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Problem Title: Bank Service Problem

  Year: 2013      
  Student Level: High School      
  Source: HiMCM      
  Commentary: Yes (1)      
  Student Papers: Yes (5)      

The bank manager is trying to improve customer satisfaction by offering better service. Management wants the average customer to wait less than 2 minutes for service and the average length of the queue (length of the waiting line) to be 2 persons or fewer. The bank estimates it serves about 150 customers per day. The existing arrival and service times are given in the tables below.

Time between arrival (min.) Probability
0 0.10
1 0.15
2 0.10
3 0.35
4 0.25
5 0.05

Table 1: Arrival times

Service Time (min.) Probability
1 0.25
2 0.20
3 0.40
4 0.15

Table 2: Service times

(1) Build a mathematical model of the system.

(2) Determine if the current customer service is satisfactory according to the manager guidelines. If not, determine, through modeling, the minimal changes for servers required to accomplish the manager's goal.

(3) In addition to the contest's format, prepare a short 1-2 page non-technical letter to the bank's management with your final recommendations.


Consortium Article

  Student Papers      

Team 3956: Queueing In A Bank

Shanghai Experimental School, Shanghai, China


Team 4100: Bank Service Problem

University High School, Irvine, CA


Team 4342: Bank Service Problem

NC School of Science and Mathematics, Durham, NC


Team 3976: Bank Service Problem

East Lansing High School, East Lansing, MI


Team 4093: Bank Service Problem

University High School, Irvine, CA