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System models of organization the use of computer equipment for mechanical engineering production

High responsibility and a wide variety of technological, design and project tasks are characteristic features of the machine-building enterprises of the space industry. The required product quality is achieved by automating engineering using computer hardware and software. The paper proposes complex system models for comparative evaluation of the effectiveness of the computer equipment allocation for the company units and controls the efficiency of their operation. The technique of using model of data envelopment analysis, aimed at both the identification of inefficient units and the definition of measures for the rational allocation of computer equipment, is proposed. A linear programming problem is formulated for a preliminary assessment of the use the computer technology in units. A mathematical model for constructing an efficiency practical frontier is proposed. The discrete programming problem for optimal computer equipment allocation is solved. Verification of the obtained solutions of the optimization problem is carried out using a simulation model based on the Petri net. The results of experimental studies are presented that confirm the adequacy and effectiveness of the proposed models.


Introduction
The modern engineering enterprise of the space industry has a complex organizational structure, which includes various purposes. It is due to the need for continuous improvement of produced spacecraft at every stage of the life cycle in tough resource constraints. Computer hardware and software (CHS), which are used to automate design, construction, engineering production and other processes, play a decisive role in the effectiveness of such production [1,2]. Such tools include individual computers, as well as computer systems, including processors, programs, peripheral equipment and communication channels. The complex of hardware and software (CCHS) is the totality of all computing equipment units in the enterprise.
The problem of optimal use of CCHS at industrial enterprises is one of the most important in modern information technologies. The wide range of computer equipment, the high cost and the special role of CCHS in the operation of a large machine-building enterprise determine the number of new management tasks. However, at present, the focus is only on the accounting of the procurement and operation of computer equipment. Effective management of computer technology in machine-building production can be ensured only by using the appropriate automated information system [3,4].
In general, the statement and solution of the resource allocation problems in complex technical and network information systems are considered in [5,6]. At the same time, attention was not paid to the following issues of optimizing the use of CCHS resources at the enterprise: • determination of the composition and CHS relationships located in the enterprise departments; • task allocation to be performed on the department computing equipment; • the formation of the CCHS overall structure of the enterprise and the distribution of selected tasks by departments.

The set of system models
The information and computing system of the enterprise, designed to ensure all production and business processes, changes its structure, adapting to the tasks performed during the life cycle. The methodology of structural synthesis of an evolving information system, built based on algebraic models, was proposed in [7]. A distinctive feature is the use of ordered algebraic structures, in particular lattices, in the description of an information system. A CCHS system is called lattice if its model L  is a triple: where a  -a model describing the behavior of the system, b  -a model of the system structure; One of the stages of managing a complex system is to evaluate how efficiently the individual departments of the enterprise work. As already noted, the machine-building enterprise space industry has a complex organizational structure. There is the problem of evaluating heterogeneous organizational and structural units. Recently, the DEA methodology (Data Envelopment Analysis) is finding more and more applications [8]. We use it to build models M1 and M2. M1 model is designed for comparative evaluation of the effectiveness of the existing CCHS system in different departments. It is an outputoriented Charnes-Cooper-Rhodes model (CRR-Output) with the constant returns to scale (CRS) [9]. The second M2 model also belongs to DEA and is the Banker-Charnes-Cooper model BCC-Output [10]. This model allows us to build a practical frontier of efficiency, which is a guideline for the further development of computer technology in specific units of the enterprise.
The M3 model is an optimization problem for the distribution of CHS among departments. The M4 model is a simulation environment based on Petri nets for studying the behavior of the obtained information system structure [11]. In the case of detection of conflict situations, critical paths, and other features of the operation of the CCHS, a repeated solution of the optimization problem M3 is carried out. The final decision on the CCHS optimal allocation is the basis for the development of control actions in the decision support system DSS, which is implemented by the M5 model.

Models for evaluating the CHS effectiveness
The CCR model is presented as follows: where θ -integral criterion for the department effectiveness, X is the matrix of inputs, Y is the matrix of outputs, xi and yi are the column vector of individual inputs and outputs for the i-th department in X and Y, respectively, λ is a semipositive vector (weighting factor), 0, 1,..., .
For each subset of units, the task of determining ways to improve efficiency further can be set. Model M2 P-DEA border makes it possible to form some artificial objects with an efficiency greater than 1. Such artificial objects are interpreted as targets for further improvement of the performance of real units. We consider N analyzed units for which R input parameters and S output parameters are given. The linear fractional programming problem for determining the criterion J0 of the effectiveness of an artificial object is formulated as follows: under constraints  where Z j I -the corresponding index set. For each configuration of CHS of the mth type, an Hml resource is specified, that is, the number of samples available for allocation. Moreover, we denote hkjmn -the number of samples of the mth type with nth configuration for unit j assigned to task k. We introduce the following notation:

Optimization model M3 for CCHS allocation
Consider the problem of minimizing the CCHS cost in solving a given set Z of tasks. Then the objective function F is as follows: where C -the capital cost of CCHS, E C -operating costs of CCHS. The components of the objective function are defined as follows: where Hmn is the number of samples with the mth type and nth configuration, that can be assigned to the department. The solution of problem (5) with constraints (7) -(11) was carried out using the branch-and-bound procedure.

CCHS life cycle simulation model
The solution to the optimization problem determines the structure of the CCHS among departments. As noted earlier, the verification of such an allocation is conducted using the simulation model M4. We assume that in the project management system was constructed Gantt chart for executed tasks. Therefore critical paths have been found, and for each task , the time t . Full Petri net is used to simulate the performance of production tasks in departments and analysis of the use of computer technology.

Experimental results
Test solutions for M1 and M2 models were performed for ten units (DMU): two construction departments C1 -C2, three design D1-D3 and five production departments P1 -P5. For this, the PIM-DEASoft-V3.0 software was used [12]. Baseline data for the analysis are presented in table 2. Input variables: X1 -number of employees in the unit; X2 is the CHS number in the unit; X3 -CHS performance (GFlops); X4 -the volume of tasks performed in the unit. Output variables: Y1 -the CHS downtime ratio per month, (%); Y2 is the CHS reliability; Y3 -the coefficient of completed tasks, (%). The examples of the obtained efficiency boundaries are shown in figure 3.
The most effective unit is the construction department C2. Close to the efficiency boundary are also construction and design units C1, D1, and D3. The worst performance indicators have production units P1 and P2. At the same time, production departments P2, P3 and P4 form a group having performance indicators close to the maximum value.
The program PIM-DEASoft-V.3.0 has tools for determining such changes in the input parameters of inefficient units that will transfer them to the efficiency boundary. To clarify the necessary changes, only a subset of units of the same type may be considered. As an example, figures 4 and figure 5 show graphs of efficiency boundaries for production departments P1 -P5 only. As already noted, the worst units are P1 and P2. The analysis of the CHS in the corresponding departments P1 and P2 showed that a large number of outdated computers are used, and this led to significant downtime and failure to complete tasks on time. In order to transfer to the efficiency boundary, it is necessary to change the number of input parameters. For unit P1 this is the target changes: δX1=-42%; δX2=-60%; δX4=-22%. For unit P2, this is the target changes: δX1=-46%; δX2=-49%; δX4=-5%. This will provide an increase in output parameters Y1 and Y3 to 83% and 86%, respectively.   The solution to the optimization problem M3 at the stage of experiments was carried out for departments of the Design Division. This is since such tasks require the use of several types of CHS: graphic, engineering, office, server. Information about the types and configurations of computers are in the CCHS database. Dimensions of the problem for the case under consideration: the unit number in the Design Division is 5; the number of design tasks -50; the CHS type number -7; the number of different configurations of CHS is 45. In the process of research, a test solution was made for the periods 2017 -2018 years to compare with the actual CHS allocation at the enterprise during these periods (see table 3). It is seen that the use of the proposed methodology would reduce the average capital cost by 7.5% and operating costs by 11%.

Conclusion
The proposed set of system models underlies the construction of an automated computer management system for a machine-building enterprise. Further development of the proposed approach lies in the path of integration with CAD / CAM and PDM systems. Thus, we achieve rapid changes in the composition and characteristics of computer hardware and software when changing market conditions and the release of new technology.