transportation problem in operational research

Network: A network can be defined as a directed graph G = (V, A), where V is the set of vertices or nodes, and A is the set of arcs or links corresponding to the feasible routes between nodes.

The Classic Transportation Problem and GIS.

Solving the Classic Transportation Problem.

Modeling the Classic Transportation Problem.

And an integrated framework is often adopted to utilize both GIS and non-GIS linear programming solvers to search for the optimal solution. Solving such a problem relies strongly on the network data models, least-cost path algorithms, other functionalities in GIS. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and improving the current solution through iteration. And the objective is to minimize the total cost of transporting all units produced at sources to meet the demands at destinations.

The three inputs of the model are total units produced at each source, total units needed at each destination, and the cost to transport one unit from each source to each destination. It is a network-flow problem that arises in industrial logistics and is often solved by linear programming (LP). The classic transportation problem concerns minimizing the cost of transporting a product from sources/supplies to destinations/demands.

Transportation problem in operational research