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a) Write down the objective function of the Integer programming consistent with the goal of Ranchi Police department b) Write down the constraints of Integer programming consistent with the goal of Ranchi Police department

a) Write down the objective function of the Integer programming consistent with the goal of Ranchi Police department b) Write down the constraints of Integer programming consistent with the goal of Ranchi Police department

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 107P
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3. Ranchi Police department schedules police officers for 8-hour shifts. The beginning times for the shifts are 8:00 A.M, Noon (12:00 P.M), 4:00 P.M, 8:00 P.M, Midnight (12:00 A.M), and 4:00 A.M. An officer beginning a shift at one of these times works for the next 8 hours. During normal workday operations, the number of officers needed varies depending on the time of the day. The department staffing guidelines require the minimum number of officers on duty, as mentioned in the following table. Now, Ranchi Police department wants to develop an integer programming to minimize the total number of officers required who begin their work in each of the time slots, as mentioned in the following table. Time Slot Time of the day Minimum officers on duty 1 8:00 A.M-Noon (12:00 P.M) 4 Noon (12:00 P.M)-4:00 P.M 8 3 4:00 P.M-8:00 P.M 10 4 8:00 P.M-Midnight (12:00 A.M) 7 5 Midnight (12:00 A.M)-4:00 A.M 12 6 4:00 A.M-8:00 A.M a) Write down the objective function of the Integer programming consistent with the goal of Ranchi Police department b) Write down the constraints of Integer programming consistent with the goal of Ranchi Police department 2.
Transcribed Image Text:3. Ranchi Police department schedules police officers for 8-hour shifts. The beginning times for the shifts are 8:00 A.M, Noon (12:00 P.M), 4:00 P.M, 8:00 P.M, Midnight (12:00 A.M), and 4:00 A.M. An officer beginning a shift at one of these times works for the next 8 hours. During normal workday operations, the number of officers needed varies depending on the time of the day. The department staffing guidelines require the minimum number of officers on duty, as mentioned in the following table. Now, Ranchi Police department wants to develop an integer programming to minimize the total number of officers required who begin their work in each of the time slots, as mentioned in the following table. Time Slot Time of the day Minimum officers on duty 1 8:00 A.M-Noon (12:00 P.M) 4 Noon (12:00 P.M)-4:00 P.M 8 3 4:00 P.M-8:00 P.M 10 4 8:00 P.M-Midnight (12:00 A.M) 7 5 Midnight (12:00 A.M)-4:00 A.M 12 6 4:00 A.M-8:00 A.M a) Write down the objective function of the Integer programming consistent with the goal of Ranchi Police department b) Write down the constraints of Integer programming consistent with the goal of Ranchi Police department 2.
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