2. 19-06-2013 Linear programming by San francisco police dept 2
 The San Francisco Police Department, also known as the SFPD , is the police
department of the San Francisco.
 San Francisco has a population of approximately 700,000 and a police force of
about 1,900 sworn officers, of which 850 perform regular patrol duties.
 The SFPD currently has 10 main police stations throughout the city in
addition to a number of police substations.
1.Metro Division: consists of 5 stations.
2.Golden Gate Division: consists of 5 stations.
3.Sub Station and Special Division: consists of 2 stations.
 The Chief of SFPD works with six deputy chiefs directing the four bureaus:
Administration, Airport, Field Operations, and Investigations, as well as the
MunicipalTransportation Authority, and the Public Utilities Commission.

3.  SFPD operated with schedules on a hit & trial method.
 With manual methods, it was impossible to know if the "hit or
miss" schedules were close to optimal in terms of serving
residents' needs.
 It was difficult to evaluate alternative policies for scheduling and
deploying officers.
 While a few precinct captains were skilled and reasonably
effective at scheduling and deploying their patrol officers, others
were not.
 Incurring huge costs by having more officers on duty than
required (surpluses) wastes resources, while having less than
required (shortages) increases response times and overburdens
officers.
19-06-2013 Linear programming by San francisco police dept 3

4.  The technique deployed here is Linear Programming .
 Linear Programming’s goal was schedule the shifts of the officers in
order to minimize the number of officers hired subject to certain
constraints and at the same time increased their services to the
community.
 Mathematical procedure for optimally allocating scarce resources
 Objective function:
 Expression for performance measure
 Profit, time duration, number of worker,
 Function to be optimized
 Values for decision variables
 Constraints:
 Expressions for physical restrictions on system
 Limited resources available
 All relationships linear
 Effects of a single variable are proportional
 Interactions among variables are additive
 Variables must be continuous
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5. s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2 s1 s2
hour
1
hour
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hour3 hour
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hour
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hour
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hour
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hour
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hour
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hour
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hour
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hour
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hour
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hour
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hour
15
hour
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hour
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hour
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hour
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hour
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hour
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hour
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hour
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hour
24
8 8 9 9 7 7 6 5 6 6 4 5 5 5
9 9 8 8 9 9 9 8 8 9 9 8 8 8 9 9 10 10 12 12 11 10 10 9 8 7 10 10 11 10 9 8 9 9
8 9 8 10
8 6 5 5 6 5
4 4 6 5
9 8 8 8 9 8 8 8 9 9 9 9 9 8 9 9 10 10
12 11 10 10 9 9 8 8
11 11 11 10 9 9 10 9
9 8 8
9
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9 9 9 9 9 9 8 9 9 9 8 8
10 10
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9 8 8 8 9 9 8 8 8 8 9 9
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5 6 5 6
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sanfransico police patrol
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
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6. HOUR 1 HOUR 2 HOUR3 HOUR 4
s1 s2 s1 s2 s1 s2 s1 s2
Monday 8 8 9 9 7 7 6 6
Tuesday 8 9 8 10 8 6 5 6
Wednesday 9 8 8 9 6 8 5 6
Thursday 9 9 9 8 7 6 6 5
Friday 8 9 9 9 7 8 5 5
Saturday 7 9 8 9 7 7 5 6
Sunday 8 7 8 8 6 7 6 5
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7. 19-06-2013 Linear programming by San francisco police dept 7
DAYS Number of
Officers on
Duty
Number of
Officers on
Duty
Monday 21 6+0+7+2+6
Tuesday 19 4+6+0+7+2
Wednesday 19 2+4+6+0+7
Thursday 18 6+2+4+6+0
Friday 20 2+6+2+4+6
Saturday 21 7+2+6+2+4
Sunday 17 0+7+2+6+2
DAYS Number of
Officers
Beginning work
on this day
Monday 6
Tuesday 4
Wednesday 2
Thursday 6
Friday 2
Saturday 7
Sunday 0
SAMPLETABLE

8.  Phase 1 — Forecasting
Requirement of data on number of calls, the
percentage or kinds of calls in each priority type
requiring two officers, the percentage mix of one-
and two-officer cars deployed, and the time spent
per call, a "consumed time" and officer need is
calculated for each hour of the week, and this
becomes the basic building block for the forecast.
19-06-2013 Linear programming by San francisco police dept 8

9. Phase 2 — Scheduling:
A specially developed integer search procedure was used to find the
schedule that best fits the hourly requirements for the number of officers
available.
The model has several constraint sets:
(1) Limitation on the number of officers available.
(2) Minimum staffing requirements for all hours of the day.
(3) Minimum staffing requirements for all districts of the day.
E.g. the decision variables are the shift start times and the integer number
of officers starting at each time. If N start times can be utilized, then the
combination of 168 times (24 hours and seven days) taken N at a time
represents the number of possible start time patterns.
Hence, Comparisons were made for small (40 to 50 officers), medium
(60 to 90 officers), and large precincts (100 to 120 officers).
19-06-2013 Linear programming by San francisco police dept 9

10.  Phase 3 — FineTuning
After the generation of the initial schedules, the user used fine-tuning
subsystem in an interactive mode.This subsystem measured the
impact on schedule quality (that is, shortages and maximum single
shortage) if a change were made to:-
(1) Add an officer to any schedule
(2) Delete an officer from any schedule
(3) Modify the number of officers on station duty or any other non
patrol duty
(4) Open a new shift starting time or close an old one
(5) Increase or decrease the percentage of one-officer cars.
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11.  The system produced approximately a 50% reduction in
shortages and surpluses.
 The new system provided annual savings of $11 million, an
annual $3 million increase in traffic citation revenues, and a
20% improvement in response times.
 Since the installation of PPSS, the computation time for the IH
portion of the model has decreased from approximately 45
minutes for a 100-officer problem to usually less than 15
minutes.
 A cost benefit analysis of the scheduling aspects of PPSS
shows a one-time cost of $50,000 and a benefit of $5.2 million
per year or a payback period of 3.5 days.
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12.  1.http://www.davidson.edu/academic/economics/foley/Taylor%20an
d%20Huxley%20(1989).pdf accessed on 15th march at 4:00pm.
 2.http://faculty.ksu.edu.sa/72966/Documents/chap12.pdf accessed
on 15th march at 4:30pm.
 3.http://www.ns2.syraa.com/blogs/695/What-is-Operations-
Research-.html accessed on 15th march at 5:00pm.
 4.http://www.purplemath.com/modules/linprog.htm accessed on
16th march at 4:00pm.
 5.http://www.coursehero.com/file/6905276/1-An-Introduction-to-
Model-Building/ accessed on 16th march at 4:30pm.
 6.http://ebook.its-about-
time.com/assets/book_files/mc_3a/pdf/se/c4/ch4_4-1.pdf accessed
on 16th march at 5:00pm.
19-06-2013 Linear programming by San francisco police dept 12

13.  Presented by:
19-06-2013 Linear programming by San francisco police dept 13
GROUP NO: 7
Utkarsh Garg 121
Sangam Lalsivaraju 138
Sugandha Arora 140
Dhruv Mahajan 141
Nitish Dubey 177