Top-Down and Bottom-Up Solutions Within One Mathematical Model on the Example of Energetics

Kulyk Mykhailo

doi:10.11648/j.ajece.20210501.14

Abstract

The TD-BU methodology covers a wide range of objects of various "physical" nature and with various analysis tasks. The feature of such objects is that they have a hierarchical structure. Mathematically, they are related by the formalization of upper-level processes by algebraic equations, while lower levels are described by means of mathematical programming. Currently being extensively researched the forecast status of ultra-large hierarchical systems such as "the country's economy - its fuel and energy complex" with certain requirements. The excessive dimensions of such systems create difficulties in their analysis in the classical formulation, so most researchers use diacoptic methods and therefore these tasks TD-BU are labor-intensive. There are a large number of objects to which the TD-BU methodology could be formally applied. We are talking, among other things, about forecasting the volume of production of all types of products, services and demand for them what is necessary for the activities of all sectors of the economy with details at hierarchical levels. For the tasks of this type the key is the problem of discrepancy of the upper and lower levels indicators. This problem cannot be solved by existing TD-BU models. This paper presents a mathematical model and methods for analytical determination of indicators of the upper and lower levels in the above problems, which solve the problem of ambiguity. The mathematical model is formed in such a way that provides an opportunity to find solutions for the upper and each of the lower (sectoral) levels in a unique, analytical form. Therefore, the search for solutions is non-iterative and not laborious. It is carried out in two stages. On the first of them, using known (standard) methods, forecasts are developed for preliminary indicators of the upper and lower levels. At the second stage a special system of algebraic equations is formed, from which analytical dependences for calculation of refined indicators of both levels are defined. This ensures a complete match between the upper indicator and the sum of the lower levels indicators, which is demonstrated by the example of forecasting electricity demand. These mathematical models and methods can also be used to reconcile the reporting indicators of the upper and lower levels of the respective objects (management structures, banks, trade network, etc.). Thus the coordinated decisions are formed in one stage.

Highlights

Both individual countries and humanity as a whole in all areas of their activities are constantly forced to solve various problems of planning and forecasting
Different hierarchical levels of such systems are described by different types of mathematical models, which complicates the mathematical relationships between levels
Even in one area of knowledge, the problems solved using the TD-BU methodology require the use of multi-criteria models, Kulyk Mykhailo: Top-Down and Bottom-Up Solutions Within One Mathematical

Summary

Introduction

Both individual countries and humanity as a whole in all areas of their activities are constantly forced to solve various problems of planning and forecasting. This study examines and improves a special group of forecasting methods that combine top-down and bottom-up approaches, abbreviated TD-BU These methods apply only to systems and objects that have a hierarchical structure. Even in one area of knowledge, the problems solved using the TD-BU methodology require the use of multi-criteria models, Kulyk Mykhailo: Top-Down and Bottom-Up Solutions Within One Mathematical. Model on the Example of Energetics and the criteria are often contradictory This refers, first of all, to the problems of development and functioning of energy systems. Some papers contain studies in which the optimization of power supply and heat supply systems was solved simultaneously with minimization of greenhouse gas emissions [1-3] This forced the authors to use the simplest optimization methods, namely, purposeful sorting of options. The methodological basis is the theory of testing and applied working-out in the development of problem-oriented software for training and coaching professionals in relevant fields

Formulation of the Problem

Mathematical Model

Example

Conclusions