A Queueing-Linear Programming Approach to Scheduling Police Patrol Cars

by Peter Kolesar, Kenneth Lloyd Rider, Thomas B. Crabill, Warren Walker


Download eBook for Free

FormatFile SizeNotes
PDF file 1.1 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.


Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback28 pages $20.00 $16.00 20% Web Discount

The arrival rate of calls for the service of police patrol cars varies considerably through the day in any city. We present a method — using queueing theory and integer linear programming — for scheduling patrol cars so that specified service standards are met at each hour of the day. Two models are used: An M/M/n queueing model with time dependent parameters which is solved numerically; and an integer linear program in which the decision variables are the number of patrol cars working each tour and the times at which they go out of service for meals, and whose constraints are determined by the output of the queueing model. Applications to real situations indicate that substantially improved schedules can be derived using this methodology.

This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.