Staff motivation management ensures increased productivity and organization of work for the staff of the organization. There are two sets of theories of motivation [1, 2] but the constructive application of these theories is limited. A number of motivational laws are known ( Yorks-Dodson, V.Vruma, Herzberg), but their practical application is complex. Methods of motivation have been developed on the basis of the utility theory [4], in which the success of the work depends on the benefit estimates applied by the motivators. The work proposed the concept of a motivation strategy based on estimates of performance-responsibility limits to changes in motivation.

If the relationship of the R result with the motive or stimulus M is considered, the reaction of the employee can be measured by the response value:

mij = ΔRi /ΔMj (1)

which within the limit determines the limit value

mij =dRi/dMj (2)

Then, if a matrix μ= [mij] sets of private derivatives Ri is known for Mj exposure managers used, we have a model for the identification of a multiplicity of employees whose results are determined by Mj values. Of course, with the probability of workers ' reactions to motivators, the determination of average mij values is at the heart of the identification procedure. On the basis of the identification model (2), it is possible to predict workers ' reactions on average to impact management sets:

ΔRi (Sk) =Σ mij ∙ ΔMj (3)

These sets of motivators form possible employee motivation strategies and allow for the calculation of the results of the Sk strategy:

ΔR (Sk) ={ΔR1(Sk), ...., ΔRm(Sk)} (4)

With S1, ..., SK, and considering the potential results of their application, it is possible to select the most effective strategy corresponding to max Δ R(Sk). The choice is based on the use of the gradient method, as the μ matrix is a gradient and is based on the direction of motivation to the target.

On the basis of the proposed approach, it is possible to address the direct and reverse management challenge. With an existing set of motivators, a vector of motivation can be calculated and the impact of the strategy adopted can be assessed. If the purpose of the motivation is set as a result vector, the proposed model can calculate the required vectors for the purpose.

The method allows for optimization. If there are limitations on financial resources and the cost of using motivators, the objective can be defined with cost constraints. In this case, Sk policies that are subject to limitations (approved strategies) are selected and a max R strategy is selected based on the calculation of the results vectors. If there are resource constraints and their specific costs for the use of motivators, a set of constraints is being addressed.

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