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San francisco police department linear programming
 

San francisco police department linear programming

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    San francisco police department linear programming San francisco police department linear programming Presentation Transcript

    • 19-06-2013 Linear programming by San francisco police dept 2 The San Francisco Police Department, also known as the SFPD , is the policedepartment of the San Francisco. San Francisco has a population of approximately 700,000 and a police force ofabout 1,900 sworn officers, of which 850 perform regular patrol duties. The SFPD currently has 10 main police stations throughout the city inaddition 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 theMunicipalTransportation 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 ormiss" schedules were close to optimal in terms of servingresidents needs. It was difficult to evaluate alternative policies for scheduling anddeploying officers. While a few precinct captains were skilled and reasonablyeffective at scheduling and deploying their patrol officers, otherswere not. Incurring huge costs by having more officers on duty thanrequired (surpluses) wastes resources, while having less thanrequired (shortages) increases response times and overburdensofficers.19-06-2013 Linear programming by San francisco police dept 3
    •  The technique deployed here is Linear Programming . Linear Programming’s goal was schedule the shifts of the officers inorder to minimize the number of officers hired subject to certainconstraints and at the same time increased their services to thecommunity. 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 continuous19-06-2013 Linear programming by San francisco police dept 4
    • 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 s2hour1hour2hour3 hour4hour5hour6hour7hour8hour9hour10hour11hour12hour13hour14hour15hour16hour17hour18hour19hour20hour21hour22hour23hour248 8 9 9 7 7 6 5 6 6 4 5 5 59 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 98 9 8 108 6 5 5 6 54 4 6 59 8 8 8 9 8 8 8 9 9 9 9 9 8 9 9 10 1012 11 10 10 9 9 8 811 11 11 10 9 9 10 99 8 896 86 55 55 56 58 8 8 99 9 9 9 9 9 8 9 9 9 8 810 1012 1110 10 10 98 811 10 11119 810 99 9 987 65 6 5 55 4668 9 9 99 8 8 8 9 9 8 8 8 8 9 99 9121211 10 10107 811 11 10 11991098 9 997 85 6 5 64 45 68 8 9 898 8 9 8 88 9 9 88 810 911111111 1097 711 11 10 119910979 897 75 5 6 65 55 68 9 9 889 8 9 8 88 9 8 99 89 911 121111998 811 11 11 1198101087 886 75 6 5 54 46 58 9 8 88 9 8 8 9 989 9 88 910 1012 1110 119107 711 10 10 11991010sanfransico police patrolMonday Tuesday Wednesday Thursday Friday Saturday Sunday19-06-2013 Linear programming by San francisco police dept 5
    • HOUR 1 HOUR 2 HOUR3 HOUR 4s1 s2 s1 s2 s1 s2 s1 s2Monday 8 8 9 9 7 7 6 6Tuesday 8 9 8 10 8 6 5 6Wednesday 9 8 8 9 6 8 5 6Thursday 9 9 9 8 7 6 6 5Friday 8 9 9 9 7 8 5 5Saturday 7 9 8 9 7 7 5 6Sunday 8 7 8 8 6 7 6 519-06-2013 Linear programming by San francisco police dept 6
    • 19-06-2013 Linear programming by San francisco police dept 7DAYS Number ofOfficers onDutyNumber ofOfficers onDutyMonday 21 6+0+7+2+6Tuesday 19 4+6+0+7+2Wednesday 19 2+4+6+0+7Thursday 18 6+2+4+6+0Friday 20 2+6+2+4+6Saturday 21 7+2+6+2+4Sunday 17 0+7+2+6+2DAYS Number ofOfficersBeginning workon this dayMonday 6Tuesday 4Wednesday 2Thursday 6Friday 2Saturday 7Sunday 0SAMPLETABLE
    •  Phase 1 — ForecastingRequirement of data on number of calls, thepercentage or kinds of calls in each priority typerequiring two officers, the percentage mix of one-and two-officer cars deployed, and the time spentper call, a "consumed time" and officer need iscalculated for each hour of the week, and thisbecomes the basic building block for the forecast.19-06-2013 Linear programming by San francisco police dept 8
    • Phase 2 — Scheduling:A specially developed integer search procedure was used to find theschedule that best fits the hourly requirements for the number of officersavailable.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 numberof officers starting at each time. If N start times can be utilized, then thecombination of 168 times (24 hours and seven days) taken N at a timerepresents 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
    •  Phase 3 — FineTuningAfter the generation of the initial schedules, the user used fine-tuningsubsystem in an interactive mode.This subsystem measured theimpact on schedule quality (that is, shortages and maximum singleshortage) 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 nonpatrol duty(4) Open a new shift starting time or close an old one(5) Increase or decrease the percentage of one-officer cars.19-06-2013 Linear programming by San francisco police dept 10
    •  The system produced approximately a 50% reduction inshortages and surpluses. The new system provided annual savings of $11 million, anannual $3 million increase in traffic citation revenues, and a20% improvement in response times. Since the installation of PPSS, the computation time for the IHportion of the model has decreased from approximately 45minutes for a 100-officer problem to usually less than 15minutes. A cost benefit analysis of the scheduling aspects of PPSSshows a one-time cost of $50,000 and a benefit of $5.2 millionper year or a payback period of 3.5 days.19-06-2013 Linear programming by San francisco police dept 11
    •  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 accessedon 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 on16th 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 accessedon 16th march at 5:00pm.19-06-2013 Linear programming by San francisco police dept 12
    •  Presented by:19-06-2013 Linear programming by San francisco police dept 13GROUP NO: 7Utkarsh Garg 121Sangam Lalsivaraju 138Sugandha Arora 140Dhruv Mahajan 141Nitish Dubey 177