Open AccessON THE SUBMODULARITY OF THE PROFIT FUNCTION IN A PROBLEM OF TRANSPORT PLANNING
Author(s) -
V.M. Montlevic
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-10-48-54
Subject(s) - mathematical optimization , profit maximization , function (biology) , profit (economics) , maximization , set (abstract data type) , computer science , mathematics , economics , microeconomics , evolutionary biology , programming language , biology
In this paper the possibility of using the method of successive calculations to solve the transportation problem on the maximum prot is investigated. The feature of this problem is that a set of consumers isn’t dened and gets out from wider set of possible consumers by the criterion of a maximum of prot. Prot is calculated on the basis of consumer demand and prices, which are determined by the contract between the consumer and the company carrying out transportation. It is shown that this problem is reduced to maximization of the prot function dened on the set of all subsets of consumers. The submodularity of prot function is proved, that justied application of method of successive calculations to solve this problem.