About transport costs calculation on the Transsiberial railway

The problem of optimal distribution of train and cargo traffic along parallel lines in the Trans-Siberian transport corridor of the Russian Federation is considered. This problem is closely interconnected with a problem of definition and optimisation of transportation expenses on the Trans-Siberian highway. The economic and mathematical model for determining costs for particular works in each type of line plants (a structural unit) in a railway rather permanent natural labour, material, energy and other norms for transport polygonon are used is offered. This model may serve as the basic part of an automated information system of cost planning on different levels of managing the transportation process

Decision-making models in marketing: dynamic optimization and differential games

ISBN 978-5-7525-1858-

Trade Discount Policies in the Differential Games Framework

We consider a vertical control distribution channel in which a manufacturer sells a single kind of good to a retailer. We assume that a wholesale price discount increases the retailer's sale motivation thus improving sales. The optimal control of manufacturer's profit via trade discounts is embedded in a differential game framework; in the special case of constant controls we compare the Stackelberg equilibria obtained considering manufacturer and retailer respectively as leaders of the game with Nash equilibrium points

Minimization of communication expenditure for seasonal products

MathSciNet: MR 195798

A model for communication in a multi-segment market

We consider a linear optimal control model for the marketing of seasonal products which are produced by the same firm and sold by retailers in different market segments The horizon is divided in two consecutive non-intersecting intervals, called production and selling periods, respectively. The production period state variables are the inventory levels and two kinds of goodwills (consumers' and retailers' goodwill, respectively) while the selling period state variables are the sales levels and the two kinds of goodwills. In the production interval there are three kinds of controls: on production, quality and advertising, while in the selling one the controls are on communication via advertising, promotion addressed to consumers and incentives given to retailers. We consider the case of several kinds of communications. The optimal control problem is transformed into an equivalent nonlinear programming problem

A fractional optimal control problem for maximizing advertising efficiency

ISBN: 978-5-7525-1858-

Why are losses from trade unlikely?

© 2015. Examining a standard monopolistic competition model with unspecified utility/cost functions, we find necessary and sufficient conditions on their elasticities for welfare losses to arise from trade or market expansion. Two numerical examples explain the losses (under unrealistic elasticities)

The Methodology of Functioning Engineering Mechanisms in the System of Auditing Controls

In connection with the crisis increases the relevance of audit control in the Russian economy. Great influence on the modern accounting in Russia have been successfully carried out reforms and existing engineering mechanisms in the system of auditing controls. The article shows the different interpretations of the concept of “engineering”, and discusses the methodology, methods and mechanisms of functioning of engineering mechanisms in the system audit trail, as well as the main directions of the use of accounting and auditing engineering and basic engineering of accounting tools of various kinds. Model instruments and statutory audit of engineering are used in a variety of processes, not only at the micro level, but also at the meso and macro levels. The article identified and grouped the main problems of further development of Russian accounting and reporting. Showing difficulties that do not allow to apply international auditing standards in full, as well as proposed solutions to these problems. As one of these solutions to the identified problems proposed accounting model for using engineering mechanisms in the audit. Keywords: Audit, Accounting, Engineering JEL Classifications: A20; L1

A global optimization approach to fractional optimal control

In this paper, we consider a fractional optimal control problem governed by system of linear differential equations, where its cost function is expressed as the ratio of convex and concave functions. The problem is a hard nonconvex optimal control problem and application of Pontriyagin's principle does not always guarantee finding a global optimal control. Even this type of problems in a finite dimensional space is known as NP hard. This optimal control problem can, in principle, be solved by Dinkhelbach algorithm [10]. However, it leads to solving a sequence of hard D.C programming problems in its finite dimensional analogy. To overcome this difficulty, we introduce a reachable set for the linear system. In this way, the problem is reduced to a quasiconvex maximization problem in a finite dimensional space. Based on a global optimality condition, we propose an algorithm for solving this fractional optimal control problem and we show that the algorithm generates a sequence of local optimal controls with improved cost values. The proposed algorithm is then applied to several test problems, where the global optimal cost value is obtained for each case

Dinkelbach Approach to Solving a Class of Fractional Optimal Control Problems

We consider optimal control problems with functional given by the ratio of two integrals (fractional optimal control problems). In particular, we focus on a special case with affine integrands and linear dynamics with respect to state and control. Since the standard optimal control theory cannot be used directly to solve a problem of this kind, we apply Dinkelbach’s approach to linearize it. Indeed, the fractional optimal control problem can be transformed into an equivalent monoparametric family { P q } of linear optimal control problems. The special structure of the class of problems considered allows solving the fractional problem either explicitly or requiring straightforward classical numerical techniques to solve a single equation. An application to advertising efficiency maximization is presented