Topics in Extremal Graph Theory: Ramsey Numbers and the Turan Function

Topics in Extremal Graph Theory: Ramsey Numbers and the Turan Function by Damon J. Gulczynsk

INTEGER PROGRAMMING-BASED HEURISTICS FOR VEHICLE ROUTING PROBLEMS

The vehicle routing problem (VRP) has been an active field of study by opera-tions researchers for over 50 years. Many practical applications have been presented in the literature, and many solution techniques have been developed. We discuss, develop, and computationally test integer programming-based heuristics for several variants of the standard VRP. We use integer programming to model the split delivery VRP with minimum delivery amounts, the multi-depot split delivery VRP, the period VRP, the standard VRP, and the multi-depot VRP. We apply our heuristics to benchmark problems from the literature and generate many new problems with high-quality, visually-estimated solutions. Our heuristics produce high-quality solutions in a reasonable amount of computer time. Overall, our new IP-based heuristics are very competitive with the best methods found in the VRP literature to date