A Type of Transportation Problem to be Solved Following the Time Criterion and Considering Vehicle Features

Abstract

The formulation of classical minimax transport-type problems involves the search for an optimal transportation plan considering only time of delivery of resources. The inevitable additional costs of processing resources at the origin and destination are usually not considered. This approach is fully justified given incommensurability of delivery times of resources along available routes and times of preliminary/subsequent processing of resources. At the same time, in a number of practical problems, the time spent on loading/unloading (for example, when organizing loading of packaged mineral fertilizers from port warehouses onto ships) can be of significant importance. In such cases, when searching for an optimal transportation plan, it is necessary to take into account not only travel times of vehicles used along the set routes, but also the costs of loading and unloading operations, considering the number of available vehicles and their characteristics, for example, payload.
In this regard, the objective of the study is not only to develop a method for calculating the optimal transportation plan, but also a method for distributing vehicles, considering their number and features.
At the same time, another no less important objective of the study is to substantiate the application of the method of successive reduction of residuals, considering the form of the objective function, which considers not only the main parameters of classical minimax transport-type problems, but also the quantitative characteristics of vehicles involved in the transport operation. It is fundamentally important that the use of the method of successive reduction of residuals determines the polynomial computational complexity of the algorithm, which makes it possible to use it in the operational solution of problems of practical dimension.
To solve the problem of distributing available vehicles according to the origin points, considering payload of vehicles, it is proposed to use the method of dynamic programming. An illustrative example of distribution of delivery vehicles, adapted for the use in MS Excel, is considered.