NCJ Number
48801
Journal
Management Science Volume: 24 Issue: 12 Dated: (AUGUST 1978) Pages: 1291-1300
Date Published
1978
Length
10 pages
Annotation
A COMPUTER PROGRAM WAS DESIGNED TO SPECIFY THE NUMBER OF POLICE PATROL CARS THAT SHOULD BE ON DUTY IN EACH GEOGRAPHIC COMMAND OF A CITY AT VARIOUS TIMES OF DAY FOR EACH DAY OF THE WEEK.
Abstract
THE PATROL CAR ALLOCATION MODEL (PCAM) WAS DESIGNED AFTER A REVIEW OF PREVIOUS ALLOCATION PROGRAMS. THE MODEL PERMITS THE DISPLAY OF QUANTITATIVE INFORMATION ABOUT THE ALLOCATION OF PATROL CARS BY TIME OF DAY AND GEOGRAPHIC COMMAND. IN THE PCAM, A TOUR IS A PERIOD OF TIME WHEN A PATROL CAR MAY BE ON DUTY AND A PRECINCT IS A GEOGRAPHIC COMMAND. THE FOLLOWING OUTPUTS ARE AVAILABLE FROM THE MODEL: NUMBER OF PATROL CARS ASSIGNED; AVERAGE FRACTION OF TIME PATROL CARS ARE BUSY ON CALLS FOR SERVICE (ACTUAL UTILIZATION); AVERAGE NUMBER OF CARS AVAILABLE TO RESPOND TO CALLS FOR SERVICE; PREVENTIVE PATROL FREQUENCY; AVERAGE LENGTH OF TIME FROM A DISPATCH OF A PATROL CAR UNTIL ITS ARRIVAL AT THE SCENE OF AN INCIDENT (TRAVEL TIME); PROBABILITY THAT A CALL WILL ENTER A QUEUE; AVERAGE TIME IN A QUEUE OF CALLS BY PRIORITY LEVEL; AND AVERAGE TOTAL RESPONSE TIME (TIME IN QUEUE PLUS TRAVEL TIME). THE PCAM ALLOCATES CAR HOURS TO SHIFTS, WITH A SHIFT DEFINED AS A COMBINATION OF A SPECIFIC TOUR ON A PARTICULAR DAY IN A SPECIFIC PRECINCT. THE TWO BASIC PRESCRIPTIVE CAPABILITIES OF THE MODEL ARE DETERMINING THE MAXIMUM NUMBER OF CARS THAT MUST BE ON DUTY IN EACH SHIFT TO MEET CONSTRAINTS ON PERFORMANCE MEASURES IDENTIFIED BY THE USER AND ALLOCATING A USER-SPECIFIED TOTAL NUMBER OF CAR HOURS AMONG SHIFTS TO MINIMIZE OBJECTIVE FUNCTIONS. OBJECTIVE FUNCTIONS THAT CAN BE MINIMIZED BY THE PCAM ARE PROBABILITY OF CALLS ENTERING A QUEUE, AVERAGE QUEUE DELAY FOR ALL CALLS OR CALLS OF A PARTICULAR PRIORITY LEVEL, AND AVERAGE TOTAL RESPONSE TIME. THE GREATEST TECHNICAL INNOVATION OF THE PCAM IS ITS ABILITY TO DEAL WITH OVERLAY TOURS; THAT IS, IT CAN DESCRIBE PERFORMANCE MEASURES AND PRESCRIBE ALLOCATIONS IF THERE IS A TOUR THAT BEGINS DURING A 'NORMAL' TOUR AND ENDS DURING THE FOLLOWING TOUR. COMPUTATIONAL ALGORITHMS INVOLVED IN THE PCAM ARE DETAILED. POTENTIAL IMPROVEMENTS TO THE MODEL ARE NOTED, AND REFERENCES ARE PROVIDED. (DEP)