FUZZY DYNAMIC LINEAR PROGRAMMING IN ENERGY SUPPLY PLANNING - Usenik, Janez (Journal of Energy Technology, 2024)
Linear programming is an important field of optimisation. Many practical problems can be expressed as linear programming problems and be solved with a simplex method. When all data in a linear program are determined and quantities are known in advance, the simplex algorithm, i.e. the simplex method, is explicit. However, in special cases the coefficients in the linear programming problem can be a) fuzzy numbers or b) functions of time with specific requests. In this manner, we have either fuzzy linear programming in the first situation or continuous dynamic linear programming in the second. The synthesis of both methods is a fuzzy dynamic linear programming problem, which is explored in this article and represents a new method in the theory of linear programming problems. Following the theory, we have some different procedures for solving an energy supply planning problem, Fabijan, Predin, [1], Usenik, [2]. One rational possibility is to define the mathematical model as a problem of fuzzy dynamic linear programming and solve it with the new simplex procedure. In this article, the simplex method for this possibility is proposed. At the end of the article, a numerical example is shown.
Keywords: dynamic linear programming; fuzzy linear programming; fuzzy dynamic linear programming; energy system