the frequently occur of the bank cases, the bank and the regulatory authorities have to add some risk control links, which increase the processing and waiting time of the customer.

The queue structure is another problem for some customers. Most banks in China use the mode of calling number to arrange the sequence of the customers. Although it seems that people can be more feasible and arrange their time during the waiting time people have to pay attention to the calling of the counters. Once you miss the number because of some other matters you have to get another number and wait for another long time before service.

Lecture Review
After I read some papers about optimizing the current banks’ queuing system, I find out that most of them focusing on the evaluating the reasonability of the bank’s queuing system and changing the number of the service counters to be more reasonable. This method can be quit effective because it is a systemic measure that not only consider the satisfaction of the customer when changing the number of service counters but also the reasonability of the whole queuing system of the banks. Then I will first introduce an evaluation mode focusing on the queuing system of the banks. This mold not only uses the formula of the queuing system but also the Analytic Hierarchy Process(AHP) based on the three aspects of the satisfaction of customers, the operation cost and the efficiency of the service to evaluate. Before I start to introduce the process of this mold, I would like to list some notations and assumption that should be used in this mold. Notation explanation
I：The overall evaluation of the reasonability
P1: The satisfaction of the customer
P2: The operation cost
P3: The efficiency of the service
P0: The probability of the system is idle λ:Average arrival rate of customers μ:Average service rate of the system
£(s):Weight combination function
Lq Average length of the queue
T: Average waiting time
1: The importance of the two factors is equal
2: One factor is more important than another s: The number of the service windows

The assumption of the mold 1. The bank operates well. The number of customers is stable everyday. 2. Every servicer of the bank is familiar with all business. 3. The number of windows is proportional to the number of staff. 4. The servicers can be assigned to the near bank offices. 5. People give up their numbers because they wait for a long time

The establish of the mode
Reasonable Degree
Reasonable Degree
1.AHP: In order to describe the reasonability of the bank comprehensively and precisely. This mold considers the problems from three aspects, respectively are the satisfaction of the customer, the operation cost and the efficiency of the service. The hierarchical mold draws below.

Efficiency of Service
Efficiency of Service

Average service time
Average service time
Average waiting time
Average waiting time
Avg. waiting number
Avg. waiting number
Number of windows
Number of windows
Average service time
Average service time
Window opening hours
Window opening hours
Customer loss rate
Customer loss rate
Operation Cost
Operation Cost
Satisfaction of Customers
Satisfaction of Customers

Using AHP to determine the weights of the indicator, the overall evaluation of the reasonability (I) will be sum of every indicator multiplies the coordinate weight.

2. Criteria layer weight calculation method: As we mentioned above, the calculation of the Reasonability of the system contains the weight of each indicator. So we should first use the Criteria layer weight calculation method to calculate the weight of the satisfaction of the customer, the efficiency of service and the operation cost. And then we focus on the next layer of the three indicators, still using this method to calculate the weight of each indicator.

We suppose that the efficiency of the service is most important, the satisfaction of the customers and the operation cost are the same important. The matrix can be listed as follows

| P1 | P2 | P3 | P1 | 1 | 1 | 2 | P2 | 1 | 1 | 2 | P3 | 0.5 | 0.5 | 1 |

From the chart, we can calculate the weight of the three indicators. The weight of the efficiency of the service is 0.5(w1=0.5), the weight of the satisfaction of customers is 0.25(w2=0.25) and the weight of the operation cost is 0.25(w3=0.25).

The next layer is based on the same calculation method. We suppose the average waiting time is the most important indicator under the satisfaction of customers index layer, the other two indicators are the same important. The average r waiting number is the most important under the efficiency of service, the rest two are the same important. In summary, we can determine the weight of each index as shown below.

| Average waiting time (a1) | Average service time (a2) | Customer loss rate (a3) | Window opening hours (a4) | Average service time (a5) | Number of windows (a6) | Average waiting number (a7) | Weight | 0.1 | 0.1 | 0.05 | 0.25 | 0.125 | 0.25 | 0.125 |

Therefore, the formula of the reasonability of the queuing system of the bank is:
I= 0.1a1+0.1a2+0.05a3+0.25a4+0.125a5+0.25a6+0.125a7

3.The queuing theory
As we all know, the queuing system of banks usually consists of several queue lines. Which means there are several service windows for each queues. So we should use the multiple-servicer model of the queuing theory to explain and form the queuing mold. Assuming there is ‘s’ number of servers. Based on the queuing system, when the service intensity ρ=λ/sμ<1,

The probability of the system is idle (P0) can be calculated as follows.
P0=n=0n=s-11n!λμn+1s!λμssμsμ-λ-1

Average length of the queue (Lq) can be calculated as follows.
Lq=sρsρs!1-ρ2P0

Average waiting time (T) can be calculated as follows.
T=Lqλ

Therefore, we can compare the different number of server(s) which meet the requirement ofρ=λ/sμ<1 to select a mode that optimize the probability of the idle system, the average length of queue and the average waiting time. The system should also be assumed that it obeys the Poisson arrival rate, then we can calculate the λandμthrough the MATLAB which can simulate the Poisson distribution function. Then we can get the certain number of λandμof the certain case. After the calculation, we may find out that the more servicers the banks have, the better quality of queuing system the banks will meet. However we need also consider the cost of the number of servers, which means the reasonability of the queuing system. After all these consideration, we may find out the most suitable queuing system of a certain bank.

Methodology
After I read some papers that are related to queuing system of banks I find out that the way that they calculate the parameters such as the probability of customers in the system, the number of customers waiting in line and the average waiting time is always somewhat similar. The formation of these parameters is based on the queue theory that I learnt from operation management. The difference of the methods that can solve the queuing problems of banks is always based on the queuing system data, carrying out some rational solutions that focus on different aspects of the queuing system of the banks. Like the above method on the lecture review, it uses the reasonability of the queuing system of the banks to find out which number of servicers are the best. After some readings, I find out that the operation cost of the bank generating when customers are waiting in lines may be a better way to explain and solve this problem. This method is also focusing on the number of servicers (the number of windows) that should be open and service for customers when people are waiting in the banks. First I still need to list some notations and assumption that should be used in this mold.

Notation explanation s: number of servers (number of service windows)
L: Average number of customer in the system
Lq: Average number of customer in the waiting line
W: Average time a customer spends in the system
Wq: Average time a customer spends waiting in line
P0: Probability of no customers in the system
Pw: Probability that customers must wait λ:Average arrival rate of customers μ:Average service rate of the system
C1: cost of setting up a new service window
C2: cost of recruiting a new server
C3: cost of depreciation and maintenance per customer per hour
C4: other cost when customers waiting in bank.

The assumption of the mold
Like the assumption in lecture review this method should also obey the rules of queuing theory. The average arrival rateλshould be described by the Poisson distribution. The service rateμis described by negative exponential distribution. Service rate must be larger than arrival rate. The queue discipline can be described as order in which customers are served. Infinite queue means length of a finite queue is limited.
The establish of the mode 1. s>λμ ,that means servers must be able to serve customers faster than they arrive. This is the first rule that when calculate number of servers should obey. Therefore we can determine the range of s. 2. After that we can set up the basic multiple-server model based on the queuing theory.
Probability that there are no customers in system (P0) can be calculated as follows:
P0=n=0n=s-11n!λμn+1s!λμssμsμ-λ-1

Probability that customers must wait (Pw) can be calculated as follows:
Pw =1s!λμssμsμ-λP0
Average number of customer in the system (L) can be calculated as follows:
L=λμλμss-1!sμ-λ2P0+λμ
Average number of customer in the waiting line (Lq) can be calculated as follows:
Lq=L-λμ
Average time a customer spends in the system (W) can be calculated as follows:
W=Lλ
Average time a customer spends waiting in line (Wq) can be calculated as follows:
Wq=W-1μ=Lqλ

Then we can choose different number of server (s) based on the inequality s>λμ (the λandμcan be calculated through the MATLAB), after that we can compare different servers that affect the data in queuing system. We may find out the more servers the bank has the better queuing system the bank will achieve. However, in order to get the certain number of servers we still need some other equations. Therefore, we need to calculate the operation cost of the bank. The relationship between waiting cost, service cost and total cost can be drawn as follows:

This diagram clearly shows that although improving the service level can greatly reduce the waiting cost of the banks, the corresponding service cost of the banks will increase at the same time. The trend of total cost is first decrease and then increase as the level of service improves. In order to find out the lowest point of the total cost of banks, we need to consider not only service cost but also waiting cost. Therefor, the formula of the operation cost should contain these two factors, the service cost and the waiting cost.

The operation cost of the bank can be calculated as follows:
C=C1s+C2s+C3LqWq+C4
Therefore, we can select a certain number of servers that optimize the queuing system of the bank and minimize the operation cost. After we find out that number we can easily apply into practice, the queuing system of the banks can be optimized based on the operation management and the impression of the bank can be improved. Finally the profit of the bank can be increased.
What I describe above is only one method that focusing on changing the number of servers to optimize the queuing system of the banks. There are some other solutions that can also improve the bank’s queuing system. We can redesign the operation time of the bank so that the customers can be served as fast as possible. Specifically the banks can change their operation time a little longer than the working hours of the people. Nowadays the operation time of a bank is usually from 9am to 5pm.It is almost the same as people working hour. If the operation hour of the banks can extend even half an hour, people can arrange their time more easily and don’t need to transact business hastily. The banks can also open more service windows at noon instead of reducing service windows when the peak period of queuing comes so that it can greatly reduce the waiting time of the customers. The reason there are few servers at noon is that servers have worked for several hours they also need to have a rest. Therefor, banks can increase the number of servers and increase the frequency of changeover. Banks can also operate at weekends and holiday or extend their service time at night so that the pressure of the queuing system can reduce. Night market banks can be a good choice to transfer the intensity of customers from daytime to night.

Because the demanding of the peak period heavily influent the queuing management banks can analyze their current peak point and then do some adjust. For example the open and close period of the banks and the midday are the peak period of the bank. The day of every month, usually the 10th of every month that most companies pay salary to their staffs and the beginning and the ending of a month that many payment service settles are also very important days that people would like to go to bank for transacting business. If banks can publish those days on the obvious places people will recognize that many people will transact business at that time and they will try not to go to the banks on those days. Then with the awareness of avoiding queuing enhancing, the queuing problems of the banks can be reduced.
The different service of the VIP and the common windows may make some people feel uncomfortable and people who are in an emergency would like to enjoy the service of VIP which fewer people wait in that line than the common windows. The banks can make some statement such as if someone is in an emergency they can pay a certain amount of money to become a occasional VIP then they can use the VIP fast track for transacting. This method can enhance the satisfactory of customers and balance the number of customers between the VIP and common windows to some extent.

Expected Outcome
The research on optimizing the queuing system of the banks can be quit significant to banks and other industries that related to queuing. There are many researches on queuing system and each has its own method to solve the existing queuing problems of banks. My R&D method carries out based on the queuing theory that I learnt from the Operation Management and the related lectures that introduce the queuing system and solutions. I believe my R&D method is helpful to solve the queuing problems of the banks and it’s also helpful to increase the satisfaction of customers and the profit of the banks. My R&D method is not only considering the factors related to the queuing system such as the waiting time, the number of customers in the waiting line but also concerned about the economic factors, the cost of setting up new service window. Therefor we can calculate the exact number of servers instead of a range of numbers. This method can calculate different numbers based on different status of a bank. Instead of a lot of limitation of some research, my method can suitable for many cases of queuing problems both in the banks and other related field. And the formula of the operation cost can be changed easily based on the actual situation of a bank. I also point out some specific improvement on the queuing problems of bank. These measurements can be also effective to optimize the queuing system and reduce the pressure of the queuing of the banks. If a bank can really implement those measurements and focus on some detail of the banks’ improvement, the satisfaction of customers and the working efficiency of staff will certainly enhance. Finally the profit of banks will increase.

Time schedule

Week 9(from 10/28/2013 to 11/03/3013)
I tried to find some books and papers that relate to my topic both in our library and from the Internet. I decided to divide my literature review task into two parts. The first part was to find out some books that related to queuing theory in our school library. The second part was to find some papers or thesis from the Internet. Then I find a book called Operation Management that related to queuing system and queuing system in school library and read some papers that related to optimize the bank’s queuing system.

Week 10(from 11/04/2013 to 11/10/2013)
This week I tried to analyze the method written in the papers included how they optimize the queuing system of banks, which method or mold they used based on the queuing theory, what the meaning of each parameters in the equation. Finally I came to know the above questions clearly based on the reading and analyzing of the method in those papers and in the book Operation Management.

Week 11(from 11/11/2013 to 11/17/2013)
I started to write my proposal based on the outline given by Pro. Sun. I wrote my proposal based on the sequence of each title given in the requirement. This week I finish the abstract, background, problem statement and the literature review part. But I did not fin out my own solutions on the queuing problems this week.

Week 12(from 11/18/2013 to 11/22/2013)
I tried my best to come up with my own ideas on the queuing problems and finally I found a way to optimize the queuing system of banks. This week I wrote up my method and the other part included methodology, expected outcome and the conclusions of my proposal.

Conclusions
Nowadays, the queuing problems of banks have become a big issue in our society. Customers always complain about the long waiting time they spend in banks. The queuing problems have resulted in the bad impression and low profit of the banks. To find a way to solve the problems and optimize the queuing system has become the most important matter of banks. The method I carry out based on the queuing theory can be a good way to optimize queuing system. It not only considers reducing the waiting time and number of customers waiting in line but also optimizing the total cost at a relatively low level. Thus, with the consideration of these two factors, the banks can finally achieve the optimization of queuing system. I also carry out some specific measurement to solve some queuing problems existing waiting in the banks. Those measures can also contribute to improve the impression and the profit of the banks. With these measure being into practice, I believe the queuing problems can be solved and the total profit of the banks can be increased.

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