Mathematical model of the optimization of fire extinguishing time length in the woodworking enterprises workshops - Статья

Department of tactics and rescue operations, Lviv state University to safety of vital functions Department of Doctoral, National University of Civil Protection of Ukraine 79007 Lviv, Kleparivska str., 35, e-mail: gulida24@meta.ua MATHEMATICAL MODEL OF THE OPTIMIZATION OF FIRE EXTINGUISHING TIME LENGTH IN THE WOODWORKING ENTERPRISES WORKSHOPS E. Hulida, O. Koval Received July 25. 2014 Abstract On the grounds of an analysis of the existing criteria of decision making during the fire extinguishing organization process the differential criteria is recommended for solving the optimization mathematical models. The mathematical model of the optimization of fire extinguishing time length in the woodworking enterprises` workshops is developed; it is based on the determination of a fire area during the time of its unobstructed development, the amount of the devices for the fire extinguishing agent supply, the amount of the fire and salvage units (hereinafter FSU), equipment and evacuation facilities, the duration of the fire isolation and extinguishing as well as its final liquidation. The Monte Carlo method is used for solving the mathematical optimization model. The solving of the mathematical optimization model is conducted by applying the computer hardware and application program package, written in C language. Key words: mathematical model, optimization, isolation, fire liquidation, fire extinguishing agent, fire extinguishing equipment. Statement of the problem In order to solve the optimization problems, the issue of the optimization criterion selection occupies the first place after the adoption of the target function; the main provisions of the optimization criterion selection are considered within the framework of the decision making theory [1]. The total expenses in the form of the proximate fire damage and the expenses of FSUs on its liquidation were used for determining the fire damage in the works under number 2-4. Nevertheless, for determining or forecasting such damage, the statistical data, similar to the investigated situation, is needed. Thus, the problem arises concerning the determining and adoption of the necessary criterion for solving the formulated optimization problem, the acceptance of which would not depend upon the statistical data. Regarding the mathematical model of the optimization of a fire extinguishing time length in the woodworking enterprises` workshops, it may be stated that such optimization models have not been analyzed yet. There are regulatory documents for the approximate determining of the fire liquidation duration that incorporate the numerous statistical data [5]. However, such an approach cannot be substantiated in every particular case. Thus, the problem arises concerning more precise forecasting of a fire liquidation time by means of the development of the mathematical optimization model for determining the effective time for the fire extinguishing in the woodworking enterprises` workshops. Analysis of recent achievements and publications In the work under number 6, the possibility of applying different decision making criteria for determining the forces and facilities the FSU needs for a fire response, is analyzed. The author analyses the following basic criteria: 1) minimax criterion (MM) as based on a pessimistic algorithm; 2) Baies-Laplace criterion; 3) Savage`s criterion; 4) Hurwicz’s criterion; 5) Hodges-Lehmann criterion; 6) Germeier`s criterion; 7) derivative criterion; 8) criterion of non-interaction; 9) optimistic criterion. woodwork fire extinguishing In order to make a decision concerning every aforementioned criterion it is necessary to elaborate a decision making matrix. One should introduce different possible variants of a fire spread and the appropriate variants of decision making with the proper amount of forces and facilities for fire liquidation into such a matrix. The appliance of these criteria for making a decision does not always yield rational results; nevertheless the sufficiently rational decisions may be obtained as based on them. Thus, for instance, an operations researcher T. Saati expresses his opinion regarding the decision making possibility as follows: “…an art of giving bad answers for those practical issues the answers for which, given by means of other methods, are much worse.” [7]. In the works under number 8 and 9 the differential criterion was applied for the fire damage appraisal; the criterion include two partial criteria, namely the difference between the proximate fire damages Во (the first partial criterion) and the expenses of FSUs that participated in its liquidation Вп (the second partial criterion). The difference with regard to modulus should approximate the minimal value and as an exception it may equal zero. The adoption of such a criterion may be substantiated on account of a general classification of the criterion problems [10]. The problems related to the fire liquidation pertain to the third class. A technical sy