On simplification of the transport problem solution with ecological criterion

The possibility of neglecting the penalty component in solving the transport problem (TP) with an environmental criterion is analyzed, when, along piece-rate payment, fixed additives are assigned, due only to the fact of a specific transportation, and not to the amount of transported cargo (penalties). It was found that, while the threshold ratios of the standard deviations of tariffs and fines in a TP with a single optimal plan can be grouped quite tightly, in a TP with a non-unique optimal plan, their use is not effective due to the large spread. However, the possibility of applying the “looping” method proposed by the authors, when the TP is solved many times, in which penalties are added to the tariffs, divided first by the maximum possible transportation, then by the transportation plan at the previous step, allows neglecting the “penalties” if the loop ends at the first step. The disadvantage and reason for the approximate nature of the “looping” method is the possible presence of other cycles with local minima. The possibility of the “exclusions” method presented in the paper is also considered, when for a TK with n suppliers and m customers cells are excluded in descending order of fines if the remaining parts of capacities and capacities are sufficient. The ability to distribute transportation after R = (nm – (n + m – 1)) steps allows you to ignore tariffs when choosing a plan. The disadvantage of this method, equivalent to allocative least cost method is the possible difficulties in arranging transportations after R steps of exclusion made under the assumption of a “saturated” use of cells.

transport problem, environmental criterion, tariff, fine, optimal plan, maximum possible value