Send-and-split method for minimum-concave-cost network flows
Mathematics of Operations Research
A faster strongly polynomial minimum cost flow algorithm
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A branch-and-bound method for the fixed charge transportation problem
Management Science
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Finding minimum-cost flows by double scaling
Mathematical Programming: Series A and B
Tabu search applied to the general fixed charge problem
Annals of Operations Research - Special issue on Tabu search
Solving to optimality the uncapacitated fixed-charge network flow problem
Computers and Operations Research
A polynomial combinatorial algorithm for generalized minimum cost flow
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Pivot Strategies for Primal-Simplex Network Codes
Journal of the ACM (JACM)
Algorithms for Network Programming
Algorithms for Network Programming
Solving the Convex Cost Integer Dual Network Flow Problem
Management Science
A survey on benders decomposition applied to fixed-charge network design problems
Computers and Operations Research
Application of fuzzy minimum cost flow problems to network design under uncertainty
Fuzzy Sets and Systems
Minimum cost flows with minimum quantities
Information Processing Letters
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The minimal-cost network flow problem with fixed lower and upper bounds on arc flows has been well studied. This paper investigates an important extension, in which some or all arcs have variable lower bounds. In particular, an arc with a variable lower bound is allowed to be either closed (i.e., then having zero flow) or open (i.e., then having flow between the given positive lower bound and an upper bound). This distinctive feature makes the new problem NP-hard, although its formulation becomes more broadly applicable, since there are many cases where a flow distribution channel may be closed if the flow on the arc is not enough to justify its operation. This paper formulates the new model, referred to as MCNF-VLB, as a mixed integer linear programming, and shows its NP-hard complexity. Furthermore, a numerical example is used to illustrate the formulation and its applicability. This paper also shows a comprehensive computational testing on using CPLEX to solve the MCNF-VLB instances of up to medium-to-large size.