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Investment in stochastic minimum cost generalized multicommodity networks with application to coal transport
Author(s) -
Wollmer Richard D.
Publication year - 1980
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230100406
Subject(s) - random variable , variable (mathematics) , mathematical optimization , flow network , stochastic programming , mathematics , variable cost , linear programming , investment (military) , stage (stratigraphy) , exploit , resource (disambiguation) , operations research , computer science , economics , statistics , microeconomics , mathematical analysis , paleontology , computer network , computer security , biology , politics , political science , law
In a generalized multicommodity network, certain resources are in limited supply. The total consumption of any resource is a linear combination of the individual arc flows. In this problem the supply of any resource is a non‐negative random variable which may be increased by an investment. The objective is to invest in resources in a way that minimizes total expected cost. This problem is formulated as a two stage linear program under uncertainty. The first stage variables are the amounts that are to be invested in each resource. The values of the first stage variables are determined before the actual values of the random variables become known. The second stage variables correspond to the amount of flow on each arc of each commodity. The values of the second stage variables are determined after the actual values of the random variables are known. The solution techniques given exploit the network structure in both the first and second stage.