The MCCNF Problem With a Fixed Number of Nonlinear Arc Costs: Complexity and Approximation
We discuss the polynomial solvability of the minimum concave cost network flow problem (MCCNFP) with fixed numbers of sources and nonlinear arc costs and present some approximation algorithms for this variant of MCCNFP. In the single source uncapacitated case the MCCNFP is shown to be polynomially equivalent to a concave production transportation problem. A new strongly polynomial-time algorithm is presented for the latter problem, together with a new efficient approximation approach based on monotonic optimization.
KeywordsMinimum concave cost flow concave production-transportation problem strongly polynomial algorithms approximation algorithms Lagrange relaxation polyblock outer approximation.
Unable to display preview. Download preview PDF.
- D.-Z. Du and P.M. Pardalos (eds): Network Optimization Problems, World Scientific, 1993.Google Scholar
- G. Guisewite: Network problems, in Handbook of Global Optimization, eds. R. Horst and P.M. Pardalos, Kluwer 1995, 609–648.Google Scholar
- K. Holmberg and H. Thy: A production-transportation problem with stochastic demands and concave production costs, Mathematical Programming,to appear.Google Scholar
- R. Horst and H. Thy: Global Optimization: Deterministic Approaches, Springer, 3rd edition, 1996.Google Scholar
- H. Konno, P.T. Thach and H. Thy: Optimization on Low Rank Nonconvex Structures, Kluwer, 1997.Google Scholar
- B. Klinz and H. Thy: Minimum concave cost network flow problems with a single nonlinear arc cost, in Network Optimization Problems, eds. P.M. Pardalos and D.,-Z Du, World Scientific 1993, 125–143.Google Scholar
- H. Konno, P.T. Thach and H. Thy: Optimization on Low Rank Nonconvex Structures. Kluwer, 1997.Google Scholar
- G.L. Nemhauser and L.A. Wolsey: Integer and Combinatorial Optimization, Wiley and Sons 1988.Google Scholar
- A. Rubinov, H. Thy and H. Mays: Algorithm for a Monotonic Global Optimization Problem. Preprint, SIMS, University of Ballarat, Australia, 1998.Google Scholar
- H. Thy: Convex Analysis and Global Optimization, Kluwer Academic Publishers, Boston, Dordrecht, London, 1998Google Scholar
- H. Thy: Strong polynomial-time solvability of a minimum concave cost network flow problem, Preprint, Institute of Mathematics, Hanoi, 1999; to appear in Acta Mathematica Vietnamica.Google Scholar
- H. Thy: Monotonic optimization: problems and solution approaches, Preprint, Institute of Mathematics, Hanoi, 1999.Google Scholar
- H. Thy, S. Ghannadan, A. Migdalas and P. Vârbrand): Strongly Polynomial Algorithm for a Production-Transportation Problem with Concave Production Cost, Optimization, 27 (1992), 205–227.Google Scholar
- H. Thy, S. Ghannadan, A. Migdalas and P. Vârbrand: Heuristics Based on Tabu Search and Lagrangian Relaxation for the Concave Production-Transportation Problem, Studies in Regional and Urban Planning 3 (1994), 127–141.Google Scholar
- H. Thy and L.T. Luc: A new approach to optimixation under monotonic constraint. Preprint, Institute of Mathematics, Hanoi, 1999.Google Scholar
- H. Thy and A. Migdalas: Lagrange relaxation, decoupling and decomposition for the minimum concave cost network flow problem. Preprint, Institute of Mathematics, Hanoi, 1998.Google Scholar