Capacitated transportation problems and an application

ABSTRACT The feasible (cost efficient) shipment of the products to wholesalers or to warehouses is a common problem for all companies. Such a problem is called a transportation problem, which is a special case of the linear programming problem. The general model, which corresponds to the classical transportation problem, comprises of the objective function, supply constraints, demand constraints, and nonnegativity constraints. However, if the decision variables which are the amounts of shipment have capacity constraints from various reasons such as capacity of trucks, warehouse capacity etc., then a capacitated transportation model is used. The objective is, generally, the minimization of cost. In this research, capacitated transportation model and solution methods are studied and applied to an actual industrial problem. In application, the objective is defined as minimizing the total transportation cost, while satisfying the capacity constraints on the decision variables as well as the demand and supply constraints. The total number of decision variables and constraints in practice made the problem so huge that the model became to be beyond the capability of the available software packages. Thus, in order to obtain a solution, an approximate solution method is developed. In the beginning, the problem is simplified to a smaller capacitated transportation problem and solved. With regards to the solution of the simplified model, sub problems are defined. The WinQSB software package is used and results are evaluated. Keywords: Transportation Problem, Capacitated Transportation Problem