A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of nonlinear variables
- 126 Downloads
We show that the production-transportation problem involving an arbitrary fixed number of factories with concave production cost is solvable in strongly polynomial time. The algorithm is based on a parametric approach which takes full advantage of the specific structure of the problem: monotonicity of the objective function along certain directions, small proportion of nonlinear variables and combinatorial properties implied by transportation constraints.
KeywordsConcave minimization Global optimization Combinatorial optimization Facility location Production-Transportation Parametric approach Strongly polynomial algorithm
Unable to display preview. Download preview PDF.
- M.L. Balinski, “The Hirsch conjecture for dual transportation polyhedra,” Collaborative paper, bf CP-83-9, IIASA, Laxenburg, Austria (1983).Google Scholar
- M.A. Efroymson and T.R. Ray, “A branch and bound algorithm for plant location,”Operations Research 14 (1966) 361–368.Google Scholar
- E. Feldman, F.A. Lehrer and T.L. Ray, “Warehouse location under continuous economies of scale,”Management Science 12 (1966) 670–684.Google Scholar
- D.S. Hochbaum and J.G. Shantikumar, “Convex separable optimization is not much harder than linear optimization,”Journal of the Association for Computing Machinery 37 (1990) 343–362.Google Scholar
- B.M. Khumawala and D.L. Kelly, “Warehouse location with concave costs,”INFOR 12 (1974) 55–65.Google Scholar
- B. Klinz and H. Tuy, “Minimum concave cost network flow problems with a single nonlinear arc cost,” P.M. Pardalos and D.-Z. DuNetwork Optimization Problems, (World Scientific, Singapore, 1992) pp. 125–143.Google Scholar
- T.L. Magnanti and R.T. Wong, “Network design and transportation planning: models and algorithms,”Transportation Science 18 (1984) 1–55.Google Scholar
- A.S. Nemirowsky and D.D. Yudin,Problem Complexity and Method Efficiency in Optimization (Wiley, New York, 1983).Google Scholar
- T.V. Thieu, “Solving the lay-out planning problem with concave cost”, in:Essays in Nonlinear Analysis and Optimization (Institute of Mathematics, Hanoi, 1987) pp. 101–110.Google Scholar
- H. Tuy, S. Ghannadan, A. Migdalas and P. Värbrand, “Strongly polynomial algorithm for a production-transportation problem with concave production costs,”Optimization 27 (1992) 205–228.Google Scholar