
Accession Number : AD0714264
Title : Least dMajorized Network Flows with Inventory and Statistical Applications.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
Personal Author(s) : Veinott,Arthur F. , Jr
Report Date : 30 SEP 1970
Pagination or Media Count : 52
Abstract : It is shown that for any feasible network flow model, there is a flow which simultaneously minimizes every dSchur convex function of the flows emanating from a single distinguished node called the source. The vector of flows emanating from the source in the minimizing flow is unique and is the least dmajorized flow. This flow can be found by solving the problem for the special case where the dSchur convex function is separable and quadratic. Once this flow is found, the solution of the dual problem is reduced to evaluating the conjugate of a function appearing in the dual objective function at the above flow. The computation is extremely simple when the function is separable. These results are extended to situations in which the variables must be integers. An important special case of the problem can be solved geometrically by choosing, from among all paths joining two points in the plane and lying between two given nonintersecting paths, the path with minimum Euclidian length. Applications of the results are given to deterministic productiondistribution models, certain of the stochastic inventoryredistribution models examined by Ignall and Veinott, a deterministic price speculation and storage model, and a zero lead time case of the ClarkScarf series multiechelon model. In addition, applications are given to several maximum likelihood estimation problems in which the parameters satisfy certain linear inequalities. (Author)
Descriptors : (*OPERATIONS RESEARCH, NETWORKS), MATRICES(MATHEMATICS), STOCHASTIC PROCESSES, INVENTORY CONTROL, INTEGRALS, DISTRIBUTION FUNCTIONS, CONVEX SETS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE