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A Police station has the following minimum requirements for policemen on duty for each 4-hour period during the day: 0.00 - 4.00 15 4.00 8.00 25 8.00 - 12.00 45 12.00 - 16.00 90 16.00 - 20.00 20.00 – 24.00 30 25 Each policeman comes on duty at 0.00, 4.00, 8.00, 12.00, 16.00 or 20.00 hrs and works for eight consecutive hours. • Formulate the problem of finding a duty schedule that minimises the total number of policemen required. Introduce required decision variables and corresponding constraints. • Implement and solve the problem formulation in Python. (Please include your code to the report). • In your problem formulation, justify the choice of variable types you made (integer variables vs con- tinuous). If your problem formulation requires integer decision variables, discuss whether integrality requirement can be relaxed. • Suppose next that every time period when the total number of policemen exceeds the minimum threshold value, there is a penalty. Specifically, there is a penalty of 2 for every policeman above the minimum threshold in each time period. Formulate the problem of finding a valid duty schedule that mimimizes the total penalty.

A Police station has the following minimum requirements for policemen on duty for each 4-hour period during the day: 0.00 - 4.00 15 4.00 8.00 25 8.00 - 12.00 45 12.00 - 16.00 90 16.00 - 20.00 20.00 – 24.00 30 25 Each policeman comes on duty at 0.00, 4.00, 8.00, 12.00, 16.00 or 20.00 hrs and works for eight consecutive hours. • Formulate the problem of finding a duty schedule that minimises the total number of policemen required. Introduce required decision variables and corresponding constraints. • Implement and solve the problem formulation in Python. (Please include your code to the report). • In your problem formulation, justify the choice of variable types you made (integer variables vs con- tinuous). If your problem formulation requires integer decision variables, discuss whether integrality requirement can be relaxed. • Suppose next that every time period when the total number of policemen exceeds the minimum threshold value, there is a penalty. Specifically, there is a penalty of 2 for every policeman above the minimum threshold in each time period. Formulate the problem of finding a valid duty schedule that mimimizes the total penalty.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A Police station has the following minimum requirements for policemen on duty for each 4-hour period during the day: 0.00 - 4.00 15 4.00 8.00 25 8.00 - 12.00 45 12.00 - 16.00 90 16.00 - 20.00 20.00 – 24.00 30 25 Each policeman comes on duty at 0.00, 4.00, 8.00, 12.00, 16.00 or 20.00 hrs and works for eight consecutive hours. • Formulate the problem of finding a duty schedule that minimises the total number of policemen required. Introduce required decision variables and corresponding constraints. • Implement and solve the problem formulation in Python. (Please include your code to the report). • In your problem formulation, justify the choice of variable types you made (integer variables vs con- tinuous). If your problem formulation requires integer decision variables, discuss whether integrality requirement can be relaxed. • Suppose next that every time period when the total number of policemen exceeds the minimum threshold value, there is a penalty. Specifically, there is a penalty of 2 for every policeman above the minimum threshold in each time period. Formulate the problem of finding a valid duty schedule that mimimizes the total penalty.
Transcribed Image Text:A Police station has the following minimum requirements for policemen on duty for each 4-hour period during the day: 0.00 - 4.00 15 4.00 8.00 25 8.00 - 12.00 45 12.00 - 16.00 90 16.00 - 20.00 20.00 – 24.00 30 25 Each policeman comes on duty at 0.00, 4.00, 8.00, 12.00, 16.00 or 20.00 hrs and works for eight consecutive hours. • Formulate the problem of finding a duty schedule that minimises the total number of policemen required. Introduce required decision variables and corresponding constraints. • Implement and solve the problem formulation in Python. (Please include your code to the report). • In your problem formulation, justify the choice of variable types you made (integer variables vs con- tinuous). If your problem formulation requires integer decision variables, discuss whether integrality requirement can be relaxed. • Suppose next that every time period when the total number of policemen exceeds the minimum threshold value, there is a penalty. Specifically, there is a penalty of 2 for every policeman above the minimum threshold in each time period. Formulate the problem of finding a valid duty schedule that mimimizes the total penalty.
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