Optimal Deployment Of Community Personnel

8/14/2019 Optimal Deployment Of Community Personnel

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Jomar Fajardo RabajanteMathematics Division, [email protected]


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Minimize the emergency response time

Increase security coverage and visibility

Reduce personnel fatigue caused by rationalizedshift-schedule

Determine the best possible number of policeofficers to be allocated given the budget constraint


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Maximize SecurityCoverage and

Visibility; Minimize

Response Time

MinimizeCost/Numberof Policemen

MaximumCoverageLocation

Problem

Binary LinearProgram

NetworkClustering

(Districting)

Minimum-sizeDominating

Sets

GOAL PROGRAM

Scheduling Algorithm


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Rt Centroid

Demandnode

Atoms determined by a circular region with radius R


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I is the set of buildings or places tobe covered

J is the set of potential policepost/patrol area centroids

Rt is the desired service distancebased on the desired response time

d ij is the shortest distance from nodei I toj J w i is the weight of nodei I Pm is the number of police officers to

be spatially located Zi is the set of police post/patrol area

centroids that are eligible to providecover to demand nodei IZi = {j J | d ij Rt}


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Av is the area of the district in consideration Ad is the desired area of an atom Pf is the number of police officers in

.predetermined fixed posts (such as guards at

.the gate) PT is the total number of police officers in the

.community k is the number of districts formed Pa is the number of additional police officers

.such as mobile unit drivers, desk officer, team.leader, etc.

S is the number of shifts per day


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AT is the total area of the whole community that needs police coverage Bu is the total allocated budget for the salaries and wages of police officers Bs is the amount of salaries and wages of a police officer

PT is the total number of police officers in the community S is the number of shifts per day Pa is the number of additional police officers such as mobile unit drivers, desk

.officer, team leader, etc. Pf is the number of police officers in predetermined fixed posts (such as

guards at the gate) Av is the area of the district in consideration


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ASSUMPTIONS: Police personnel must work eight hours a day and, if possible,

with two consecutive vacations per week; The schedule must be rotational for 24 hours and 7 days a

week; A police officer must have at least 16 hours rest before

returning back to work; and Equity among personnel must be satisfied (e.g. equally getting

opportunity of having vacation during Saturdays and Sundays).

Least common multiple of the number of shift per day and thenumber of days per week or LCM(4,7) = 28 days The schedule will be created for 28 days or four weeks


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1st Week Mon Tue Wed Thu Fri Sat SunShift 1Shift 2Shift 3Vacation T1 T1

Generated rotational schedule for four weeks

2nd WeekShift 1Shift 2Shift 3Vacation T2 T23rd WeekShift 1Shift 2Shift 3Vacation T3 T3

4th WeekShift 1Shift 2

Shift 3Vacation T4 T4

1st Week Mon Tue Wed Thu Fri Sat SunShift 1 T2 T2Shift 2 T3 T3Shift 3 T4 T4Vacation T1 T1

2nd WeekShift 1 T1 T1Shift 2Shift 3Vacation

2nd WeekShift 1 T1 T1 T4 T4 T3 T3Shift 2 T2 T2 T1 T1 T4 T4Shift 3 T3 T3 T2 T2 T1 T1Vacation T4 T4 T3 T3

2nd WeekShift 1 T1 T1 T4 T4 T3 T3 T3Shift 2 T2 T2 T1 T1 T4 T4 T4Shift 3 T3 T3 T2 T2 T2 T1 T1Vacation T4 T4 T3 T3 T1


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1st Week Mon Tue Wed Thu Fri Sat SunShift 1 T4 T4 T3 T3 T2 T2 T2Shift 2 T1 T1 T4 T4 T3 T3 T3Shift 3 T2 T2 T1 T1 T1 T4 T4Vacation T3 T3 T2 T2 T4 T1 T1

Generated rotational schedule for four weeks

2nd WeekShift 1 T1 T1 T4 T4 T3 T3 T3Shift 2 T2 T2 T1 T1 T4 T4 T4Shift 3 T3 T3 T2 T2 T2 T1 T1Vacation T4 T4 T3 T3 T1 T2 T23rd WeekShift 1 T2 T2 T1 T1 T4 T4 T4Shift 2 T3 T3 T2 T2 T1 T1 T1Shift 3 T4 T4 T3 T3 T3 T2 T2Vacation T1 T1 T4 T4 T2 T3 T3

4th WeekShift 1 T3 T3 T2 T2 T1 T1 T1Shift 2 T4 T4 T3 T3 T2 T2 T2

Shift 3 T1 T1 T4 T4 T4 T3 T3Vacation T2 T2 T1 T1 T3 T4 T4


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1st Week Mon Tue Wed Thu Fri Sat SunShift 1 T2 T3 T1 T2 T3 T1 T2Shift 2 T1 T2 T3 T1 T2 T3 T1Vacation T3 T1 T2 T3 T1 T2 T3

Generated rotational schedule for three weeks

2nd WeekShift 1 T3 T1 T2 T3 T1 T2 T3Shift 2 T2 T3 T1 T2 T3 T1 T2Vacation T1 T2 T3 T1 T2 T3 T13rd Week

Shift 1 T1 T2 T3 T1 T2 T3 T1Shift 2 T3 T1 T2 T3 T1 T2 T3Vacation T2 T3 T1 T2 T3 T1 T2


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ASSUMPTIONS: Frame of reference is Euclidean geometric distance. The weights of the edges of Network G=(V,E) are distances. An

edge is an element of E, if and only if the distance between thenodes connected by that edge is less than or equal to the desiredservice distance.

The desired service distance, Rt , is set at 150m. This comes fromthe assumption that the lead time of emergency response is fiveminutes.

There are two mobile patrol units to be deployed. Blue guards arealso considered in the study.

The scenarios used are based on year 2005. The amount of budgetis confidential in nature and will not be presented.

RABAJANTE, JOMAR F., BAUTISTA, MIRZA S., CUARESMA, GENARO A. (Adviser). 2005. University Police Force Operations Personnel Allocation.

..Mathematics Division, Institute of Mathematical Sciences and Physics, University of the Philippines Los Baos, Philippines.


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Comparison of results usingMethod 1 and Method 2

Method 1(maximum security)

Method 2(with budget constraint)

PT (total number of police officers) 100 60

Pm for Pili Drive district 4 2

Pm for Lower Campus district 8 5

Pm for UPCO district 3 2

Pm for CVM district 2 1Pm for CFNR district 4 2

Radius of the atom (in meters) 150 255.14

Comparison of results using Method 2and the scenario in year 2005.*CVM and Pili Drive area share one police officer.

Method 2(8-hour shift)

Year 2005 Scenario(12-hour shift)

PT (total number of police officers) 60 36Number of policemen per shift 15 12Pm for Pili Drive district 2 1 + *Pm for Lower Campus district 5 5Pm for UPCO district 2 1Pm for CVM district 1 *Pm for CFNR district 2 1

Radius of the atom (in meters) 255.14 404.17

Approx worst-case response time (in minutes) 13 20Number of uncovered nodes 44 53

OPTIMAL POSTS CENTROID COVERED DEMAND NODES


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OPTIMAL POSTS CENTROID COVERED DEMAND NODES

PILI DRIVE AREA

Police 1 AMTEC Experimental Fields, Biological Control Lab., National AgroMet Station, AMDP, Old EngineeringBldg.

Police 2 CEAT Fruit Crops Orchard, PhilRice, Experimental Field, Old Agronomy Bldg., ASH, SPMO, GasolineStation, UPLB Central Parking Area, CPDMO, Chem. Engineering Bldg., IFST, Post Harvest

LOWER CAMPUS

Police 1

Police 2 and 3 Main GatePolice 4 NCAS CEM Secretarys Office, BioSci Bldg., Carabao Park, CDC Bldg., DZLBTower, ACCI, CEM Deans

Office, OVCCA and Department of AgEcon, Department of Economics, Department ofAgriBusiness, Raymundo Gate, SESAM, DAERS, Old PLDT Bldg.,CHE, Greenhouse and

Headhouse (BioSci), OUR, NCAS, SEARCA, COOP, Humanities Bldg., Oblation, Old Chem. Bldg.

Police 5 ACCI Dorm Graduate School, Business Affairs Office, DL Umali Auditorium, Public Toilet, Freedom Park,Track and Field and Soccer Field, Grandstand, YMCA, Swimming Pool, Baker Hall, Basketball

and Tennis Court, DMST, Palma Bridge, Hortorium, SU, Womens Dorm, IH Dorm, Mens Dorm,

PahinungodUPF

Headquarters

UPF Headquarters PhySci Bldg., Nutrition Bldg., Ornamental Crops Nursery, Ornamental Crops Division, FruitCrops Nursery, Post Office, UPLB Foundation, Senior Social Garden, Home Tech. and Child

Development Lab., Math Bldg.

UPCO

Police 1 Executive House

Police 2 Guard House UPCO Staff Housing, Substation, Doa Aurora St. Entrance/Exit, Sampaguita St. Entrance/Exit,Jasmin St. Entrance/Exit, Gumamela St. Entrance/Exit

CVM

Police 1 NCPC Dorm, NTC, RTP-FNP, UPLB Corral, CEC, Old Animal Husbandry Bldg., GYM, UPLBMedicinal Plants Garden and Gene Bank, PCRDF, Admin. and Office of College Secretary, IAS

Villegas Hall (Admin. Bldg.), IAS Fronda Hall, Vet. Med. Library (Communal Bldg.)

CFNRPolice 1 CPAF UHS, College Country Club, SEARCA Four-Door Apartments, IAS-CVM Housing

Police 2

(sector 3)

Morning: FPRDCNight: MAREHA

FPRDC, MAREHA, Botanical Garden, Wood Science and Tech. Bldg., Wood Chemistry andPhysics Research Lab., CFNR Admin. Bldg., Forestry Biological Science Bldg., ERDB, UPLB

Museum of Natural History, Institute of Forest Conservation, Forestry Info. and Library Bldg.,FOREHA, New FOREHA, Sawmill, Heavy Equipment Garage, Forest Reserve Entrance/Exit,

Forestry Alumni Guesthouse, Tennis Court/Soccer Field, Makiling Heights Housing UPCF, CF-IFCGuesthouse 1, 2 and 3, Forestry COOP and Canteen


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IPB area

PiliDrive

CVM

CFNR

UPCOLowerCampus

These twonodes formdominatingsets in thenetwork.

The five districts with IPB area partitioned into two patrol zones


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At the end of every Operation Research methodology, thedecision-maker should verify the result.

The policymakers in various communities can use the

generalized models to optimize their police forcedeployment. In fact, the models are suitable not only topolice force deployment, but also to the allocation of othertypes of security personnel, such as contractual guards.

The use of Geographic Information System would improvethe digitization of maps to graphs/networks.


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The decision-maker still has the choice if other shiftingschedule will be applied, since the eight-hour shift schedulenecessitates a significant increase in the number ofpersonnel.

Deterministic models are used for planning purposes.However, the models can be extended for operationalscenarios by adding stochastic and fuzzy elements of police

deployment (e.g. Larsons M/M/n Hypercube QueuingModel).

Maximum Coverage Location Problem can also be used inlocating other emergency and service facilities such as firestations, hospitals, and public markets.


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Jomar Fajardo RabajanteMathematics Division, [email protected]

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Optimal Deployment Of Community Personnel