P3. Austin Police Department The city of Austin is considering expanding its numbers to reduce the response times to 911 calls. To keep things simple, we will focus on three districts in the city: Central, South, and North. The three districts vary in terms of the rate at which they generate calls to 911 and in the number of patrol cars that are currently assigned to them: Central South North 911 calls per hour 11 14.5 5 Current patrol cars 8 10 4 For all districts, the standard deviation of the interarrival times is identical to the average time between arrivals (i.e., Ca = 1; this is often the case when customer arrivals are generated by a large number of independently-arriving customers). The city manager would like your help in deciding how to allocate three additional patrol cars among these three districts. In the Excel file titled APD Model and Data.xls, there are three worksheets: Service Time Data. This worksheet contains data on 100 calls to 911 that required a patrol car to respond. For each call, the data includes the date and hour that the call was received, the duration of service from the patrol car (including the time to travel to and from the incident), and the type of call (Vehicle Collision, Burglary, Public Intoxication, etc.). The calls were collected across all three districts, and the distribution of service time is independent of the district from which the call originated. Cells C103 and C104 calculate the mean and standard deviation of these service times. APD Model. This worsheet contains a queuing model that predicts the waiting time in each district based on the number of patrol cars assigned there. For any allocation of patrol cars across districts in cells B27:D27 (with car capacity exceeding demand in every district), the model will calculate the average waiting time in each district, the average waiting time in the city, and the maximum waiting time in any district. Specifically, rows 1-6 contain the basic data on service times, drawing from the average and standard deviation that is estimated in the Service Time Data worksheet. Rows 10-13 focus on the Central District; 15-18 focus on the South; and 20-23 focus on the North. Row 27 allows you to specify a number of patrol cars for each district. Given this assignment, row 28 draws from the calculations above to tell us the average waiting time in each district and rows 29 and 30 tells us the overall average waiting time in the city, and the maximum average waiting time among the three districts. Service Time Data-DAreassigned. This worksheet contains a modified version of Service Time Data's data. You will find a detailed explanation of this worksheet in part (c). (a) The calculation in Cell B29 for the average waiting time across the city is: Avg Wait time in Austin 11calls hr Scalls hr x Wait Time South + hour Ex Wait Time North 11 calls 14.5calls 5calls hr hr hour An alternative approach to calculating the average waiting time would be: Wait Time Central + Wait Time South + Wait Time North Alt. Avg Wait time in Austin = 3 Which of these provides a better measure of the waiting time that a randomly chosen 911 caller in the city of Austin experiences? Why? ** Wait Time Central + 14.5calls (b) How would you recommend the three additional patrol cars be assigned? Why? (Hint: Note that there may be more than one way to evaluate response-time performance. And an allocation that optimizes one objective may perform relatively poorly according to another objective.] (c) In response to a proposal that the city make greater use of social workers for 911 calls for Domestic Arguments (call type DA), the city manager has asked for some additional analysis. It is expected that police will continue to respond to these calls, but will spend only 40 minutes on them. DA calls often require much more time than most other calls, partly because police are not well prepared for these situations. In Service Time Data-DAreassigned, the service times for the DA calls have all been replaced with 40 minutes. All 10 calls that were type DA are highlighted in yellow. Using the updated average and standard deviation for service times (cells C103:C104), what would be the average waiting time in each district with the current allocation of patrol cars, i.e., 8 in Central, 10 in South, and 4 in North? What does this tell you about the potential impact of finding ways to eliminate or truncate service activities that have unusually long durations? P3. Austin Police Department The city of Austin is considering expanding its numbers to reduce the response times to 911 calls. To keep things simple, we will focus on three districts in the city: Central, South, and North. The three districts vary in terms of the rate at which they generate calls to 911 and in the number of patrol cars that are currently assigned to them: Central South North 911 calls per hour 11 14.5 5 Current patrol cars 8 10 4 For all districts, the standard deviation of the interarrival times is identical to the average time between arrivals (i.e., Ca = 1; this is often the case when customer arrivals are generated by a large number of independently-arriving customers). The city manager would like your help in deciding how to allocate three additional patrol cars among these three districts. In the Excel file titled APD Model and Data.xls, there are three worksheets: Service Time Data. This worksheet contains data on 100 calls to 911 that required a patrol car to respond. For each call, the data includes the date and hour that the call was received, the duration of service from the patrol car (including the time to travel to and from the incident), and the type of call (Vehicle Collision, Burglary, Public Intoxication, etc.). The calls were collected across all three districts, and the distribution of service time is independent of the district from which the call originated. Cells C103 and C104 calculate the mean and standard deviation of these service times. APD Model. This worsheet contains a queuing model that predicts the waiting time in each district based on the number of patrol cars assigned there. For any allocation of patrol cars across districts in cells B27:D27 (with car capacity exceeding demand in every district), the model will calculate the average waiting time in each district, the average waiting time in the city, and the maximum waiting time in any district. Specifically, rows 1-6 contain the basic data on service times, drawing from the average and standard deviation that is estimated in the Service Time Data worksheet. Rows 10-13 focus on the Central District; 15-18 focus on the South; and 20-23 focus on the North. Row 27 allows you to specify a number of patrol cars for each district. Given this assignment, row 28 draws from the calculations above to tell us the average waiting time in each district and rows 29 and 30 tells us the overall average waiting time in the city, and the maximum average waiting time among the three districts. Service Time Data-DAreassigned. This worksheet contains a modified version of Service Time Data's data. You will find a detailed explanation of this worksheet in part (c). (a) The calculation in Cell B29 for the average waiting time across the city is: Avg Wait time in Austin 11calls hr Scalls hr x Wait Time South + hour Ex Wait Time North 11 calls 14.5calls 5calls hr hr hour An alternative approach to calculating the average waiting time would be: Wait Time Central + Wait Time South + Wait Time North Alt. Avg Wait time in Austin = 3 Which of these provides a better measure of the waiting time that a randomly chosen 911 caller in the city of Austin experiences? Why? ** Wait Time Central + 14.5calls (b) How would you recommend the three additional patrol cars be assigned? Why? (Hint: Note that there may be more than one way to evaluate response-time performance. And an allocation that optimizes one objective may perform relatively poorly according to another objective.] (c) In response to a proposal that the city make greater use of social workers for 911 calls for Domestic Arguments (call type DA), the city manager has asked for some additional analysis. It is expected that police will continue to respond to these calls, but will spend only 40 minutes on them. DA calls often require much more time than most other calls, partly because police are not well prepared for these situations. In Service Time Data-DAreassigned, the service times for the DA calls have all been replaced with 40 minutes. All 10 calls that were type DA are highlighted in yellow. Using the updated average and standard deviation for service times (cells C103:C104), what would be the average waiting time in each district with the current allocation of patrol cars, i.e., 8 in Central, 10 in South, and 4 in North? What does this tell you about the potential impact of finding ways to eliminate or truncate service activities that have unusually long durations