This grant provides funding for the development of novel numerical techniques to solve computationally hard mathematical problems in operations research that have relevant applications in telecommunications, biology, scheduling, electronic bandwidth allocation, VLSI design, facility layout design, and coding theory. The developed techniques will used to increase the scalability of problems solved in this research area. Specifically, the research will integrate novel decomposition techniques, called branch decomposition techniques, with the existing traditional methodology to find new inequalities for the polyhedra related to the problems of interest. The developed techniques will be compared with other exact algorithms in the literature to validate and assess the computational efficacy of the techniques.
If successful, the results will increase the scalability and efficiency of solving the problems of interest. Applications of these problems are in fields seeing increased demand for services. In addition, the results can be used to solve other related computationally hard problems in operations research which have a wide range of applications apart from the aforementioned applications. Thus, the results will advance the knowledge base in operations research and offer new effective techniques for solving large-scale problems related to real-world applications.
