Modeling operations in project management. Modeling of management decisions References

07.02.2024

Basic definitions in project management. Monitoring the progress of the project. Organizational structures. Network diagram. Temporary models. Resource management. Project progress tracking. Gangt Chart. Early-Start/Late Start Schedules. Matrix Project. Critical Path Method (CPM). Method of evaluation and review of programs (Program Evaluation and Report Technique - PERT). Time-Cost Model. Separate project (Pure Project). Project Work Breakdown Structure (WBDS). Project Management. Functional Project. Modeling product development and process selection in the manufacturing sector Product design. Design of production flow. Process analysis. Criteria for the perfection of the product creation process. Break-Even Analysis. Virtual Factory Process map. (PROCESS FLOW DIAGRAM). Matrix “House of Quality”. Continuous Flow. Production shown (Job Shop). Product-Process Matrix. Functional and cost analysis (Value Analysis/Value Engineering). Technologies in production. Integrated manufacturing systems. Technologies in the service sector. Measuring the return on investment in technology. Automated Manufacturing Planning and Control Systems (MP&CS). Automated Materials Handling Systems (AMN). Flexible Manufacturing Systems (FMS). Integrated manufacturing systems (Computer-Integrated Manufacturing - CIM). Office Automation. Computer-Aided Design (CAD). Client/Server Systems. Decision Support and Expert Systems. Image recognition systems (Image Processing Systems. Electronic Data Interchange - EDI). MODULE 3 “SERVICE DESIGN MODELS AND SERVICE PROCESS SELECTION” The essence of services. Operational classification of services. Design of service organizations. Structuring service contacts. Three types of service systems. Service in the client environment (Field-Based Services). Facilities-Based Services. Service Package. Service Guarantees. Service Blueprint. Service-System Design Matrix. Service Focus. Simulation of Queue Management The economic essence of the queuing problem. Queuing system. Queue models. Computer simulation of queues. Arrival Rate. Service Rate. Finite Queue. Multichannel, multiphase structure (Multichannel, Multiphase). Single-channel, single-phase structure (Single Channel, Single Phase). Queue. Poisson Distribution. Queuing System. Exponential Distribution. Quality Management Modeling Quality requirements and costs of quality assurance. Continuous improvement. Shinto system. Total Quality Management (TQM). Cost of Quality (COQ). Design Quality. Quality at the Source. Continuous Improvement (CI). "Zero Defects" Definition of the standard (Benchmarking). Dimensions of Quality. Poka-Yoke procedure. Conformance Quality. ISO 9000 standards. Plan-Do-Check-Act Cycle (PDCA Cycle - Plan-Do-Check-Act). MODULE 4 “MODELING PRODUCTION CAPACITY AND LABOR PROCESS” Strategic capacity planning. Capacity Flexibility. Decision Tree. Capacity Utilization Rate. Production capacity (Capacity). Capacity Cushion. Strategic Capacity Planning. Capacity Focus. Economies of scale of production (Economies of Scope). Just-in-time (JIT) production systems JIT logic. The Japanese approach to productivity. North American JIT variants. Requirements for the JIT system. JIT in the service sector. Automated Inspection. Total Quality Control (TQC). “Pull” (pull) production system “Kanban” (Kanban Pull System). Group Technology. Quality at the Source. Quality Circles. Freeze Window method. Preventive Maintenance. Network of specialized factories (Focused Factory Network). Just-In-Time (JIT) system. Level Schedule. Bottom-Round Management. Location of production and service facilities Criteria for the location of production facilities. Methods for locating industrial enterprises. Placement of service objects. Analytical Delphi model. Center of gravity method. Regression model. Factor-rating systems. Ardalan Heuristic Method. Equipment placement and room layout Basic methods of equipment placement. Placement of equipment according to technological principles. Placement of production according to the subject principle. Assembly-Line Balancing. Systematic Layout Planning (SLP) method. Office Layout. Precedence Relationship. Equipment placement according to the subject principle (Product Layout). Equipment placement based on the Group Technology Layout principle. Equipment placement based on the principle of servicing a fixed object (Fixed-Position Layout). Equipment placement according to technological principle (Process Layout). Placement of premises of service and trade enterprises (Retail Service Layout). "Service landscape" (Servicescape). Comparative method of computerized allocation of production facilities (Computerized Relative Allocation of Facilities Technique - CRAFT). Tact (Cycle Time).

MODULE 5 “MODELING THE LABOR PROCESS AND LABOR STANDARDING” Decisions made when planning the labor process. Behavioral aspects in planning the labor process. Physiological aspects in planning the labor process. Working methods. Measurement and standardization of labor. Systems of financial incentives for labor.

Work Measurement. Method of selective observations (Work Sampling). Standardization method MOST (Most Work Measurement Systems). Methods Time Measurement. Microelement standards (Elemental Standard-Time Data). Microelement standardization systems (Predetermined Motion-Time Data Systems - PMTS). Standard Time. Normal Time. Labor process planning (Job Design). Labor systems with extended responsibilities (Job Enrichment). Financial incentive plans (Financial Incentive Plans). Sociotechnical Systems. Specialization of Labor. Gain Sharing. Profit Sharing. Work Physiology. Timing (Time Study). Supply management modeling. Procurement management Supply chain management. Procurement. Just-in-time purchasing. Global sourcing. Flows of electronic information in procurement. Outsourcing. Quick Response (QR). Cargo value (Value Density). Just-in-Time Purchasing. Logistics. “Make or Buy” Strategic Partnership. Materials Management. Supply Chain. Efficient Consumer Response (ECR). Forecasting Demand management. Types of forecasting. Components of demand. Qualitative forecasting methods. Time series analysis. Causal (causal) forecasting. Choosing a forecasting method. Focusing forecasting. Computer forecasting.

Time Series Analysis. Panel Consensus. Dependent Demand. Market Research. Smoothing Constants Alpha. "Grass Roots". Delphi Method. Executive Judgment. Independent Demand. Causal Relationship. Forecasting based on linear regression (Linear Regression Forecasting). Seasonal Factor. Moving Averages. Deseasonalization of Demand. Mean Absolute Deviation. Tracking Signal. Trend Effect. Focus Forecasting. Exponential smoothing.

Aggregate planning

Types of planning. Hierarchical production planning. Cumulative production planning. Cumulative planning methods. Long-, medium- and short-range planning (Long-, Intermediate- and Short-Range Planning). Inventory on Hand. Master Production Schedule (MPS). Capacity Requirements Planning (CRP). Preliminary planning of production capacity (Rough-Cut Capacity Planning). Mixed Strategy. Aggregate Planning. Production Planning Strategies. Pure Strategy.

One of the features of modern management science is the use of models. As M. Mescon, M. Albert and F. Khedouri note, the most visible and perhaps the most significant contribution of the scientific management school is the development of models that allow objective decisions to be made in situations that are too complex for a simple cause-and-effect assessment of alternatives.

As defined by R. E. Shannon, “a model is a representation of an object, system, or idea in some form other than the whole itself.” In this sense, all management theories are, in fact, models of the operation of an organization or any of its subsystems. The main characteristic of a model is its simplification of the real situation to which it is applied. After the model is created, the variables are given quantitative values. This allows each variable and the relationships between them to be objectively compared and described.

Reasons for the active use of the modeling method:

The natural complexity of many organizational situations;

The inability to conduct experiments in real life, even when they are necessary;

Management's orientation to the future.

Thus, situation modeling is a powerful analytical tool that allows one to overcome many of the problems associated with decision making in complex situations.

Main stages of building a model:

1. Clarification of the problem statement.

2. Formulation of laws connecting the main parameters of the object.

3. Recording the formulated patterns in mathematical expressions.

4. Study of the model based on a comparison of actual performance indicators with those calculated by the model (theoretical and/or experimental analysis).

5. Accumulation of data about the object under study and adjustment of the model in order to introduce additional factors, restrictions and criteria.

6. Application of the model to solve object management problems.

7. Development and improvement of the model.

When modeling a management situation, three basic types of models can be used: physical, analog and mathematical models.

Physical model allows you to explore something using an enlarged or reduced description of an object or system. For example, a designer's drawing reduced to a certain scale.

Analog model represents the object under study as an analogue that behaves like a real object, but does not look like one. For example, a graph illustrating the relationship between production volume and costs, or an organizational chart of an enterprise.

A mathematical (symbolic) model uses symbols to describe the properties or characteristics of an object or event. This type of model is probably most often used in organizational decision making.

In the 1930s XX century At the intersection of mathematics, statistics and economic theory, a new branch of economic science arose - econometrics. Methods of econometric analysis were quickly in demand in management theory.

Econometrics– a scientific discipline, the subject of which is the study of the quantitative side of economic phenomena and processes by means of mathematical and statistical analysis.

The main tool of econometrics is the econometric model, the task of which is to test economic theories on factual material using the methods of mathematical statistics. Among its ultimate applied tasks in management, two are distinguished: forecasting the development of the management situation and simulating various possible scenarios for its development.

When constructing an econometric model, analysis methods such as regression analysis, time series analysis, systems of simultaneous equations, as well as other methods and tools of probability theory and economic statistics are used.

In its most general form, any econometric model constructed in the form of a system of linear equations can be written as follows:

where y is the vector of current values of endogenous variables of the model;

A is the matrix of interaction coefficients between the current values of the endogenous variables of the model;

Z – matrix of coefficients of influence of lagging (lag) variables of the model on the current values of endogenous and modeled indicators;

C – matrix of external influence coefficients;

x – vector of values of exogenous indicators of the model;

t – time period index;

I – delay index (lag);

p – duration of the maximum lag.

The number of different specific models used in management is as large as the number of problems for which they were developed. The most common types of models used in analysis, solution development and forecasting of management process development are: game theory, queuing theory model, inventory management model, linear programming model and simulation modeling.

Game theory is a method for modeling the assessment of the impact of a decision on competitors. This is a mathematical method for studying optimal strategies in games, or analyzing optimal decision making in conflict conditions. In this case, conflict and game are a kind of mathematical synonyms. A game is a process in which two or more parties participate, fighting for the realization of their interests.

American mathematician made a great contribution to the development of game theory John Nash. Before J. Nash, mathematicians worked on so-called zero-sum games, in which one side's gain is equal to the other's loss. J. Nash developed a methodology for analyzing non-zero-sum games - a class of games in which the winning sum of the winning participants is not equal to the losing sum of the losing participants. An example of a non-zero-sum game would be negotiations over a salary increase between a union and company management. Such a conflict situation can end either in a long strike in which both parties will suffer, or in the achievement of a mutually beneficial agreement. J. Nash also mathematically modeled a situation in which both parties use an ideal strategy, which leads to the creation of a stable equilibrium.

The practical application of game theory makes it possible, on the one hand, to predict the actions of an organization’s competitors, and on the other hand, it makes it possible to overcome intra-organizational conflicts by modeling them taking into account all components. Because real-life management situations are very complex and change rapidly, game theory is not used as often as other described models. Nevertheless, it is necessary when it is necessary to determine the most important factors that require consideration in a decision-making situation in a competitive environment.

Queuing theory model, or optimal service model, is used to determine the optimal number of service channels in relation to the demand for them. Queuing models are a tool for determining the optimal number of service channels to have in order to balance the costs of too few and too many service channels. Situations in which this model is applicable include, for example, bank clients waiting for a free teller, waiting in line for machine data processing, equipment repair technicians, etc.

Inventory management model used to determine the time of placing orders for resources and their quantities, as well as the mass of finished products in warehouses. The purpose of this model is to minimize the negative consequences of stockpiling, expressed in certain costs. These costs come in three main types: ordering, storage, and losses associated with insufficient inventory levels.

Linear programming model used to determine the optimal way to allocate scarce resources in the presence of competing needs. Linear programming is usually used by headquarters specialists to resolve production difficulties.

According to surveys, the most popular models among practicing managers are linear programming and inventory management.

Since all the models discussed are “reality substitutes,” they imply the use of imitation. But imitation as a method modeling denotes the process of creating a model and its experimental application to determine changes in a real situation. As a rule, simulation is used in situations that are too complex for mathematical methods such as linear programming. This is due to a large number of variables, the difficulty of mathematically analyzing certain relationships between variables, or a high level of uncertainty.

One form of model building is economic analysis. A typical “economic model” is considered to be a break-even analysis.

A specific modeling method is neuro-linguistic modeling. At the same time, NLP is not entirely a quantitative method. It is based on mechanisms and ways of modeling people's subjective experience. The main tasks of NLP are to model specific or exceptional abilities for their subsequent assimilation by other people. NLP modeling is quite often used in personnel management, for example, when building effective communications.

Decision making methods. Decision making theory aims to improve the rationality of management decisions. This theory can be considered as a further development of operations research. The subject of the theory of management decisions is the decision-making process itself, the formation of selection principles, the development of evaluation criteria and methods for selecting decisions that are most consistent with the goals set.

Almost any decision-making method used in management can technically be considered a type of modeling. However, traditionally the term “model” refers only to methods of a general nature. In addition to modeling, there are a number of methods to help make objectively informed decisions about choosing among several alternatives.

the one that most contributes to achieving the organization's goals. In this sense, the main methods of decision making are the payment matrix and the decision tree.
Payment matrix is one of the methods of statistical decision theory. This method helps the manager in choosing one of several solution options. For example, in choosing a strategy that is most conducive to achieving goals.

A decision tree is a method used to select the best course of action from available options. A decision tree is a diagrammatic representation of a decision-making problem. Like the payoff matrix, the decision tree allows the manager to “consider different courses of action, relate financial results to them, adjust them according to the probability assigned to them, and then compare alternatives.” From this perspective, an integral part of the decision tree method is the concept of expected value. This tool is most applicable for making sequential decisions.

It must be emphasized that the methods presented in this chapter do not represent a complete list of quantitative research methods used within the framework of modern management science. However, they provide a general idea of the different classes (types) of research and decision-making methods.

Thus, the quantitative approach to management consists of the application of statistical methods, optimization models, information models and computer modeling methods. The use of various methods developed within the framework of a quantitative approach can significantly improve the quality of decisions made based on the use of a scientific approach, situation modeling and systemic orientation of research.

______________________________________________________________________________________________________________________

Meskon M., Albert M., Khedouri F. Fundamentals of management: trans. from English Moscow: Delo, 2005. P. 226.

Ayvazyan S. A. Fundamentals of econometrics. Moscow: UNITY, 2001. pp. 19–20.

Meskon M., Albert M., Khedouri F. Fundamentals of management: trans. from English Moscow: Delo, 2005. P. 236.

Meskon M., Albert M., Khedouri F. Fundamentals of management: trans. from English Moscow: Delo, 2005. pp. 241–242.

Output of the tutorial:

History of management: textbook / E. P. Kostenko, E. V. Mikhalkina; South Federal University. - Rostov-on-Don: Southern Federal University Publishing House, 2014. - 606 p.

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

Posted on http://www.allbest.ru/

1. Methodsituational modeling in management decision making

Situational modeling is based on a model theory of thinking, within the framework of which the main mechanisms for regulating decision-making processes can be described. At the center of the model theory of thinking is the idea of the formation in the structures of the brain of an information model of an object and the external world. This information is perceived by a person on the basis of his existing knowledge and experience. Expedient human behavior is built by forming a target situation and mentally transforming the initial situation into a target one. The basis for constructing a model is the description of an object in the form of a set of elements interconnected by certain relationships that reflect the semantics of the subject area.

Modeling complex economic, political, and social situations with feedback and a large number of control parameters requires specialized tool packages, including an internal model description language, numerical integration tools, optimizers, and a developed interface.

Today, one of the effective ways to analyze critical situations, as well as the functioning of complex organizational and technical complexes, is situational modeling systems.

The implementation of the formation of an enterprise strategy based on the use of situational modeling methods involves the implementation of a number of stages:

Justification for the formation of a strategy based on a strategic analysis of the actual operating conditions of an industrial enterprise;

Development and use of a certain type of models or their combination for a formalized description of situations;

Modeling the development of situations under various scenarios of changes in the external and internal environments of the enterprise;

Involving as many managers, specialists and performers as possible in the process of modeling situations.

It is traditionally believed that the situational approach should be used only when solving current organizational problems. But the formation of a development strategy involves taking into account the current circumstances, the internal and external environment of the enterprise and other factors. This allows us to draw a conclusion about the advisability of using a situational approach in the case under study.

Situational modeling allows you to solve problems such as monitoring data, analyzing trends in the situation, forecasting and modeling behavior at the strategic and operational levels. Situation modeling systems are a universal tool for managing and supporting decision-making in major organizations, government agencies and various other companies. The most important component here is dynamic (simulation) modeling tools, which allow one to calculate the possible consequences of different scenarios. The process of situational modeling uses optimization methods to find the best solution, assess risks, forecast and conduct business games.

In recent years, knowledge discovery in databases (KDD) technologies have been actively developing. Based on KDD technology, a large number of software products have been developed that are suitable for solving information and cognitive problems. Elements of automatic data processing and analysis are becoming an integral part of the concept of “data warehouses” (data mining). Text-analytical systems (TAS) can be of greatest importance, allowing one to extract and analyze the knowledge necessary for decision-making from large information arrays.

Document management and knowledge extraction software, as well as powerful report builders, allow you to aggregate elements of different descriptions into a single workspace and provide a view of the problem from different points of view simultaneously. A special section of the situation center organizes monitoring and visualization of key parameters, extraction of tacit knowledge from texts and data, as well as generation and publication of reports. Thanks to the implementation of the above functions, it becomes possible to organize computer data processing not from application to application, but from one problem to another, which makes it possible to build a unified system for making collective decisions.

To define a situational system, it is necessary to first understand the concept situations. The word itself is used every day in a variety of aspects and is sometimes inseparable from such concepts as state, event, process, position, etc. The founders of situational management, Klykov [Klykov, 1974a] and Pospelov, in their early works clearly identify the situation with the state. A situation (discrete set) is understood as a set of transactions (operational elements) located at certain points of a static system [Pospelov, 1972]. Later, the authors expand the concept by adding information about connections between objects: "the current situation is the totality of all information about the structure of an object and its functioning at a given moment in time"[Pospelov, 1986]. All information also implies cause-and-effect relationships, which can be expressed by many sequential events or processes. In this sense, the situation is fundamentally different from the state and event, which can correspond to only one point in time.

Rice. 1 - Classification of situations.

Some authors, trying to separate a situation from a state, consider it as a synonym for the word relationship. Other researchers of this issue present the situation as a kind of generalizing concept. In Fig. 1. classification of situations is given.

This approach is quite controversial and controversial, but nevertheless indicates the basic elements that can be used to determine the situation. Based on this, two important properties of the situation can be identified: multiplicity and heterogeneity of source data. It is important to note that the situation always represents some kind of assessment (analysis, generalization) of a set of data. Moreover, this assessment is subjective, because it depends on the means and methods of generalization of a particular person (human-machine system).

Summarizing all the above formulations, the situation can be defined as follows: The situation of the system is an assessment (analysis, generalization) of a set of characteristics of objects and connections between them, which consist of constant and cause-and-effect relationships, depending on the events that have occurred and ongoing processes.

A generalized description (display) of a system using situations is called situational model(CM). In this regard, all situational systems can be called situational modeling systems (SMS). The abbreviated name for this class of systems is more euphonious than “SS” and differs from frequently used abbreviations of such terms as semiotic system, semantic and situational networks.

Quite often, SM is mistakenly called simulation, thereby equating situational modeling with simulation. If the system only displays information, and the understanding of the situation is formed exclusively by the subject, then it (the system) is no different from tracking systems. Any program where a model is created, or a device that broadcasts real objects, can be called SSM, SC or situation room.

To narrow the class of systems under consideration, we introduce the following definition: SMS is understood as a set of software and hardware that allows you to store, display, simulate (imitate) or analyze information based on MS.

It is quite difficult to give a clear definition of the term “situation center” (SC). In the most general terms a situation center (room or hall) can be called a room where a current situation is observed or a possible situation is analyzed. However, with this approach, any room in which there is an observer and a television broadcasting news about the situation in the country can be considered a situation room. If the room also has a radio, telephone, fax, computer and geographic map, then the room can be called a personal SC.

SC can be divided into external And internal. External SCs serve as a technical or information environment necessary for operational personnel to assess the situation. Internal SCs operate with the concept of a situation at the level of display, modeling, analysis or management. In fact, internal SCs automate the processing of the situation itself, and external ones automate the initial data necessary for its identification and analysis. For further consideration, we will accept the following definition of SC (internal):

SC is a set of software and hardware, scientific and mathematical methods and engineering solutions for automating the processes of display, modeling, situation analysis and control.

SC is a set of various SMS, scientific and mathematical methods and engineering solutions for automating control processes.

The structure of the SC, like any automated control system, includes various types of software (software, technical, linguistic, etc.). The SC has 4 main levels: scientific and mathematical, engineering, software and technical. The scientific and mathematical level is a set of scientific theories, methods, algorithms, research and development necessary for the implementation of other levels. It allows you to justify the feasibility of creating a SC, determine the effectiveness of its functioning, integrate heterogeneous components, and carry out correct and timely correction of errors.

The engineering level represents specific decisions in the selection and development of hardware and software. It includes the necessary technological and design calculations, models of technical devices and premises, program specifications, operating algorithms, etc.

The software and technical levels contain the appropriate software necessary to implement the tasks and functions set at the upper levels. The levels include the following required components:

--measuring (sensory environment);

--information (situational or simulation) model of the environment;

--information support environment;

--hardware support environment;

--visualization environment;

--operational staff.

Under measuring (or sensory) The SC environment is understood as a set of hardware and software used to obtain information about the state of the problem environment. These can be antenna systems, communication channels, video and audio transmissions, sensors, etc. The main task of the measurement environment is to ensure the adequacy of the SC information model to some selected fragment of the real world.

Information (situational or simulation) model of the environment is a set of at least the following components [Gasov, 1990]: a thematic component that defines the set of modeled concepts of the problem environment; the spatial component, which specifies the spatial relationships between model objects; the graphic component, which specifies the mapping of model objects into a set of graphic symbols (graphic primitives). resolution management decision storage

Information support environment -- This is a set of programs and information flows that ensure the functioning of the information model and visualization environment of the SC. First of all, this includes SMS, expert systems and simulation systems. A characteristic feature of any SC is the linking of the situational model to the terrain, so it may include geographic information systems. For example, the report [Friedman, 1999] discusses a decision support system using situational modeling based on GIS. To assess the development of situations, forecasting systems based on neural networks and genetic algorithms can be used. The effectiveness of graphic and text presentation can be achieved through the use of fractal and cognitive graphics.

Hardware support environment-- this is a set of technical computing tools that ensure the functioning of the information support environment of the SC: computers, office equipment, network equipment, etc.

Visualization environment is a set of screens for collective and individual use, providing an information and command interface between a human operator and the hardware and software environment of the SC.

Operational staff -- This is a team of specialists that has its own internal organizational structure. The purpose of the operational staff is to provide a solution to a set of regular tasks of the SC based on an analysis of the information model of the real world situation, generated by the hardware and software environment of the system.

2. Ethical basis for preparing management decisions. Moral decision

The process of making a management decision is inextricably linked with its information support. In a market economy, independent, independent producers of goods and services, as well as all those who ensure the continuity of the cycle “science - technology - production - sales - consumption” will not be able to successfully operate in the market without information. An entrepreneur needs information about other producers, about possible consumers, about suppliers of raw materials, components and technology, about prices, about the situation in commodity markets and capital markets, about the situation in business life, about the general economic and political situation not only in his own country, but and throughout the world, about long-term trends in economic development, prospects for the development of science and technology and possible results, about the legal conditions of business, etc.

The reasons for the existence of different approaches to the problem of choosing a solution and its rationality can be found only when it is clear that since decision-making in management is a systematized process, then the systematicity of this process should be a function of the influence of some factor that acts as the basis or the foundation on which all these approaches are built - economic, social, behavioral, etc. If we assume that the decision-making process consists of four phases: motivation for developing a solution; technology and mechanism for developing a solution; choice of decision (volitional act - motivation); the results of the decision (the consequence of the choice are motivated in advance), then the starting point is motivation. However, motivation in the psychological understanding is nothing more than the conditioning of volitional actions by certain motivating reasons.

The issue of responsibility for making management decisions places a heavy material, moral and political burden on decision makers. However, responsibility in this context is intertwined with the concept of property, or more precisely with the ownership of property rights, be it direct (as in a private organization) or indirect (as in the case of collective or public organizations). And power and its hierarchies in an economic organization are inseparable, as is known, from the right of ownership.

Ethical issues often arise in management. They go far beyond the commonly discussed issues of bribery, collusion, and theft, penetrating into areas such as corporate borrowing, politics, marketing, and capital investment.

“Right”, “right” and “fair” are ethical concepts. They express judgments about human behavior that is considered fair. We believe that there are right and wrong ways to behave towards other people, right and wrong actions, fair and unfair decisions. These beliefs are our moral standards. Moral standards vary from person to person because the values on which these standards are based are also different; and no one can say with certainty that a given moral norm is right or wrong, provided that this norm actually reflects our duties to other members of the community, and is not just beneficial to us. The problem is that it is quite difficult, even in the simplest situation, to distinguish between “us” and “others” and between “benefits” and “responsibilities”, and it is especially difficult to make this distinction in management. Why? Business always involves different groups of people - managers at different levels and with different functions, workers with different skills and degrees of training, suppliers of different materials, distributors of different products, lenders of different types, shareholders of different holdings, and citizens of different communities, states, and countries - and the benefit for one may serve as a negation of responsibilities in relation to other specific groups of people.

Ethical dilemmas are in fact management dilemmas because they represent a conflict between the economic performance of an organization (measured by revenues, costs, and profits) and the social reflection of its activities (manifested in obligations to people both inside and outside the organization). The nature of these obligations, of course, can be interpreted in different ways, but most often they include measures to protect loyal employees of the organization, create competitive markets, and produce products and services that are useful and safe for members of the community.

Upon closer examination of the relatively minor problem that an anxious manager faces in trying to understand the nature of the above-mentioned ethical dilemma, five conclusions can be drawn regarding the complexity of managerial ethics:

1. Most ethical decisions have broad implications.

The results of management decisions and actions are not limited to the consequences of the first level. On the contrary, their effects spread throughout society, and this spread is the essence of the ethical dilemma: managers' decisions have an impact on other people - both within the organization and within society - who are beyond their control, but must nevertheless be taken into account during decision making. Bribes change government procedures. Environmental pollution affects the health of community members. The use of hazardous materials can ruin the life of an individual. There is a dilemma here because most people recognize the broad consequences of management actions. The dilemma stems from the existence of multiple alternatives, mixed results, doubtful cases and personal involvement, which complicate the decision-making process leading to the above actions.

2. Most ethical decisions have multiple alternatives.

It is generally believed that ethical issues in management are fundamentally dichotomous - a choice between "yes" and "no" and no other alternatives. Should a manager pay a bribe or not? Should a factory pollute the air or not? Should the company produce dangerous products or not? Although the dichotomous structure presents ethical issues in sharp contrast, it does not accurately reflect the managerial dilemma. As numerous examples demonstrate, multiple alternatives must be considered in making ethical choices.

3. Most ethical decisions have mixed results.

It is generally believed that ethical issues in management are largely the antithesis of financial returns and social costs. Pay an indirect bribe, but retain the commercial volume of imported goods through instant delivery. Cause some harm to the air or water environment, but avoid unnecessary costs for the installation and operation of treatment facilities. Develop some product that is dangerous to humans, but reduce material and labor costs. Like the dichotomous structure, the antithesis model for outcome assessment acutely represents ethical issues but does not accurately depict the managerial dilemma. Social benefits and costs as well as financial income and expenses are associated with almost all alternatives in ethical choices.

4. Most ethical decisions have questionable consequences.

Ethical issues in management are generally considered to be free of risk or doubt, having a known outcome for each alternative. Pay the bribe and receive the imported goods quickly. Invest in a wastewater treatment plant and emissions will be reduced by X percent for Y cost of operation. Produce a completely safe product at an additional cost of Z dollars per unit. A deterministic model - that is, one without probabilities - simplifies the analysis process, but does not accurately describe the management dilemma. Because it is not at all clear what consequences any of the alternatives under consideration will lead to, and it is not at all clear what consequences most of the ethical decisions made will lead to.

5. Most ethical decisions are self-interested.

It is generally believed that ethical issues in management are largely impersonal, separate from the lives and careers of managers. In fact, every character trait of an individual manager is unmistakably present in the decisions he makes, and often the desire to advance his own career outweighs the manager's obvious obligations to other members of the organization or community, although in his own eyes his actions may be well motivated from his point of view. morality.

Ethical decisions are not simple choices between right and wrong; they are complex judgments about the balance between the economic and social behavior of an organization. Should there be a balance between economic and social behavior? How to achieve this balance? Three methods of analysis are relevant here: economic, legal, and ethical.

1. Economic analysis-- the ability to consider many of the problems of management as having a certain ethical content from the point of view of microeconomic theory, relying on impersonal market forces in choosing a solution between economic and social behavior.

2. Legal analysis- the ability to consider each of the problems that have ethical content on the basis of legal theory, relying on impersonal social forces in the choice between “right” and “wrong”. The core belief here is that a democratic society can make its own rules and that if people and organizations follow those rules, then the members of that society will be treated as fairly as possible.

3. Ethical analysis-- the ability to consider each of the problems that have moral content, using the structure of normative philosophy, relying on basic principles in choosing between “right” and “wrong.” The belief underlying normative philosophy is that if all rational individuals in a society act on the same principles of utility and logic, then the members of that society will also be treated as fairly as possible.

So there are three forms of analysis that can help achieve a relatively correct balance between economic and social behavior. These forms of analysis are: economic, based on impersonal market forces; legal, based on impersonal social forces; and philosophical, based on personal principles and values.

But neither economic, nor legal, nor philosophical analysis alone is completely satisfactory as a means of resolving ethical dilemmas. When we try to find a balance between the economic and social behavior of an organization, neither form provides us with a method of deciding on a course of action that we can say with certainty is “right,” “true,” and “fair.”

Economic analysis. The pursuit of Pareto Optimality through impersonal market forces is quite attractive - all we have to do is maximize revenues and minimize costs, and markets coupled with political decisions will eliminate or negate the harm and loss we cause to others. However, there are both practical and theoretical problems with microeconomic theory. We must admit that markets are not that efficient and voters are not that generous.

Legal analysis. The concept of impersonal social processes is also attractive - all we have to do is obey the law, and then we can feel that we are following the collective moral standards of the majority of the population. However, this concept falls apart when we are faced with the process where individual norms, beliefs, and values are institutionalized into a legal structure. It must be admitted that there are too many differences, too many compromises between individual moral values and standards, and national legal laws.

Philosophical analysis. The concept of personal rational analysis is also attractive - all we have to do is base our decisions on a particular moral principle (preference or consistency) or a particular value (justice or freedom) - but rational analysis has an inherent flaw. When attempting to use any of the principles or any of the values in moral resonance, we find that we must add a second principle or a second value (often directly contradictory to the first) into the chain of cause to reach the logical conclusion. We must recognize that a combination of conflicting principles or values cannot be rational.

If one of the decisions or actions produces adequate financial returns, is consistent with current legislation, provides significant benefits to the majority of members of the community, when one would want everyone to act in this way, faced with the same set of alternatives and underlying factors, that it is “fair” in in the sense of increasing the potential for social cooperation, and "impartially" in the sense of realizing the ability of others to make their own choices - then a decision or action can be said to be "right", "correct" and "fair".

List of used literature

1. Mardas A. N., Mardas O. A. Organizational management. St. Petersburg: “Peter”, 2003 - 336 p.

2. Pereverzev M.P., Shaidenko N.A., Basovitsky L.E. Management M.: INFRA-M, 2003 - 288 p.

3. Khomutskaya L. P. Ethical problems of management. // Ethical and aesthetic: 40 years later. Materials of the scientific conference. September 26-27, 2000 Abstracts of reports and speeches. SPb.: St. Petersburg Philosophical Society, 2000. P.160-164

4. Emerson G. Modern management. M.: “NORMA”, 2005 - 434 p.

Posted on Allbest.ru

1. Project model

In accordance with PMBoK 5 (1), several areas of project management knowledge are distinguished (we will not touch on all of them). In each of the areas, the project is examined from different angles, various entities/objects, management methods and their impact on the project are highlighted, as a way of organizing work to achieve a specific goal or solve a problem. Here we will only briefly describe typical objects that can be identified in project management, their characteristics, relationships, as well as the general mechanics of simulation modeling and its correspondence to the project life cycle.

Typical objects and their characteristics
Project has the following characteristics: manager, name, type, planned start date, actual start date, planned end date, actual end date, current life cycle status, initial project balance, current project balance.
Characteristics calculated or determined on the basis of other objects: project team, percentage of work completed, backlog or lead in the amount of work completed, backlog or lead in terms of deadlines, planned cost.
Task/Job– similar characteristics with the project are indicated here, to which the following are added: receiver, responsible executor, type of work performed, project, location, percentage of completion.
Characteristics calculated or determined on the basis of other objects: sequence of execution within the project, composition of performers, history of state changes, cost of completing the task/work.
Material resource(fixed assets): type of object, date of registration, date of commissioning, name, book value.
Calculated or determined: depreciation, current condition, where it is currently used, schedule of use.
Consumable resource(raw materials, spare parts): resource type, initial inventory, location, delivery date, expiration date.
Estimated or determined: current reserves, consumption rate
Staff: Full name, permanent location.
Estimated or determined: availability for work, compatibility with other employees, current placement for the duration of the work, where involved, work schedule.
Risk: probability of occurrence, cost of damage, description, duration of impact, risk trigger indicator.
Calculated or determined: measures to eliminate consequences, measures to prevent occurrence or evasion, cost, implementation deadlines.

Relationships and dependencies
Project - task– are carried out within the project time limits.
Task--task– may have a hierarchical connection (vertical), or may have a connection in the form of an indication of the execution sequence (horizontal).
Material resource - task– is linked through the schedule relationship to the task indicating the usage schedule.
Consumable resource - task– is linked through the relationship of the schedule to the task, indicating the required reserve for its implementation.
Personnel is a task– can be used within several tasks, for which a work schedule and the percentage of use in the task are indicated.
Risk--[Object]– when indicating a relationship with [Object], the probability of occurrence is indicated.
Of course, this is not a complete list of objects.

Mechanics
Each modeling cycle corresponds to a fixed time - 1 day/hour of the project being carried out. To do this, we will accept all deadlines and intervals in the project as multiples of 1 day/hour. The simulation cycle diagram is shown below:

The modeling cycle is as follows:

Sets the initial values for the project for the simulation. A project is created, a project schedule and a risk tree are prepared. At this stage, the functions of intellectual support for project management are also available, but this step cannot be completed without the decision-maker.
The iteration begins with determining the effective values.
Performing a beat. Each simulation cycle performs the following operations:
- resources are spent on tasks,
- the probability of failures (risks) is checked,
- a certain amount of work from the list of works for the project is performed,
- financial transactions for the project are carried out.
Calculated values for a specific cycle are saved
Checking the conditions for completing the simulation.
Completion of the simulation and output of results (analytical, aggregated and detailed values by modeling steps). When the simulation ends, the last (final) values and reasons for stopping the simulation are saved.
Providing information to the user (or decision maker - decision maker) about the status of the project without using optimizations, analytics modules and decision support. The user is required to react to the current state (if necessary) or continue the simulation.
Evaluation of the user's management decisions based on current values, as well as a retrospective of their changes and management decisions made by the user using optimization algorithms, analytics modules and decision support.

In accordance with the project life cycle, we will distinguish:

initialization and planning of the project - step 1
project implementation – 2-5, 7 and 8 steps of the cycle
completion of the project - step 6

General remarks
All data from intermediate simulation steps is saved and accumulated within the current simulation. During further operation of optimization algorithms (at step 8 of the simulation cycle), data from both the current and previous completed simulations can be used (adjusted for the result of the completion of the simulation).
When there are several simultaneously executed works of a project, the simulation for them is performed as if in parallel (i.e., simultaneous execution is simulated), in the absence of disagreements on the resources used.
When there are multiple employees/resource types, the simulation is performed for each of them in parallel (i.e., consumed simultaneously), unless there is disagreement about the resources used.

2. Implementation technologies

Key issues addressed:

storing the project data structure in the database
interface for user interaction with the database structure
tools for implementing a simulator server
interface for interaction between the database and the simulator server
storing the neural network and intermediate steps of the simulator iteration
interaction between the application interface and the neural network

It’s easy to notice that project objects and the connections between them can be easily represented as relations in a relational database and stored in this form is also not difficult, i.e. A relational database will suffice - MySQL, for example.
To develop the interface, we will choose the Yii 2 framework (and the corresponding technology stack - PHP, HTML, etc.).
Simulation server implementation – Node.js
Implementation of a neural network for Node.js, for example -
Interoperability with frontend (Yii2) and Node.js - github.com/oncesk/yii-node-socket
The question remains open about the storage format of the neural network itself, which is subject to the following requirements:

Reflection of the properties of a neural network (interrelations, weights of connections, etc.)
Secure access (to exclude direct user influence on the network)
Possibility of network training.

3. Control logic

For each area of project management knowledge, there are problem statements and described mathematical methods for solving them, with which the author is superficially familiar. Depending on the control model, knowledge of these rules and methods for solving problems should be redistributed between the system and the user. The following management models are identified: (1)

management with notifications– the system does not affect the object (project), but displays notifications about changes in indicators and the ability to perform actions (decision making and maximum knowledge are required from the decision maker).
interactive control– the system offers control actions, but the decision remains with the decision maker (decision making remains with the decision maker).
heuristic control– the system makes decisions and carries out some actions independently (the decision maker is excluded from the management process).

The implementation of management itself consists of monitoring and analyzing the totality of project characteristics and assessing their deviation from “normal” for a given time, taking into account the dynamics of their change. Control actions are selected based on the data obtained (i.e., if there is a correspondence to such a combination of characteristics of any influence), and similar projects with similar situations and the decisions made in them are also analyzed. In accordance with the degree or level of deviation, certain methods of influence can be used:

Redistribution of resources between tasks;
Redistribution of labor resources between tasks;
Changing the task execution schedule;
Procurement planning;
Avoiding or taking measures to eliminate the consequences of risks.

For methods of influence, the following characteristics are important: degree of compliance with the situation, duration of implementation, cost of implementation, possible start time of implementation. To determine the applicable method of exposure it is important:

Characteristics specified by experts.
Availability of information in the accumulated database of completed projects.

It is logical to build these mechanisms using neural networks and fuzzy logic. These algorithms can be used both at the initialization and planning stage of the project, and at the stage of its implementation. It is possible to perform an analysis of how the characteristics change after applying a control action.

4. Intellectualization of imitation

That. At the step execution stage, it is possible to completely exclude the decision maker from the control process. What is needed for this? To model events, some characteristics need to be clarified (approximately). To perform control actions, the system must “know” some additional information regarding the subject area, for example:
1. Redistribution of resources between tasks.

interchangeability of resources - can be specified by correspondence tables-matrices;
probability of resource failure – the probability is indicated in the range from Xmin to Xmax;
the possibility of parallel use by several executors - as a logical property of the task.

2. Redistribution of labor resources between tasks.

interchangeability and incompatibility of personnel - can be specified by correspondence tables-matrices;
productivity of labor resources - as a calculated value based on data on: work experience, age, advanced training, etc.
the relationship between the types of work performed and the skills required to perform it is similarly solved by matrices;
probability of absenteeism of labor resources (probability of illness) – the probability is indicated in the range from Xmin to Xmax;
the possibility of parallel execution of one job by several executors - as a logical property of the task.

3. Changing the task execution schedule.

is it possible to suspend the task, or should execution be continuous - as a logical property of the task;
whether a task is included in the “critical path” (i.e., the timing of its completion directly affects the timing of the completion of the project) is determined by the system “on the fly”.

4. Procurement planning.

the intensity of resource consumption is determined by the system “on the fly”.
the possibility of purchasing the necessary equipment - as a logical property of the task.

5. Avoiding or taking measures to eliminate the consequences of risks.

probability of equipment failures – the probability is indicated in the range from Xmin to Xmax;
possible options for evasion and elimination of consequences - are solved by matrices or lists of compliance (indicating the degree of compliance).

This is not an exhaustive list of tasks. Here it is also necessary to note the fact that there cannot be a universal solution for any project and what is good for one project is death for another. That. certain key characteristics are needed, their combinations, and their values, which would allow typing and classification, selecting similar projects for training the system, for example:

types of resources involved;
types of tasks assigned;
qualifications and skills of the personnel involved;
budget size;
duration of the project;
project success;
number of participants, etc.

Not the least role will be played by the uncertainty factor of both the characteristics described above and the characteristics of the project itself.

5. Multi-agency

As noted above, disagreements on the use of resources can occur both within a project between tasks, and between different projects using the same resources. To simplify the work with resources, we will select an agent, which we will call “Resource Arbiter”. It is to him that the “Projects” agents will turn for the necessary resources, which will make it possible to redistribute even reserved resources depending on the importance (criticality) of the tasks or projects being performed.

Conclusion

What will such simulation or project management simulation provide? The answer is simple:

management with notifications- can be used as training or testing of decision makers for knowledge of certain principles or the ability to solve problems related to project management.
interactive control- practicing some practices and testing them on a model. This will make it possible to change the model to suit the situation or, conversely, to assess the mastery of methods for solving PM problems by the decision maker himself (self-test).
heuristic control- the possibility of a large number of simulation runs and the accumulation of certain experience (data) about these simulations for their further analysis.

However, imitation and simulation itself is not the final goal. As a result of the accumulation of sufficiently accurate simple and complex models in the simulation base, development and debugging of the behavior of the simulation model and modules that carry out interactive interaction and heuristic control (without decision-makers), it is possible to use the accumulated rules and algorithms for managing (or intelligently supporting management) real projects ( 3).
The implementation of such a system in the form of a SaaS solution, with the involvement of a certain number of participants, will allow access to the (impersonal) work experience of other participants (with the possibility of training the system).

Modeling is the main method for studying production and economic systems. Modeling is understood as a method of displaying objective reality in which a specially constructed model is used to study the original, reproducing certain (as a rule, only essential) properties of the real phenomenon (process) being studied.

A model is an object of any nature that is capable of replacing the object being studied so that its study provides new information about the object being studied.

In accordance with these definitions, the concept of modeling includes the construction of a model (quasi-object) and operations on it to obtain new information about the object under study. From the point of view of use, a model can be understood as a representation of the system that is convenient for analysis and synthesis. There is a correspondence relationship between the system and its model, which allows one to study the system through the study of the model.

The type of model is determined primarily by the questions that it is desirable to answer using the model. Various degrees of correspondence between the model and the simulated system are possible.

Often the model reflects only the function of the system, and the structure of the model (and its adequacy to the system) does not play a role; it is considered as a black box.

The simulation model already includes a unified representation of both the functions of the system and the essence of the processes occurring in it.

Modeling as a method of cognition is based on the fact that all models in one way or another reflect reality. Depending on how and by what means, under what conditions, in relation to what objects of cognition this property is realized, a wide variety of models arises. There are a number of principles for classifying models of different natures, of which the most significant are the following:

– according to the method of displaying reality, and consequently, according to the apparatus of construction (form);

– according to the nature of the modeled objects content).

Based on the method of display or construction apparatus, two types of models are distinguished (Fig. 7.2): material and mental, or ideal.

Rice. 7.2. Model classification

Material models are models that are built or selected by man, exist objectively, being embodied in metal, wood, glass, electrical elements, biological organizations and other material structures.

Material models are divided into three subtypes.

Spatially similar models are structures designed to display the spatial properties or relationships of an object (models of houses, factories, city districts, transport networks, arrangement of equipment in a workshop, etc.). A prerequisite for such models is geometric similarity.

Physically similar models are material models that aim to reproduce various kinds of physical connections and dependencies of the object being studied (models of dams for power plants of ships and aircraft). The basis for constructing such models is physical similarity - the same physical nature and the identity of the laws of motion.

Mathematically similar models are models that have, to one degree or another, the same mathematical formalism that describes the behavior of the object and the model (analogue of a computer, cybernetic functional models). Mathematically similar material models are material or physical shells of some mathematical relations, but not the relations themselves.

Mental (or ideal) models are divided into three subtypes:

– descriptive (conceptual) models in which relationships are expressed in language images;

– visual-figurative models, the images of which in the mind are built from sensory-visual elements;

– symbolic (including mathematical models in which the elements of an object and their relationships are expressed using signs (including mathematical symbols and formulas).

It does not seem appropriate to present a classification of models according to the nature of the objects being modeled due to their extreme diversity.

The ultimate goal of modeling is to study not the model as such, but some genuine object of study that is different from it, but reproduced by it.

Obviously, no models can and should not fully reproduce all aspects and details of the phenomena being studied: an enterprise can be characterized from various points of view - the director or chief engineer, accountant, supplier or power engineer.

In accordance with this, both the nature and construction of the model will be different.

Modeling, as a method of scientific knowledge, is based on a person’s ability to abstract the initial characteristics or properties of various phenomena (processes) and establish a certain relationship between them. Thanks to this, it is possible to study phenomena or processes indirectly, namely by studying models that are similar to them in some strictly defined respect.

In general, the following sequence of system modeling is appropriate: conceptual description (research) of the system, its formalization and, finally, if necessary, algorithmization and quantification of the system.

When modeling production and economic systems, along with formalized, mathematical methods of analysis used for individual subsystems or private processes, it is also necessary to use heuristic methods for analyzing production in those of its elements and connections that cannot be formalized. And when using mathematical methods, due to the many variables, one often has to resort to simplifications, using methods of decomposition and aggregation of variables. As a result, decisions acquire an approximate, qualitative character.

Due to the presence in large complex systems of organizational and production management of links and connections that are difficult or not formalized at all, to study them it is necessary to use mainly descriptive models, subjecting the system to decomposition into separate functional subsystems; then look for those subsystems that are amenable to mathematical formalization, thus modeling individual elements of the overall production process.

The ultimate goal of modeling the production and economic system is the preparation and adoption by the head of the enterprise of a management decision.

Models of production and economic systems can be distinguished by the following characteristics:

– for modeling purposes;

– according to management tasks (functions);

– by stages (procedures) of management;

– on mathematical modeling methods.

Depending on the purposes of modeling, there are models intended for:

– design of control systems;

– performance assessments;

– analysis of the enterprise’s capabilities in various conditions of its activity;

– developing optimal solutions in various production situations;

– calculation of organizational structures of the management system;

– calculation of information support, etc.

The specificity of the models of this classification division is expressed primarily in the selection of appropriate performance criteria, as well as in the procedure for implementing the modeling results.

Depending on the tasks (functions) of management, there are models of scheduling, enterprise development management, product quality control, etc. The models of this division are focused on specific production and economic tasks and, as a rule, must provide results in numerical form.

Depending on the stage (procedure) of automation control, models can be informational, mathematical, or software. The models of this division are aimed at the corresponding stages of movement and information processing.

Depending on the mathematical apparatus used, models can be divided into five large groups: extreme, mathematical programming (planning), probabilistic, statistical and game-theoretic.

Extremal models include models that make it possible to find the extremum of a function or functional. This includes models constructed using graphical methods, Newton’s method and its modifications, methods of the calculus of variations, Pontryagin’s maximum principle, etc. Based on the capabilities of these methods, they are used primarily to solve operational control problems.

Mathematical programming (planning) models include models of linear programming, nonlinear programming, and dynamic programming. This also usually includes network planning models.

Mathematical programming combines a number of mathematical methods designed for the best distribution of available limited resources - raw materials, fuel, labor, time, as well as for drawing up the corresponding best (optimal) action plans.

Probabilistic models include models constructed using the apparatus of probability theory, models of random processes of the Markov type (Markov chains), models of queuing theory, etc.

Probabilistic models describe random phenomena and processes, for example those associated with all sorts of unsystematic deviations and errors (production defects, etc.), the influence of natural phenomena, possible equipment malfunctions, etc.

Statistical models include models of sequential analysis, statistical testing methods (Monte Carlo), etc. This also includes random search methods.

The method of statistical testing is that the course of a particular operation is played back, as if copied using a computer, with all the accidents inherent in this operation, for example, when modeling organizational tasks, complex forms of cooperation between various enterprises, etc. The use of this method is called simulation modeling.

Random search methods are used to find extreme values of complex functions that depend on a large number of arguments. These methods are based on the use of a mechanism for randomly selecting arguments used for minimization. Random search methods are used, for example, in modeling organizational management structures.

Game-theoretic models are designed to justify decisions under conditions of uncertainty, ambiguity (incomplete information) of the situation and the associated risk. Game-theoretic methods include game theory and statistical decision theory.

Game theory is a theory of conflict situations. It is used in cases where the uncertainty of the situation is caused by possible actions of the conflicting parties.

Game-theoretic models can be used to substantiate management decisions in conditions of production and labor conflicts, when choosing the right line of behavior in relation to customers, suppliers, counterparties, etc.

The theory of statistical decisions is applied when the uncertainty of the situation is caused by objective circumstances that are either unknown (for example, some characteristics of new materials, the quality of new equipment, etc.) or are random in nature (weather conditions, the possible time of failure of individual components of a product and so on.).

It is advisable to use game-theoretic models in the preparation, conduct and evaluation of the results of business games.

All mathematical models can also be divided into efficiency assessment models and optimization models.

Performance assessment models are designed to develop production and management characteristics. This group includes all probabilistic models. Performance assessment models are “input” to optimization models.

Optimization models are designed to select the best course of action or course of action under given conditions. This group includes extreme and statistical models, mathematical programming models, as well as game-theoretic models.

Below we will consider some of the most common models used in solving production problems, as well as for forming organizational structures for production management.

The main direction of modeling the management of production and economic systems is the creation of production management models.

Currently, models of the following production management functions have been developed and are being used:

– planning the production and economic activities of the enterprise;

– operational management;

– operational regulation;

– management of material and technical supply of production;

– sales management of finished products;

– management of technical preparation of production.

A system of interconnected production and management models has also been developed.

Models for planning production and economic activities of an enterprise. The target function of the models of this group provides:

– maximizing the criterion for the efficiency of the enterprise’s production activities based on the available capacities and supplied resources;

– minimizing resource consumption within a given efficiency criterion.

Models for planning the production activities of an enterprise are divided into: forecasting models, models of technical and economic planning, models of operational production planning.

Forecasting models are models that are either based on mathematical methods (least squares, thresholds, exponential smoothing) or on expert judgment methods.

Models of technical and economic planning are based on methods of mathematical programming (planning). The final results of production, for example the amount of profit, are usually chosen as the main efficiency criterion (target function) when developing an optimal plan. Limitations on the complexity of products, equipment operating time, resources, etc. are taken as restrictions. Since the value of some of these restrictions is random in nature (for example, equipment operating time), a probabilistic approach is used when solving such optimization problems. Typical optimization models of technical and economic planning are models for calculating the optimal plan, distributing the production program over calendar periods, and optimal equipment loading. These models are built using mathematical optimization methods.

Operational production planning models are usually combined with operational management models.

Models of operational management. The main tasks of operational management are operational calendar planning of production, systematic recording and monitoring of the implementation of calendar plans, as well as operational regulation of production progress.

Typical models of operational management are models for calculating the optimal size of batches of products and calculating the optimal schedule for the launch and release of batches of parts (scheduling).

Models for calculating the optimal size of product batches can be created in relation to both simple and complete formulation of the problem. In a simple formulation, determining the size of production or purchasing a batch of parts, at which the annual costs are minimal, comes down to the usual problem of finding the minimum of a function. In the full formulation, a set of batch sizes is found that corresponds to the minimum total costs for equipment changeover and deductions for work in progress, subject to restrictions on the duration of changeovers, equipment resources, interdependence of batch sizes in related operations and worker employment. The solution to this problem is achieved using mathematical optimization methods.

Models for scheduling calculations can be:

– statistical with optimization by random search method;

– imitation with a set of preference rules;

– heuristic, used in cases where it is impossible to create strict algorithms, but there is a need to use information and evaluate facts that do not have quantitative expression.

Models of operational regulation. These models are intended to ensure that deviations of production results from planned indicators are kept within specified limits. In this case, two types of models are used: control models based on the optimality criterion, control models based on deviation.

Control models based on the optimality criterion are based on the fact that after a specific measurement of the actual state of the production process, a plan is drawn up that optimally leads the process to a predetermined state at the end of the planning period.

Deviation control models are based on the fact that after a specific measurement, the production process is brought back to the originally drawn up schedule in the shortest possible time.

The construction of both models is carried out using the mathematical optimization apparatus used in the theory of automatic control.

Models of production logistics management. The central problem of managing the material and technical supply of production is the task of determining the required volume of stocks of all types of supplies. In this case, two fundamentally different inventory management models can be built - with a fixed order size and with a fixed inventory level. There is also an intermediate model in which both the upper inventory level and the lower order level are fixed.

The construction of material and technical supply management models is carried out using special mathematical optimization methods, which are called “inventory management theory”.

Models of sales management of finished products. The main problem of managing the sales of finished products is the task of calculating the annual supply plan for finished products. To solve this problem, using mathematical optimization methods, an optimization model of the annual finished product supply plan is constructed. The objective function in this case is the cost of products sold, the restrictions are the requirement that the total volume of products shipped to all consumers in a certain time interval does not exceed the volume of production for the same time, and the total volume of supplies to the consumer for all time intervals does not exceeded the monthly application.

Models of management of technical preparation of production. Technical preparation of production includes the stages of design and technological preparation.

Using mathematical modeling, three main problems of managing technical preparation of production can be solved:

– determination of the minimum period for completing a set of measures for technical preparation of production under restrictions on the level of available resources;

– determination of the minimum cost of performing a set of measures for technical preparation of production with restrictions on the timing of its implementation and on the level of resource availability;

– determination of the minimum level of consumption of scarce resources with restrictions on the cost and timing of technical preparation of production activities.

The process of technical preparation of production is most fully and conveniently reproduced by the network model. The network model makes it possible to take into account the probabilistic nature of such basic parameters of technical production preparation operations as the duration of work and the intensity of resource consumption.

Optimization is achieved by using mathematical programming methods (in particular, the simplex method) and random (statistical) search.

Along with the individual models considered that implement the basic functions of managing the production process, there is also a system of interrelated models of production and management. The essence of this system of models, constructed using the mathematical apparatus of set theory, graph theory and re-calculus, is as follows. The set of products produced by the enterprise and the set of resources used are considered as sets. The production process, which ensures the production of many products, is described by an aggregate graph, and the technological process of producing an individual product is described by its design and technological graph. The set of resources that support production consists of subsets of labor resources, equipment, and scarce components and materials. The state of production at any point in time can be described by a vector, which is a set of finished products, semi-finished products and parts assembly units produced up to that moment. Similarly, the state of resources at any point in time is determined using a vector. The planned trajectory of the production process will be described by a vector function.

With this formulation of the problem, optimal management of the enterprise during the planning period can be found based on the following requirement: on the set of admissible plans determined by the vector function, find a plan that maximizes profit, provided that the probability of its implementation and obtaining a profit of the established level is no less a given level, and the resources spent will not exceed those available.

Modeling of organizational management structures is aimed at improving and optimizing the enterprise management system. It is a necessary preliminary step to automate the management of production and economic systems, which requires serious preparatory work.

Queuing theory is used as a mathematical tool for modeling organizational management structures. In this case, the elements of the queuing system are accepted as elements of the management system, each of which is designed to solve a specific management problem. For all tasks - elements, a system of priorities in the order of solution is provided. For each task, the characteristics of the incoming flows of service requirements are also known - the solution of the corresponding control problems.

An element of a control system that solves a particular problem has one or more information converters, which are either specialists of a certain qualification or technical means.

The effectiveness of the management system is assessed by the quality and duration of service for solving management problems, taking into account their priorities and complexity.

Modeling of queuing systems can be performed using both analytical and statistical methods. The most widely used method in modeling organizational management structures is the statistical method, the so-called statistical test method (Monte Carlo method). This method is preferred on the grounds that it allows solving problems of great complexity for which there is no analytical (formular) description or the latter is extremely complex.

The statistical model allows you to set up a mathematical experiment similar to a full-scale one, to simulate the organizational management structure in the cheapest way and in an acceptable time. At the same time, it is necessary to take into account the specific disadvantages of the statistical test method, the main ones being the relatively long simulation time and the partial nature of the solutions obtained, determined by the fixed values of the parameters of the queuing system.

When modeling using the mathematical apparatus of queuing theory, the structure of the enterprise management system is considered as a set of interconnectedly functioning elements. Such elements in a real system are the directorate and functional management departments: production and technical, planning, supply, etc.

As a result of the joint functioning of these elements in the control system, state information is converted into command information, which is the basis for enterprise management.

The mentioned elements - divisions of the enterprise management system - form a chain, the analysis of the functioning of which can be sufficiently formalized in order to optimize the management process. The simplest chain that gives a good approximation to reality is a strictly sequential chain of elements. When modeling such a chain, two approaches are possible: quasi-regular and random representation. In a quasi-regular model, modeling is carried out for each element separately using averaged indicators.

In the random model, statistical estimates are calculated for each service request, passing not through individual elements, but through the system as a whole.

Along with modeling organizational control structures using chains of elements, there is a method for mathematically describing the organizational structure of a control system using linear stochastic networks, which are one of the classes of multiphase queuing systems. In this model, information also passes sequentially through a number of elements of the control system, each of which is described using the mathematical apparatus of queuing theory. When information sequentially passes through network elements, Markov-type transitions take place. The structure of such a network with the corresponding transitions is represented by a certain graph. A stochastic transition matrix is compiled.

Since the target function (performance criterion) in mathematical modeling of organizational management structures, as a rule, can only be described statistically, optimization is carried out mainly by numerical methods, of which the methods of dynamic programming and statistical search are most widely used.

The solution to the optimization problem using the dynamic programming method is implemented by constructing a functional recurrent equation (Bellman equation) for each step of the control process.

Optimization of organizational management structures using the statistical search method, despite less stringent restrictions imposed on the efficiency criteria and assumptions describing the physics of the phenomenon with this method, has not yet received, in relation to the problem under consideration, sufficiently widespread.

Game modeling occupies a special place among the methods used to automate the management of production and economic systems. A distinctive feature of this method is the involvement of people involved in the development and implementation of a business game to model the management process. A business game is understood as an imitation by a group of individuals of solving individual problems of the economic or organizational activity of an enterprise, performed on a model of an object in an environment as close as possible to the real one.

The introduction of a person into the model as an element of the management organization makes it possible to take into account his behavior in cases where it cannot be adequately described using the mathematical models known today; allows you to solve management problems that do not fit into the framework of existing formalized methods.

A business game introduces psychological and emotional aspects into the process of preparing and making management decisions, encouraging the use of past experience of managers and their intuition in this process, developing the ability to make heuristic decisions. A business game is played in relation to a specific management task according to a carefully developed scenario in advance. The general game model is formed as a set of private models created by participants - persons preparing and making management decisions.

The business game model includes both formalized and informal parts. Participants in the game act according to certain rules. They are guided by specially developed instructions for playing the game, as well as the situational data at their disposal.

In accordance with the game scenario, participants periodically receive introductory information about changes in the situation. When preparing their decisions, participants in the business game assess the situation and make the necessary calculations manually or using a computer. In this case, formalized, pre-prepared elements of the game model are used, corresponding to modern methods of operations research.

By managing the course of a business game, its leader evaluates the decisions of the participants, establishes the results of their actions and communicates the results to the players. If necessary, the game director can change the setting, bringing these changes to the participants in the form of introductory notes. The actions of the game participants are assessed by calculations, expert methods, as well as based on the manager’s experience, intuition and common sense.

The main type of game simulation carried out at enterprises is an industrial business game. Its goal is to improve existing and develop new forms of organizing production management, develop governing documents, restructure production, etc.

Network planning and management (NPC) methods built on the basis of network graphs are widely used as models for conducting business games. When solving planning problems, dynamic programming methods are used, and when solving resource allocation problems, linear programming is used.

To train management personnel, a production business game can be carried out in an educational version, i.e. an educational business game. Its main task is to train employees and improve their management skills. If necessary, an educational business game is also used to certify management employees of enterprises in the performance of their official duties, as well as when promoting them to the highest position.