Speaker:
András PrékopaProfessor of Operations Research, Statistics, and MathematicsRutgers University
Date, Time, Location:
Friday, April 13, 20122:30pm - 3:30pmMohler Laboratory, Room 451
Title:
Single Commodity Stochastic Network Design Under Probabilistic Constraint
Abstract:
Single commodity networks are considered, where demands at nodes are random. The problem is to find minimum cost optimal capacities at the nodes and arcs subject to the constraint that all demands should be met on a prescribed probability level (reliability constraint) and some constraints on the capacities should be satisfied. The probabilistic constraint is formulated in terms of the Gale-Hoffman feasibility inequalities but their number is reduced by elimination technique. The concept of a p-efficient point is used in a smart way to convert and then relax the problem into a large scale LP. Two solution techniques will be presented. In one of them all p-efficient points are known while in the other one they are simultaneously generated with the LP algorithm, The joint distribution of the relatively small number of the demands is used to obtain the p-efficient points for all non-eliminated stochastic inequalities and the solution of a knapsack problem is used to generate new p-efficient points. The network design method can be applied to interconnected power systems, flood control and water supply networks, design of shelter and road capacities in evacuation, parking lot capacities, financial networks, etc. Numerical examples will be presented.
Biography:
András Prékopa was born in Nyíregyháza, Hungary. He received his BA and MA degrees in mathematics and physics from the University of Debrecen in 1949 and, 1952, respectively. In 1952 he became a PhD student (aspirant) at the Institute for Applied Mathematics of the Hungarian Academy of Sciences (HAS) and defended his thesis, entitled “On Stochastic Set Functions”, in 1956. Between 1956-68 he was first assistant, later associate professor at the Department of Probability Theory of the L. Eötvös University. In 1968 he became full professor at the Department of Mathematics of the Technical University of Budapest, where he remained until 1983. In that year he returned to the Eötvös Univesity, and became the founder, professor and first chairman of the Department of Operations Research (OR). He retired from there in 2000. Since 1985 he has been distinguished professor of OR, statistics and mathematics at Rutgers University. Currently he is the graduate director of the PhD program in OR. Prékopa’s part-time appointments were also very important in his scientific career in Hungary. In 1958 he founded the first research department in OR at the Math. Inst. of the HAS and in 1977 the Department of Applied Math. at the Computing and Automation Inst. of the HAS. Prékopa is the father of the Hungarian OR in many ways: developed research school, education curricula, organized international and local conferences, formed academic committee, founded scientific periodical, etc. He published more than a dozen books about 350 papers and supervised 52 PhD students, many of them are internationally known academics and industrial leaders, all-over the world. In 1979 he was elected a corresponding member and in 1985 full member of the HAS. He was also elected a foreign member of the National Academy of Engineering of Mexico, fellow of the Econometric Society, member of the International Statistical Institute, honorary president of the J. Bolyai Math. Society and the Hungarian OR Society, among others. He is the recipient of the Széchenyi Prize (1996) and Middle Cross of the Republic of Hungary (2005). The highest recognition he was awarded for his achievements is the Gold Medal of the European OR Societies, a major international distinction that Prékopa received in 2003. He is married to Kinga Széchenyi, educator, sculptor and writer, they have two children and two grandchildren.
All full-time ISE PhD students are required to attend.
