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Decision Making Under Uncertainty Homework 3 Summer 2014




Question;1. I have put the outputs in a structure that answer the questions (shown the attached spreadsheet). We are looking at the yellow highlighted parts. If you ?deviate? from that structure (which is acceptable), you still need to highlight the key answers and outputs.2. You should be using the Q.xls worksheet provided in the Chapter 13 content for these questions. (You may attach necessary copies into your Answer Sheet on separate tabs.)3. Points awarded:a. Q1 = 25 pointsb. Q2 = 20 pointsPROBLEMS1. A IT support department is trying to get a sense of how many support technicians it should hire, in order to support software user groups that range in size from small (15 users) to large (300 users). As a rough cut, let us assume the company thinks of this as a steady state finite population queuing model. Each user generates a question or problem every two weeks, on average, about which they would like to get technical support. Hence, the average arrival rate of need for support is 0.1 perworkday per user in the population. The support technicians spend can only service 8 users per workday. The performance metric of interest to the company is the proportion of users at any given time who are waiting for support (i.e., have a question or problem that has not yet been resolved). That is Lq / # of users in population.a. Calculate the following intermediate values: (5 points)? Utilization? P(0), empty queue? Lq? L? Wq? W? Probability that a user waits? Proportion of the population that is waiting for serviceb. Use a 2D data table to show how this performance metric depends on (5 points)? # of software users, ranging from 5 to 300 in steps of 51 # of support technicians, ranging from 1 to 10 in steps of 1.(Vary # of users by row, so the table is 60 X 10, not 10 X 60.)c. Create a plot (scatter plot, connecting dots with smooth curves) of the performance metric vs. # of users, with separate lines for 1 support technicians, 2,.., up to 6 technicians. (5 points)d. What if you were limited to 4 support technicians with a user base of 200 ? To what level would you have to increase your daily support rate in order to reduce the proportion of waiting customersbelow 10%? (5 points)e. Give two good reasons why this type of steady state analysis may not be very realistic. (5 points)?2. This problem is similar to the first, but pertains to a finite queue and adds cost parameters. Suppose an organization receives 30 jobs per hour that its servers can resolve in an average of 10 minutes, with service times being exponentially distributed. Suppose further that servers cost $20 per hour, and to discourage solutions with arbitrary long potential queues, the organization assesses itself a penalty of $1 per hour per maximum queue size allowed. The cost per hour of customer waiting is low, at $2 per hour since these jobs are not urgent, but the cost of having a customer balk is high ($100).a. Calculate the following intermediate values: (5 points)? Utilization? P(0)? Lq? L? Wq? W? Probability that a customer waits? Probability that a customer balksb. Create a data table showing how total cost depends on (5 points)? the # of servers (from 1 to 10 in steps of 1, defining tables? columns) and? the # of queue positions (0 to 100 in steps of 1). Use conditional highlighting to help make the table easy to readc. Identify the cost minimizing combination (#) of servers and queue positions (5 points)d. As well as the associated total average cost per hour. (5 points)


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