A SIMPLICIAL BRANCH-AND-BOUND ALGORITHM FOR PRODUCTION-TRANSPORTATION PROBLEMS WITH INSEPARABLE CONCAVE PRODUCTION COST

In this paper, we develop a branch-and-bound algorithm to solve a network flow problem of optimizing production and transportation simultaneously. The production cost is assumed to be a concave function in light of scale economy. The proposed algorithm generates a globally optimal solution to this nonconvex minimization problem in finite time, without assuming the separability of the production-cost function unlike existing algorithms. We also report some computational results, which indicate that the algorithm is fairly promising for practical use.

[1]  H. Tuy,et al.  Strongly polynomial algorithm for a production-transportation problem with concave production cost , 1993 .

[2]  Kaj Holmberg,et al.  A production-transportation problem with stochastic demand and concave production costs , 1999, Math. Program..

[3]  Peter Värbrand,et al.  A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of nonlinear variables , 1996, Math. Program..

[4]  Hanif D. Sherali,et al.  Linear Programming and Network Flows , 1977 .

[5]  Hanif D. Sherali,et al.  Linear programming and network flows (2nd ed.) , 1990 .

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[8]  Richard M. Soland,et al.  Optimal Facility Location with Concave Costs , 1974, Oper. Res..

[9]  Abdellah Salhi,et al.  Global Optimization: Deterministic Approaches (2nd Edition) , 1994 .

[10]  Panos M. Pardalos,et al.  Minimum concave-cost network flow problems: Applications, complexity, and algorithms , 1991 .

[11]  Takahito Kuno,et al.  A decomposition algorithm for solving certain classes of production-transportation problems with concave production cost , 1996, J. Glob. Optim..

[12]  Hoang Tuy,et al.  Strongly polynomial time algorithms for certain concave minimization problems on networks , 1993, Oper. Res. Lett..

[13]  Takahito Kuno,et al.  A Lagrangian Based Branch-and-Bound Algorithm for Production-transportation Problems , 2000, J. Glob. Optim..

[14]  Takahito Kuno,et al.  A Pseudo-Polynomial Primal-Dual Algorithm for Globally Solving a Production-Transportation Problem , 1997, J. Glob. Optim..

[15]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .