Mathematical model of optimum additional charge of recreation enterprise

Mathematical model of optimum additional charge of recreation enterprise for seasons with low intensity of demand is offered. Appropriate heuristic GREEDY algorithm for the decision of the task determined by this model is presented.

Recreation enterprises are counted on maintenance of customers and possess resources, many of which can be used whole-yearly. However much the stream of customers has different intensity which depends on the temporal seasons of year. When a recreation enterprise stands from the shortage of customers, expediently addition loading of him, providing services to other customers, possibly even not on the basic type of enterprise. To that end marketing researches are conducted and new targets accounts come to light. Such actions must be executed constantly with the purpose of filling of store of basic specific resource – input stream of customers.

A store is a file in which with attachment at times descriptions and quantitative indexes are brought on the found targets accounts. It contains information about the possible users of recreation resources of enterprise – additional customers, foremost such which can take advantage of services of recreation enterprise in the seasons of the least demand.

The purpose of this paper is the revision of mathematical model and improvement of algorithm of addition loading of recreation enterprise with the purpose of his steady functioning in the seasons characterized by low intensity of input customer stream. The article continues the researches begun in [2,3].

It is assumed that the number of places in a recreation enterprise is fixed and equal $n$. In every discrete moment of time $t = t_0,t_0 + 1,t_0 + 2,...,t_0 + T - 1$ the current planned load is permanent and equal $n^*$ , and possible addition load makes a size $\Delta n = n - n^*$. Customer with a number $j$ can occupy $k_j$ places of service in the interval of time $T$ (that corresponds to the height of rectangle with a mark $\tau_j$) and to stay in the enterprise of service $\tau_j$ in succession going time units (that corresponds to the width of this rectangle). In geometrical interpretation the decided task consists of receipt maximally dense packing of the set rectangular region by the set of the fixed rectangles with limitations on piling.