Problemi Ekonomiki (Sep 2018)
Solving a Three-Index Transportation Problem under Risk Conditions Using a Genetic Algorithm
Abstract
The complication of economic relations, on the one hand, and the increase in processing power of computers, on the other hand, led to the development of economic and mathematical methods and models, the use of which in solving economic problems was previously limited. In particular, multi-index transportation problems are becoming popular as resource allocation problems that arise in manufacturing, supply chain management, information technology, distribution, etc. Multi-index transportation problems allow considering more parameters of real problems in comparison with two-index transportation problems. But along with the increase in the number of indices of a transportation problem and its dimension, the time required to solve this problem also increases. This necessitates using adequate tools to address them. A genetic algorithm can be considered as one of such tools. It allows to simultaneously analyze several potential solutions to the problem at every step of its operation, which significantly reduces the time to search for the optimal or, in some sense, best solution. The article describes the steps of the genetic algorithm to solve a triplanar and triaxial transportation problem, upon the encoding is in real numbers; shows how risks can be considered; presents the steps of the procedure for “returning” a chromosome to the region of feasibility; describes the use of the elitism strategy in order to preserve the best chromosome in the genetic algorithm. In further studies, it is advisable to develop the procedure for “returning” a chromosome to the region of feasibility along with specifying the use of various genetic operators in the genetic algorithm to solve three-index transportation problems in order to reduce the number of chromosomes that fall beyond the region of feasibility, which, in turn, should significantly reduce the time of performing the genetic algorithm as a whole. In addition, the aspects of assessing risk in multi-index transportation problems also need further research.
