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Journal of Optimization
Volume 2016, Article ID 8518921, 9 pages
Research Article

A Hybrid Dynamic Programming for Solving Fixed Cost Transportation with Discounted Mechanism

Sharif University of Technology, Azadi Avenue, P.O. Box 11155-9414, Tehran, Iran

Received 2 December 2015; Accepted 28 January 2016

Academic Editor: Manlio Gaudioso

Copyright © 2016 Farhad Ghassemi Tari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of allocating different types of vehicles for transporting a set of products from a manufacturer to its depots/cross docks, in an existing transportation network, to minimize the total transportation costs, is considered. The distribution network involves a heterogeneous fleet of vehicles, with a variable transportation cost and a fixed cost in which a discount mechanism is applied on the fixed part of the transportation costs. It is assumed that the number of available vehicles is limited for some types. A mathematical programming model in the form of the discrete nonlinear optimization model is proposed. A hybrid dynamic programming algorithm is developed for finding the optimal solution. To increase the computational efficiency of the solution algorithm, several concepts and routines, such as the imbedded state routine, surrogate constraint concept, and bounding schemes, are incorporated in the dynamic programming algorithm. A real world case problem is selected and solved by the proposed solution algorithm, and the optimal solution is obtained.