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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 Municipal Transportation Authority, and the Public Utilities Commission.

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.

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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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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

hour1

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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

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10

sanfransico police patrol

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

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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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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

SAMPLE TABLE

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.

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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).

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Phase 3 — Fine Tuning 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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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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1.http://www.davidson.edu/academic/economics/foley/Taylor%20and%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.

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Presented by:

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GROUP NO: 7 Utkarsh Garg 121 Sangam Lalsivaraju 138 Sugandha Arora 140 Dhruv Mahajan 141 Nitish Dubey 177