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

Abstract

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.

On Solution to ASUU Strike and Consolidated University Academic Salary Structure II (CONUASS II) in the Nigerian Universities Using Optimization Method

“…This restriction is known as the "curse of dimensionality"; the curse of dimensionality occurs when the complexity of the problem increases rapidly because of a little increase in the number of inputs [4]. Empirically, dynamic programming was used by the author to model transportation and logistics problems and to demonstrate the robustness of dynamic programming [5]. The author noted that due to the decomposed nature of the mathematical model developed to handle transportation and logistics problems, dynamic programming was proposed and found to be suited for such a complex model.…”