A linear programming approach for the construction of energy and resource flow models

A linear programming model of an energy production and consumption system is a mathematical representation of resource allocation alternatives in the system. Such a model is developed for the solution of feasible and optimal resource allocation schemes under different assumptions. These assumptions define availabilities of primary resources, technological development patterns, requirements on final production and the objectives applied in optimisation. The scope of potential applications depends on the existence of interesting resource allocation alternatives within the boundaries of the system. In this respect models which cover both energy production and consumption processes are more interesting than more production models. Linear programming energy flow models may be dynamic, they may be divided regionally, and they may have stochastic features. In every case the one-period technological resource allocation module forms the core of the model. Dynamic, stochastic or regionally divided models are most naturally seen as extensions of the basic static model. Mathematical methods of linear programming are highly developed, and the nature of those resource allocation questions which can be formulated as linear programming problems is well understood. Applying linear programming to national energy problems is, however, not always as easy as one might expect. This is often due to the fact that the resource allocation alternatives in the real system are poorly known, and they are not defined with the exactness required by the use of a mathematical model. In the work an approach for the construction of linear programming energy models is proposed. The approach can be summarised as follows: Linear programming is a mathematical theory of resource allocation. To construct an LP model of a system amounts to a thorough study of the real resource allocation alternatives in the system. The results are documented in the form of the constraint matrix of the problem. The mathematical methods are thus the tools available for the analyst, the problems to be solved define the goals for the work, and the real system is the object of study. Mathematical analysis leads to a better understanding of the structure of resource allocation alternatives in the system. This is the most valuable result of the work, which only can be achieved by understanding the different sides of the process: mathematics, resource allocation problems and the real system.