Optimal management of combat

The article proposes a method for solving the problem of adapting a discrete inventory management model to the problem of combat operations of two armies. The aim is to identify the control effect on the linear system of difference equations, which allows it to be transferred from the initial to the final state in the specified parameters provided that costs are minimized. Discrete controlled processes play an important role in the theory and practice of optimal control since many planning tasks are described precisely by systems of difference equations. A system of equations of this type is characterized by a discrete type of control of the number of combat units at the current stage. Deliveries are formed at fixed intervals. The effectiveness of management is controlled (verified) by a quadratic quality criterion, which characterizes the cost of conducting combat operations. The criterion shows the total cost of supplies and maintenance of combat units, the change in the number of which is determined by three factors: the rate of losses as a result of hostilities, natural losses and the rate of receipt of reinforcements. The construction of an optimal control effect is carried out by the feedback method. It is noted that the solving this task is complicated by the fact that it is necessary to find among all possible solutions those that will make it possible to achieve your goals with the least expenditure of human and material resources. These costs are presented as functions of several variables, the values of which are known at the initial time. The article proves that in order to solve the problem of optimal resource management in relation to the case of combat operations of two armies, the feedback method is the most preferable. Several examples have been analyzed. The implementation of the feedback method clearly shows that a longer period of confrontation significantly reduces losses. The materials of the article are of practical value for strategic planning in the context of military conflicts.

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