The first report provides the background for routing solid waste collection vehicles. Problems encountered with existing methods and possible solutions are given. Appendixes A and B are solutions to two classic routing problems. Appendix A takes the integer programming formulation of Dantzig, Fulkerson, and Johnson which is relaxed to a linear program and a column generation scheme found for its dual. Appendix B (separately bound) is a study applying network theory to the problem of routing a solid waste collection vehicle through a street network. The problem can be described mathematically as a linear program whose optimal solution is guaranteed to be integer.