Due to diverse geological and mining conditions of specific longwalls, amortization of mining machinery, as well as costs structure in different coal mines, daily coal output should be designated for each longwall face separately. In view of definite reserves of a given longwall panel, daily coal output determines its extraction time, thus, the analysis should also consider the time factor. Unlike popular cost allocation methods in accordance with the criteria of the relations between costs and changes in coal output, the proposed method is based on a different approach to a longwall face, including the analysis of the costs of the preparatory works stage previous to extraction works. The inclusion of the time factor has led to the derivation of three costs categories: absolutely fixed costs KBS, relatively fixed costs KWS, variable costs KZ. On the grounds of the above mentioned three costs categories an economic model was designed, enabling the designation of daily coal output depending on the reserves of a given longwall panel and its extraction time, for the assumed profit level, or for the assumed balance between the costs of coal production and the incomes from coal sales. The model incorporates the total costs of coal production, including all stages of the production process: preparation works of the longwall panel, longwall moves, extraction works, longwall shut down. The grounds for the model, in accordance with the assumed methodology, were provided by economic modelling used in diagnosing critical functional zones of longwall faces or coalmines. The three dimensional model used for designating daily coal output from a given longwall face is derived as function Q = ƒ(t, Zp) describing the surface of daily coal production Q and a function in the form of a line of intersection equation (1) constituting a boundary line between two intersecting surfaces Q and Q1:

The economic model involves the required daily output treated as an explained (dependent) variable and longwall coal resources and extraction time as explanatory (independent) variables. Other impact factors were expressed as model parameters. The selection of coal reserves and extraction time as the in consideration of the simultaneous change in coal reserves and extraction time.

The analysis of the possibilities of obtaining high concentration of extraction under definite mining and geological conditions of a given longwall face requires a model that should make it possible to designate the coal output in view of the technical potential of the longwall system. If it is assumed that the coal output is mainly conditioned by the technical parameters of the shearer loader, the model of the production process in the longwall may be utilized, as it includes: theoretical capacity of the shearer loader, the degree of its utilization under given mining conditions, parameters of the longwall face, actual worktime of mining machinery on a face, cutting sequence.

Thus, the analysis entails the technical, organizational and technological aspects. Considering a different course of the production process in the longwall, related to a specifi c nature of the two basic cutting sequences, the daily coal output from the longwall may be calculated as: WQ = Qt . T . ψT . ηt (2) where: Qt — theoretical capacity of the shearer loader, T — available worktime of mining machinery on a face, ψT — index of worktime availability, ηt — operational efficiency index. The theoretical capacity of the shearer loader under given mining conditions is derived from the following equation, in consideration of the technical parameters of the shearer loader (vmax, z) and other parameters associated with the natural conditions and a given extraction system (H, γ):

The analysis of the costs components as a crucial factor for designating the coal output was made in exemplary longwall faces in coal mine “X”. The economic model of the costs balance was used in the analysis, as well as the model enabling the designation of coal output from the technical potential of the longwall system and the proposed costs allocation system related to the longwall workings in consideration of the actual structure of the coal mine. The possibility of achieving the required coal output was examined for each longwall face in view of the balance between the production costs and incomes from sales.

Due to the range of the analysis entailing all the costs components of coal production, including: preparation of the longwall field, moves of the technical equipment, extraction of the longwall face, basic production processes in the underground section and the surface section, sales costs and overheads, six longwalls were selected for the analysis under different mining and geological conditions and various mining equipment.

The impact of the daily output to changes in the values of the costs components and coal sales prices was assessed in the course of the sensitivity analysis. The results indicate that the greatest impact on the change in the required daily output is exerted by the sale price of coal. Forecasts of coal sale prices at the stage of designing the longwall face are difficult, because the sale price does not only depend on the quality of coal, but also on management decisions undertaken by a given coal company and on some external conditions.

Relatively fixed costs constitute another factor that exerts an important impact on daily coal output. For the longwalls with extensive coal field length and, consequently, long extraction time, where the contribution of relatively fixed costs is the biggest, the main objective is to provide a higher degree of the utilization of the face production potential, which would facilitate the balance between the costs and incomes. In the case of longwall faces with short coal field length and short extraction time, the contribution of relatively fixed costs is smaller.

Absolutely fixed costs and variable costs have a certainly smaller contribution. The impact of absolutely fixed costs depends; to a large extend, on the coal field length. The sensitivity analysis indicated that for the longwalls with short coal field lengths, the impact of absolutely fixed costs is certainty stronger than for those with extensive coal field lengths, which is caused by a signifi cantly bigger contribution of these costs in the total costs of coal production. Accordingly, in case of shorter coal field lengths, special attention should be drawn to the costs of the preparatory operations and longwall moves.