Q1. During the previous presidential elections in the United States, very long wait times have been witnessed at precincts (voting stations) in states that ultimately decided the election (for example, Florida in 2000, Ohio in 2004). In New Jersey, as well, some voters complained about the long lines in some precincts, with most complaints coming from a particular precinct in Hoboken, NJ. The average number of voters arriving at this precinct was 35 per hour and the arrival of voters was random, with CVa=1. The officials had deployed 1 voting machine in this precinct. Service times were random as well, with CVp=1; each voter spent on average 100 seconds in the voting booth (this is the time needed to cast her/his vote using a voting machine).

(a) Suppose that the disabled citizens are prioritized over the others. If the percentage of the disabled voters in this precinct is 5% of the total number of voters, how long do the citizens who are not prioritized wait before voting on average?

(b) If the average time a voter spends in the voting booth increases to 4 minutes, what would be the utilization rate of a stable queuing system with the minimum number of voting machines?

(c) Still assume that the average time each voter spends is 4 minutes. If each voting machine costs $100/hr to operate, and the cost of waiting is assessed at $2/min, what would be the optimum number of voting machines that should be utilized?

Q2. John Smith needs to decide where to get a haircut. He decides to pick one based on how much time he has to take off from work. He has narrowed the choice down to two local hair salons -Large Hair Salon (LHS) and Small Hair Cutters (SHC).  During busy periods, a new customer walks into LHS every 15 minutes (with a standard deviation of 15 minutes).  At SHC, a customer walks in every hour (with a standard deviation of 1 hour). LHS has a staff of 4 barbers, while SHC has 1 barber. A typical service time at either salon lasts 30 minutes (with a standard deviation of 30 minutes).

(a) If John's office is at a 10-minute walking distance from both hair salons, how much time (on average) does John need to take off from work to get a hair-cut and get back to work?

(b) Consider the scenario where LHS buys out SHC, closes SHC's operations and serve all customers, including existing SHC customers, at the LHS location only. Assuming that the previous traffic of SHC customers now flows to the LHS location (with the same coefficient of variation), and that SHC's personnel also joins LHS what is new average wait time?

Q3. Consider the NYPD case. Assume, the managers decide to devise a performance metric that considers the i) waiting time before a patrol car is dispatched, and ii) the size of the precinct at the same time. More specifically, they would like to minimize the sum of the weighted time in queue as the metric for allocation, wherein the size of the precincts are used as weights.

(a) Set-up a Solver model to find the best way to allocate 20 cars across 6 precincts, solve the model to find the optimum allocation, and send the Excel file you use to solve the problem by e-mail. (Assume all calls are responded to in a FCFS manner.)

(b) Repeat part (a), but this time, assume the emergency (i.e., high-priority) calls are assigned patrol cars with priority. Also assume that the waiting times for high-priority calls are 300 times as important as the regular calls.