__Keywords:__mathematical modeling capacity of enterprise competence of employee multitude of features evolution of multitude

Z.I. Rizaev, R.T. Sirazetdinov

This article proposes the approach and the algorithms how to solve problem of assessment of accomplishment new projects coming to company by existing staff using mathematical modeling of employee’s competence. Today the problems of shortage of qualified personnel are becoming more urgent for Russian companies. Therefore there is a need for thoroughly study and use of skills, knowledge and competencies of each employee of an enterprise, as well as more careful attention to recruitment. This problem is especially actual for companies whose activities can not be strictly normalized, such as software development, design, repair and adjustment of equipment, etc. The use of automated systems of personnel management can help alleviate this problem. However, the adequacy of the models of qualification of employees used in these systems comes to the forefront. An important task as part of this problem is to build the mathematical model of competence of an employee, of group of employees, of departments and of the enterprise.
In this paper, mathematical models of manpower of single employee and enterprise's manpower as multitude in the linear space of works performing in the company are built on the basis of formalized definition of employee's competence level as a vector in a linear space. These multitudes can evolve in time depending of the changing of competence, fluctuation of personnel, personnel training and adequately describe the ability of employees in every time moment.
Company consisting of structural departments is considered. Each department has its own list of works and executes the specified set of everyday tasks from this list. The set is defined by some predetermined time interval. The company expects the new order. It is necessary to determine whether company will manage the execution of a new order in time by their employees and to distribute the work on the new order among the workers.
The set of performed tasks by department determines the corresponding space of competencies of this department. For each department the plan of orders for each time interval is given. Each order is divided into production tasks, which are characterized by vectors of the volumes of specific types of work and deadlines. For each department the list of the performed work for each time interval is given. The new project enters to the enterprise, which is divided into stages. These stages in general do not match in time with intervals of production targets. The production tasks with the types and the volumes of works of project at each stage are given. The types of works and their total volumes at each time interval are determined on basis of the production tasks.
The production task’s accomplishment is determined by whether its work's vector is a member of manpower multitude. The project’s accomplishment in common with everyday tasks is determined by accomplishment of work’s vector in each corresponding time interval. This approach considers that manpower is the multitude of all types of work that an employee can perform.
The manpower is described by the system of equations and inequalities. The existence of solutions of the system, which is obtained after substituting into it concrete vectors of the total volume of work, means that the project is feasible. Any solution of system gives a variant of the distribution volumes of work for the project and for everyday tasks in each time interval, without prejudice to the current activities of departments. If necessary, you can enter the objective function, which allows you to select the most effective with some point of view variant distribution of works among employees. For example, the optimization problem is solved, which minimizes the total cost of salaries of employees. It is a linear programming problem and it can be solved by the simplex method. An example illustrating the application of this algorithm is given.

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