Conducting military operations in optimal conditions must take into account the organization of the maintenance service as well. This study presents a computer application intended to design The Optimal Plan for the Organization of the Maintenance Service. This application has as theoretical support , but also intends to complete the module on the supply of spare parts shown in . It is a useful application in the process of planning a military operation, the two modules, the one presented in  and the one presented in in this study, covering the logistic support in terms of the military equipment which includes the combat means, supply and storage of spare parts, supply and storage of fuel, maintenance facilities, as well as the human resource necessary to ensure this service.
An important step in preparing a military operation is the planning one where resource requirements and related costs are assessed needed to conduct it under optimal conditions. One of the most important issues to be considered at this stage is that concerning the means of warfare which are necessary for fulfilling the tasks of the military operation. In this regard both the types of combat capabilities that are required and the number of each type of combat capabilities should be established. After evaluating the necessary means of combat, an important aspect to be considered is that of ensuring the maintenance service for the means of combat planned to participate in military operations. In this study, based on technical specifications related to maintenance operations to be carried out to maintain the operational state of combat means is shown, depending on the tasks to be fulfilled within the military operation, a way of assessing maintenance needs in order to design a plan to ensure optimal maintenance service.
Ever since the onset of algorithms for determining the optimal solution or solutions for a linear programming problem (LPP), the question of the possibility of occurrence of cycling when one or other of these algorithms are applied was born. Thus, the fundamental question regarding this issue is under what conditions the cyclic phenomenon appears for a problem of linear programming and how to construct examples in which to do so, and as a continuation of it, which methods can be developed to avoid this phenomenon. In this study we will present some aspects regarding this issue starting from the primal simplex algorithm, by highlighting some general aspects that occur when this phenomenon happens
For n-th order linear differential equations with constant coefficients, the problem to be solved is related to determining a particular solution, and then, with the general solution of n-th homogeneous linear differential equation with constant coefficients attached, to write the general solution of n-th linear differential equation with the given constant coefficients. In all the works that deal with this issue three situations are analyzed: the situation in which the free term is a polynomial P(x), the situation in which the free term is like P(x)· eα·x and lastly, the situation in which the free term is like eω·x · (P(x)· cos(β·x)+ Q(x)·sin(β·x)). In this study we aim to analyze if the free term is a combination of the three cases mentioned.
As with the n-th order linear differential equations with constant coefficients, the problem to be solved is related to determining a particular solution, and then, using the general solution of the attached homogeneous system of linear differential equations with constant coefficients, to write the general solution of the initially given system. For homogeneous systems of linear differential equations with constant coefficients, the determination of the general solution is the method of eliminating or reducing which make the system a linear differential equation of the same order as that of the system, and its methods of solving it applies or the method of own values and vectors. If the system is non-homogeneous, then we also have to determine a particular solution that can be done in the same way as in the case of n-th order differential equations with constant coefficients, if the method of reduction or elimination was used, or the method of variation of constants, regardless of the method used to determine the general solution of the attached homogenous system of linear differential equations with constant coefficients. Whichever method is used, determining a particular solution for a system of linear differential equations with constant coefficients is difficult, in this study being proposed a method similar to that of n-th order linear differential equations with constant coefficients.
A number of methods and techniques for determining “effective” solutions for multiple objective linear programming problems (MPP) have been developed. In this study, we will present two simple methods for determining an efficient solution for a MPP that reducing the given problem to a one-objective linear programming problem. One of these methods falls under the category of methods of weighted metrics, and the other is an approach similar to the ε- constraint method. The solutions determined by the two methods are not only effective and are found on the Pareto frontier, but are also “the best” in terms of distance to the optimal solutions for all objective function from the MPP. Obviously, besides the optimal solutions of linear programming problems in which we take each objective function, we can also consider the ideal point and Nadir point, in order to take into account all the notions that have been introduced to provide a solution to this problem
A complete analysis of the cycling phenomenon in the case of the linear programming problem (LPP) is far from being achieved. Even if  states that the answer to the fundamental question of this problem is found, the proposed solution is very difficult to apply, being necessary to find a solution of a complex system of inequalities. Additionally, it is difficult to recognize a problem that, by applying the primal simplex algorithm, leads us to the occurrence of this phenomenon. The example given by Marshall and Suurballe, but also the example given by Danzig, lead us to draw some useful conclusions about this phenomenon, whether the given problem admits the optimal solution or has an infinite optimal solution
Analysing the current maintenance system, one can obviously notice a disadvantage to be found in all the cases in which the maintenance activities prove useless, not resulting in finding the flaws or the conditions leading to them, the verified equipment being declared as functioning well. Thus, it becomes indispensable that a rapid and efficient strategy should be implemented for the diagnosis of the component parts of the vehicles, the maintenance based on reliability respectively, which constantly monitors the evolution of parameters so that the permanent state of the vehicle is made known, as well as the necessary maintenance activities. As such, the maintenance based on reliability promotes an efficient policy of the maintenance activities throughout the period of using the vehicle, all the expenses being offset by reducing the maintenance costs through the decrease of the immobilisation time and the number of repair operations. The paper deals with a new approach of the aspects related to the maintenance system of vehicles, relying on mathematical statistics which allows for modelling the strategies likely to be applied within the system. The results of a mathematical approach should not be neglected since the future strategies of managing the maintenance processes of the technical systems cannot be based on simple empirical reasoning, which has most often proved costly.
This paper aims to analyze the stage reached in the development and application of stochastic optimization models, highlighting some of the most important moments and achievements in the field. The author tries to identify particular aspects that define the classes of stochastic optimization models, specifying the level reached in certain directions of research and implementation of these models in order to identify possible directions of development of these specific techniques.
The determination of a particular solution for the systems of linear differential equations with constant coefficients that have on the column of free terms functions such as ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, or/and eb·x·Q(x) sinnx, n ∈ N, is based on the expansion of cosn x and sinn x, and, on the other hand, on how a particular solution for a column of free terms with functions such as ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, n ∈ N, looks like. We can also write the way a particular solution looks like when we have a combination of two or more functions on the form ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx, n ∈ N in the column of free terms.