BUS 370 QUEUEING CASE 1. Cases for BUS 370 are take-home, open-book, open-notes, open-library, etc. You may consult any written materials other than another (past or present) team's case or work papers. Please do not discuss any aspect of the case with anyone except your partners, my staff, or me. To collaborate or seek other assistance is a breach of academic integrity and is viewed as a serious offense by the University. 2. Please submit one solution package per team with its answers neatly worked out in detail. To earn partial credit, you must show all work (including Excel input). 3. For each question requiring a new add-in run, please submit the following: a. A printout of the input data. b. A printout of all reports that support your answers. Please label each add-in run with the corresponding question number(s) and insert comments on them to indicate the sources of your answers. There is no need to submit printouts that are not supportive of your final answers (e.g., runs that bombed, runs with incorrect input, etc.). 4. Please be neat. Sloppiness, disorganization, spelling, etc. may, in the aggregate, result in a point reduction of up to the equivalent of one letter grade. 5. Please submit your solution package for this case via email on the due date. In fairness to the teams that submit their solution package on time, unexcused lateness will result in a loss of one letter grade per late-day or fraction thereof. 6. Some very important advice regarding teamwork: a. Past experience shows that team effectiveness and efficiency are greatly enhanced if partners work independently first and then convene to share individual results. Please proceed in this fashion. b. It is critically important to maintain an atmosphere that fosters open, honest communication among team members. So, please establish clear expectations for individual performance on each case assignment and always discuss deviations in individual performance as work progresses. 7. GOOD LUCK AND HAPPY LEARNING! College Credit Union College Credit Union (CCU) was created several years ago in order to provide the students and alumni of a local college with convenient banking options complete with school-related financial services that larger retail banks in the area did not offer. Due to increasing enrollment and a growing body of alumni who use CCU's services, more and more customers are visiting the bank. Recognizing this trend, Adrien, the CCU's Vice President of Operations, has decided to model the system in hopes that he can make informed resource-allocation decisions to support the increasing demand for CCU's teller services. Every weekday, customers arrive randomly during the 3:00 P.M. to 4:00 P.M. peak hour (right before the bank closes) at an average rate of one person every 40 seconds. Since CCU's inception, Adrien has collected historical service-time data during this one-hour period, and has determined that a teller spends an average of 4 minutes with each customer, no matter what weekday it is. The queuing model assumptions of Poisson arrivals, exponential service times, and infinite customerpopulation size were evaluated and found to be appropriate for use in modeling CCU's teller operations. Adrien is worried that, if the customer base grows too fast, the tellers will frequently become overloaded. This is especially worrisome, since CCU lacks a significant number of ATM's around the city where people tend to make night deposits and withdrawals. While Adrien is not meeting these two service criteria at present, he is committed to having a high level of customer service and wants the tellers to be able to service at least 90% of arriving customers immediately, (i.e., without any waiting in the queue). He also, wants no more than 1% of the customers to find the waiting area full because there is no other appropriate space in which to wait. With the current configuration, the bank has enough space to accommodate 5 waiting customers in a single line, which feeds all of the tellers on a first-come-first-served basis. Some tellers are more senior than others, but on average, the cost of a teller is $17 per hour. Adrien has hired you as a consultant to conduct a separate analysis to complement his own work. Please help Adrien address the congestion issues facing CCU by using your understanding of queuing systems to answer the following questions: Part A. Please use your understanding of the Poisson and negative exponential probability distributions to address the following: 1. What is the probability that no customers enter the teller system during a 3-minute period between 3:00 P.M. and 4:00 P.M.? Five customers? More than five customers? 2. What is the probability that a bank teller spends less than 4 minutes with a customer? Between 3 and 5 minutes? More than 6 minutes? 3. What is the probability that a teller spends at least 4 more minutes with a customer who has already been in service for 4 minutes? Part B. Please use Excel (as appropriate) and your understanding of queuing models to address the following questions, all of which assume that CCU remains with its current waiting-permitted teller system: 1. Please conduct a sensitivity analysis to determine the minimum number of tellers required to meet the 90% immediate-service goal? Does this level of staffing meet Adrien's 1% blocking probability criterion? Please explain how you arrived at your answer. 2. Currently, CCU has only enough space in the existing bank to accommodate a maximum of 7 tellers, which is not enough to house the number of tellers that you determined were required in question B.1. So, you decide to examine two scenarios to help CCU with its current predicament. The bank can transfer a loan officer to another bank location and use the officer's space to add up to 7 new windows to the bank of existing teller windows (Option 1). Alternatively, it can create an ATM center across the street to meet the increasing demand (Option 2). Under Option 2, assume that the number of ATM's is equal to the number of bank tellers, that there are also only 5 waiting spaces for ATM customers, that the ATM service time distribution is identical to that of the tellers, and that arriving customers split evenly between the ATM and teller server groups. The incremental cost per server is the same for both expansion options. a. Which option should CCU pursue in order to meet both the 90% immediate-service and the 1% blocking criteria? Please explain how you arrived at your answer. b. What does this analysis tell you, in general, about the efficiency of larger server groups? Please explain. 3. Now, suppose that Adrien conservatively feels that a customer who is blocked from entering the system will find a new bank and close their account(s). Adrien knows that the vast majority of customers who enter the branch seek to deposit money rather than to withdraw it because of the broad implementation of the \"cash back\" option available at every grocery store in the area. Since the bank makes a profit on deposits by lending that money out in the form of higher interest rate loans, Adrien estimates the average present value of lost earnings from each blocked customer to be $300. He also feels that the loss-of-goodwill penalty cost for customers waiting in the queue is about $30/hour. Please recall that the cost of a teller is $17 per hour. a. Under Option 1 in question B.2., what is the optimal number of tellers required to minimize the expected total cost per hour? Please conduct a sensitivity analysis to determine the new optimal staffing-level that is based on minimizing expected total hourly cost rather than meeting the two service-level criteria. b. What percentage of the customers will have to wait for service? What percentage will be blocked? Please compare these numbers to the comparable percentages found in question B.1., and explain why they differ the way they do. 4. Now suppose that Adrien has decided to evaluate the attractiveness of encouraging higher teller productivity by increasing hourly wages by $1.00 for an average teller hourly service rate of 16 and by $1.00 more for a rate 17 as provided below: Average Teller Service Rate/Hour 15 16 17 Average Hourly Cost/Teller $17.00 $18.00 $19.00 Please note that the cost of a customer being blocked is still $300 and the loss-of-goodwill penalty cost for customers waiting in the queue is $30/hour. a. Please conduct a sensitivity analysis two more times to determine the optimal average teller service rate/hour to minimize the expected total cost/ hour from among the three possibilities (15, 16, and 17), and complete the table below summarizing the results of your search process. (Please note that the optimal number of tellers may change as you change the service rate per hour.) Average Teller Service Rate/Hour 15 16 17 Average Hourly Cost/Teller $17.00 $18.00 $19.00 Expected Total Cost/Hour Optimal # of Tellers b. Please explain the underlying queuing-resource logic for the form of this discrete, threepoint, expected total cost function. 5. Recall that the customer arrival rate of 90 calls per hour is just for the 3:00 P.M. to 4:00 P.M. time period during each weekday. Not surprisingly, the average arrival rate and the average service rate of incoming customers are expected to change from hour to hour over the course of the workday. Describe how your queuing analysis in question B.3. could be expanded to develop a teller staffing plan that would enable CCU to provide different levels of staffing for the branch's teller system at different times during the workday from 8:00 A.M. to 4:00 P.M. Please indicate the information that you would need to develop this staffing plan and how you would proceed in developing a work schedule for the full eight-hour workday