Combinatorics and Graph Theory

2006 Submissions

[2] viXra:2006.0192 [pdf] submitted on 2020-06-21 11:15:01

The Vertices of a Graph and its Dimension

Authors: Volker Thürey
Comments: 7 Pages.

We show that the dimension of a graph is less or equal to the cardinality of the set of its vertices
Category: Combinatorics and Graph Theory

[1] viXra:2006.0174 [pdf] submitted on 2020-06-18 18:12:14

An Examination of Resourcing and Scheduling Within the RCMP

Authors: Bruce Rout
Comments: 74 Pages. MSc Thesis Simon Fraser University Dept. of Mathematics

The problem of resourcing and staffing, or finding how much manpower is needed to meet demand, can be traced back to the times of the Roman Empire. We examine here the various means used by the Royal Canadian Mounted Police in trying to solve this problem efficiently. We also examine their latest attack in building a simulator to determine future demands on resources and we provide a solution to determine efficient staffing levels through an application of a scheduling algorithm using “rods”. This algorithm is characterized as a rod-scheduling method which can be reduced to a linear program. It has been found that the previous methods used by police departments in Canada and the United States are extremely cumbersome. The methods suggested here correct this. Although the methods are very similar to those used before in other industries they haven’t been applied to police work. What was previously done in policing is to optimize very simple constraints first and then try to fit the results to the needs of the user. In this work I have suggested first obtaining all legal inputs and then optimizing to obtain a final answer. The author uses this method to investigate different types of demand data. Furthermore, different integer programming techniques are investigated. This document is meant for different users. It is hoped it can be read by various police departments as well as administrators and academics. In light of this the tone of the thesis is conversational. Much of the mathematical work is in sections three to seven.
Category: Combinatorics and Graph Theory