N. Begashaw, G. Comert, and N. G. Medhin. Determining an Optimal Scheduling of Freight Transportation to Maximize Revenue
Neural Parallel and Scientific Computations 30 (2022), No. 1, 17-22

https://doi.org/10.46719/NPSC202230.01.02

ABSTRACT.
In this paper we present a nonlinear programming approach for selecting an optimal scheduling of freight transportation from sources to destinations to maximize revenue. The decision variables in the model are number of batches to be transported from sources to destinations. These decision variables take on integer values. In our model we treat them as continuous variables and add a nonlinear constraint which will enforce the variables to take on integer values at the optimal solution. The nonlinear constrained problem is transformed to an unconstrained optimization problem using a penalty method. We use gradient descent to find the optimal solution of the unconstrained optimization problem. A numerical example with two sources and two destinations is provided.

Key Words and Phrases. Penalty method, constrained and unconstrained optimization