Mathematical model of forecasting services for car services

Abstract

The method of drawing up of mathematical model of forecasting of demand for car service is offered in the work.

The development of appropriate models is an important task. The following factors were taken into account during the development:

- it is possible to change the total number of cars Navt, which are in the area of business activity of the service station;

- intensity of operation, ie the average annual mileage of cars in the region, as well as the dynamics of its change at different times of the year (j);

- average operating time per car-arrival at the service station;

- possible change in market share Kj, which occupies this company in the area of business activity;

- the share of α owners who apply to the service station.

Comprehensive consideration of the above factors allows you to predict changes in the average daily number of applications for different types of work (i), taking into account its seasonality (j).

In order to simplify the obtained model, as well as taking into account the short-term forecasting period, without losing the accuracy of the obtained result, the following constant values were adopted:

- average annual mileage;

- coefficient that takes into account the dynamics of seasonal changes in the average annual mileage - Kdj;

- the share of owners who use the services of service stations in this region α;

- the mode of operation of the service station, which is determined by the number of working days of the enterprise at these periods of the year;

- - the average complexity of one application.

Thus, forecasting the demand for service stations is reduced to estimating the change in the average daily number of calls to the service station, for which the dynamics of changes in its components was considered (1). In general, the method of forecasting the demand for service stations is determined by the average daily number of calls to the service station, and includes five stages.

The disadvantage of using this method is that missing, respectively, one or two, respectively, the first and last points of this time series. To determine them, the following expressions are used: for the moving average of three points - expressions (17) and (18), for the moving average of five points - formulas (19) - (20), respectively [1, p. 90]:

Keywords :, car services, reconstruction, efficiency, mathematical model, optimization.