Robert G. Bland
Professor, Operations Research and Industrial Engineering
233 Rhodes Hall, 607/255-9144; bland@orie.cornell.edu
B.S. 1969, M.S. 1972, Ph.D. 1974 (Cornell)
Biography
Bland joined the Cornell faculty in 1978 after four years as an assistant professor of mathematical sciences at the State University of New York at Binghamton. From 1975 until 1977 he held a research fellowship at the Center for Operations Research and Econometrics in Louvain, Belgium, and a visiting professorship at the European Institute for Advanced Studies in Management in Brussels; from 1978 to 1980 he was an Alfred P. Sloan Foundation research fellow. At Cornell, Bland is affiliated with the Center for Applied Mathematics. He is a member of the Operations Research Society of America, the Mathematical Programming Society, and the Society for Industrial and Applied Mathematics.Research Interests
Linear programming is concerned with certain kinds of problems related to the optimal allocation of scarce resources among competing, but otherwise independent, activities. It is applicable when the consumption of each resource is a linear function of the levels at which the activities are pursued, and the measure of goodness of an allocation--for example, cost (to be minimized) or profit (to be maximized)--is also linear. For more than forty years linear programming has been an extremely effective tool in widespread use by decision-makers in business and government. In order to develop more efficient algorithms capable of broader applicability, it would be helpful to have a better understanding of linear programming problems. A principal focus of our work has been to provide a precise and concise description of the combinatorial structure underlying linear programming duality theory. This mathematical simplification of the usual vector space setting has revealed surprisingly simple variations on traditional algorithms--variations that exhibit interesting theoretical properties and, sometimes, interesting computational properties. Related work concerns variations on linear programming. How can we best exploit special structure in linear programming problems? How can we cope with problems in which additional complicating conditions have been imposed on an otherwise easily tractable structure? For example, certain production-scheduling problems are complicated by the possibility that items loaded at different times may be scheduled to be simultaneously resident on a machine with fixed capacity. For a particular class of problems, we have shown that the capacity conditions can be incorporated in a surprisingly easy way into an alternative model that is solvable by special-purpose techniques used in network flow theory. The main tool used here is geometric duality of planar graphs. We have also done extensive computational work on network flow codes, employing statistical methods to model how execution times respond to variations in input characteristics.
Further work involves the approximate solution of large-scale, specially-structured, hard combinatorial-optimization problems. For example, one project investigated the use of heuristic techniques in the efficient sequencing of x-ray diffraction readings in crystallographic experiments.
Current Research Projects
- Computational and Mathematical Investigations in Optimization (National Science Foundation; Air Force Office of Scientific Research; Office of Naval Research)
- Other participants: D. Shmoys, E. Tardos, M. J. Todd, and L. E. Trotter, Jr. (Operations Research and Industrial Engineering), and T. F. Coleman, Y. Li and S. Vavasis (Computer Science)
Selected Publications
Last revised: 3/15/95
Photo from 10/31/02 lecture on convexity:
