Application of linear programming to the standard maximum problem in the field of transportation

Abstract

The paper presents the analysis of the transport plan by applying the geometric interpretation of linear programming, dual approach and simplex method to the optimization of the transport plan. The goal is to optimize the transport plan from the aspect of choosing the type of transport task, type and scope of engagement of transport means, in order to maximize the functions of the goal that represents the earnings. The approach to analysis is illustrated by a characteristic task that is solved in the paper in the described way. The main difference between this and the tasks analyzed so far is that the imposed restrictions represent a system of inequalities which, by introducing fictitious variables, is transformed into a system of equations to which the standard maximum problem is applied. The benefit of this approach is a simpler but also more comprehensive approach to the analysis of the transport plan. It is especially suitable for relatively small transport systems when there are a number of limitations and where it is not convenient to buy and use software packages. The emphasis in the paper is on maximizing earnings while meeting the imposed limits. The analysis yielded identical results in all three ways.