A strongly polynomial minimum cost circulation algorithm
Combinatorica
A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
A faster strongly polynomial minimum cost flow algorithm
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Derivative evaluation and computational experience with large bilevel mathematical programs
Journal of Optimization Theory and Applications
Computational difficulties of bilevel linear programming
Operations Research
A strongly polynomial algorithm for the transportation problem
Mathematical Programming: Series A and B
Finite Exact Branch-and-Bound Algorithms for Concave Minimization over Polytopes
Journal of Global Optimization
The steepest descent direction for the nonlinear bilevel programming problem
Operations Research Letters
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For a given time minimizing transportation problem comprising m sources and n destinations, the set of m sources is to be optimally partitioned into two mutually disjoint subsets L"1 and L"2 where, L"1 contains m"1 sources called Level-I sources and L"2 contains the remaining (m-m"1) sources termed as Level-II sources. First, the Level-I decision maker sends the shipment from Level-I sources to partially meet the demand of destinations. Later, the Level-II decision maker sends the material from the Level-II sources to meet the left over demand of the destinations. A finite number of cost minimizing transportation problems are solved to judiciously generate a few of Cm"1m partitions of the set of m sources. The aim of this study is to find an optimal partition of the set of m sources such that the sum of times of transportation in the Level-I and Level-II shipments is the minimum. The proposed polynomial bound algorithm to find the global minimizer has been successfully coded in C++ and run on a variety of randomly generated test problems differing in input data.