Veronika Novotná

The Application of Functions of Several Variables Analysis in an Optimal Replenishment Policy for Deteriorating Items

Abstract Very often must be taken into account the gradual deterioration of goods in inventory management. This fact is not taken into account in multiple management systems. Traditional inventory models at the same time assume that a retailer pays for the goods the moment they are received. Nowadays, however, it is becoming a common practice that a supplier offers a retailer the option to pay for the goods with a certain delay. If the retailer is not able to meet his obligations within the deadline, he is charges an interest.In this study we introduce a newly constructed suitable model which enables a retailer to set an optimal price of deteriorating goods under permissible delay in payments, and to determine the maximum repayment term. We considered a deterministic inventory model with time-dependent demand, holding costs variable in time where deterioration is directly proportional to the time. The model is based on the assumption of time-dependent demand and has been developed for deteriorating goods. The paper further analyses a situation in which the retailer sell all the goods in time, and a situation in which the deadline was not met. Further assumption is that the inventory is depleted only by demand. The scientific aim is to verify if such an optimizing problem can be solved. Theoretical results are illustrated with numerical example for the model. Results show that the developer model is capable of solving the theoretical problem illustrated by an example. It helps to the retailer to set the selling price and the replenishment interval in order to maximize profit. The authors of the paper used methods of analysis and synthesis, and the method of mathematical analysis (differential calculus of multivariable functions, solution of ordinary differential equations, Taylor series).The model suggested in the paper can be expanded in the future. One option is generalization of the model, allowing for the lack of goods, bulk discounts, time value of money, inflation etc.

Numerical Solution of the Inventory Balance Delay Differential Equation

Inventory represents an essential part of current assets, which are typically characterized by their transience. This paper aims to outline a numerical solution of the inventory balance equation supplemented by an order-up-to replenishment policy for a case in which the problem is described by a differential equation with delayed argument. The results are demonstrated on a specific example and the behaviour of the model is presented using a computer simulation. The results are graphically shown in the Maple system. The solution makes use of the theory of functional differential equations, especially the part dealing with differential equations with delayed arguments.

Solution of Dynamical Macroeconomic Model Using Modern Methods

Modelling of the phenomena following from the economic reality and reflected by the statistical data is based in particular on the mathematic disciplines like statistics, numerical methods, operations research, linear and dynamic programming, optimization, etc. The use of a suitable computer system is inevitable both for modelling, analyses, diagnostics and/or possible solution of issues by quantitative methods, and for economic reinterpretation and application.

Optimal replenishment policy for deteriorating and non deteriorating items

The purpose of the paper is to present a model allowing the retailer to determine the optimal price of three kinds of items in a situation where the supplier provides the retailer with an interest-free loan for a contractually agreed period. The scientific aim is to verify whether an optimization problem is solvable, and determine the maximum length of the interval over which the goods can be sold with a profit in a situation where the model features two kinds of deteriorating items and one non deteriorating item. The economic theory is explained in the introductory section and serves as a basis for the drawing up of the model. Methods of analysis, synthesis, dynamic modeling and differential calculus of multivariate functions are also used. The situation where the dealer sells all his goods in time and the situation where this period is not observed are analyzed. Thanks to the exact expression of the model it is possible to assess the effect of any changes in external factors. Authors’ findings are that the used variables form compact set and analysed function is continues on this space, we can use Weistrass Theorem for additional calculation with success. Thanks to the exact expression of the model it is possible to assess the effect of any changes in external factors. The model proposed in the paper may be expanded in the future. One possibility is to consider a generalization of the model allowing for shortage of items, quantity discounts, inflation, etc. DOI: http://dx.doi.org/10.5755/j01.ee.29.3.14204

Electronic Communication in Private Doctors' Surgeries in the Czech Republic

Doctors’ surgeries are facing increasing demands on the time required for sending out reports, referra ls and diagnoses of various kinds. This leads to a shortag e of the time needed for the most important thing ‐ patient care. The development of information technology and its increased use means ever-increasing possibilit ies for its use in simplifying the administrative work facing d octors’ surgeries. Many doctors, however, are still not taking as much advantage of such software as they might. T he aim of this paper is to determine how much inter est there is in this simple and effective form of communicati on in private doctors’ surgeries in the Czech Repub lic, to determine the level of use of electronic communicat ion in dependence on doctors’ areas of speciality, and to summarise the demands on information security laid down by the law. The exploratory analysis and multi variate statistical analysis method has been used for a dee per analysis of the data..

Software Solution of Delay Differential Equations

Methods used for ordinary differential equations cannot generally be used to solve delay differential equation, which is reflected in the choice of suitable software. The paper shows possibilities of software solution of delay differential equations. The aim of the paper is to present the possibilities of current software packages and programme systems (e.g. Matlab, Maple, R). The paper further shows how the aforementioned equations can be used in solutions of dynamical models. The conclusion of the papers demonstrates a solution of a specific dynamical model - the Phillips curve applied to the Czech Republic. Setting up the model required the use of analytic and synthetic methods, dynamical modelling and solving the system of two delay differential equations. In the conclusion the authors claim that although the quality of the available software, suitable for solving delay differential equations, is not as good as that of software used for solving ordinary differential equations, such software that meets basic requirements can be found. Therefore such software can be used as a supportive tool for exact modelling methods in practice.