Modelling and Simulation in Management

Systems theory requires the use of undistorted information in approaching both the system as such, and its components, including the relation established between them. In the study of systems, the analysis of components is used to start with, and then their synthesis is done. The analysis-synthesis interdependence approach enables the development of some models that are simulated in practice in order to ensure an efficient management of systems. Systems theory places the study of automatically adjusted systems at its very centre. The management of systems must provide those actions of eliminating the negative consequences caused by distorting the information used in the system. Due to the constantly changing environment where any system performs its activity, its smooth operation involves assuming a particular risk from the managing system. Thus, a true theory of risk has developed, which in this issue highlights several opinions of specialists. Along with the theoretical approach of risk, there is also a pragmatic handling of it, meaning the actual way in which it manifests in practice. Concurrently with the development of the theory of risk, a theory of attitude has also developed, manifested to risk by the systems managers. There is a differentiation of managers regarding the attitude they have to risk. Opinions were developed for assuming the risk by managers and opinions according to which managers refuse the risk.

The use of the systems theory in dealing with the industrial companies enables the use of cybernetics to this effect. This leads to considering the company as a cybernetic system highlighting all company’s characteristics. In this context, we may also speak of a system of the company’s functions, regardless of the environment where it operates. In the same context, there is also a systemic structure of the company, which emphasises the existence of several structures of the industrial company. Regardless of the company’s structure, there is a complete operational cycle of its operation. Regardless of the environment where it operates, the entire activity of the industrial company is subject to a rigorous control by the managing system. This is so much more under conditions of ambiguity that characterises the current global economy. The management of the industrial company must organise and lead the decision-making process by which the best decisions would be adopted, regarding the industrial company’s development under the current conditions.

During the current period, the world economy is characterised by a process of globalisation, which implies that the national economy is part of the global economy which it influences, but the latter also determines a certain trend of developing a national economy. In this context, industrial companies are part of the globalised economy, which determines a certain complexity in the development of any industrial company. Along with the globalisation of the contemporary world economy, we may also speak of a globalisation of the market, where the company must capitalise its industrial products. Taking into account the evolution of mankind and of the society in general, Alvin Toffler defines several “waves” in the development of the society in general, and of the economy in particular. Each of these society and economy development stages determines a certain structure of the industrial companies, including an internationalisation of their structure and of the industrial companies’ activity. The current feature of the industrial companies is their increasingly greater involvement on the international market, which has led to the appearance of the “nomad industrial companies”, which change their space of existence on the globalised world market, so that it would ensure its maximum profit. Under the current globalisation conditions, the existence and development of any industrial company depend on the type of formal and informal organisation which it adopts.

Econometrics or the science of econometric models takes into account the use of economic researches closely related to the researches in statistics and mathematics. It includes theories aiming at the new scientific discoveries obtained by intersecting the discoveries of the scientific researches in economy with those in mathematics and statistics. This science is based on the econometric research that faces some contradictions, such as: the structural-phenomenological ones, the causal-stochastic ones, the rational-empirical ones, etc. Econometric research regardless of the models used always encounter a whole series of difficulties on the implementation of econometric models in practice. Such difficulties targeting structure and nature of the phenomenon studied, the causal relationships between system elements and differences between rational and empirical model. The essence of the econometric research is the relation between the object and signal reflected in the econometric model created. Econometrics operates with econometric functions which are the expression of the connections between the elements of economy. At the same time, it is closely related to inter-conditioning with managerial sciences.

Modelling and simulation are important working techniques of econometrics, but they are also a series of peculiarities, which form them in a distinct category. Any econometric model has the variables: the subject, theory, object of the research and information. These econometric models are always subject to a matrix calculus. In the category of econometric models, the input-output model used in the theory of Leontieff is a series of special features that distinguish it from other models. Production and optimisation models are also used, and the model of the IQ calculated for each employee is used for human resources. Unlike modelling, as an econometric technique the simulation applies in production a model that has been created based on the conclusions drawn from reality, but which have great power of generalisation. The simulation technique uses models to simulate the industrial production and particularly models based on artificial intelligence. Any expert system used in the modeling of industrial production involves studying specificity of production technology and then adapting it to a specific expert system.

Estimating the connection between factors and the results of production is a difficult problem any econometric model faces. Such models are achieved by creating and motivating the production functions. These functions have a dynamic feature determined by using the time variable expressed by the trend of the production functions. Any production function may be calculated by using calculation techniques, but there are however some difficulties in these calculations. Such difficulties can be overcome by using specific methods. In the production functions, the Cobb-Douglas functions have a special place and are in a certain relation with the functions used by the Leontief model. The functions used in the Leontief model actually express the inputs and outputs that characterise such a model. Coob-Douglas function and the model Leontieff occupies an important place in the design of econometric models. This allows emphasizing connections with science management cybernetics. Science subjects of the category of management components such as political economy, types of management, economic statistics, etc. interrelated with econometrics.

In econometric modelling, we commonly use linear programming based on the existence of an objective function that must be optimised in certain conditions, of which the non-negativity condition is essential. Any econometric model of this category is based on linear programming and consists of a set of linear relations, of which some reflect the objective pursued and the others the economic restrictions and technological restrictions in which the phenomenon reflected by that econometric model is performed. Solving such models based on linear programming uses the Simplex algorithm which has the property of both convergence and duality. The problem of duality is solved in such models by the dual Simplex logarithm. For managers, the use of these models essentially involves the achievement of some re-optimised programs and with parameters that should be consistent with the actual situation the econometric model expresses. Managerial efficiency of organizational entities involved in the adoption of decisions by managers. For this managers in their work reoptimization algorithms and parameterization of the solution obtained by a linear programming model.

In dynamic econometric models, the characteristic and also essential element is the time factor expressed by a specific form of application in such mathematical models and namely by the “trend” function. This is because the activity of any organisational entity and its evolution are not static. It is constantly adapting to the environment wherein it performs its activity. It is only thus that organisational entities can withstand the environmental changes. Determining factor time to obtain solution considering that it has changed from one period to another. In this sense the solution obtained by a dynamic programming model is actually a sequential solution in that it provides a size for each time period. The final solution is actually a solution technique improved by successive steps starting from the size of the solution obtained at the beginning of the period considered. Iterative calculations obtain the solution related to the size of the end time of the period. Discreet dynamic econometric models and stationary models are used. The interpretation of such dynamic programs is done based on the graph theory, using a graph attached to that dynamic model. A separate issue is the strategic management that uses very often the econometric models to optimise the decisions of the organisational entities based on multiple criteria.

The graph theory enables the econometrics to be applied in the management of organisational entities. This theory is based on the concept of undirected and directed graph, including the circuits that may occur in a graph. The graph is a specific form for representing the activities performed by organisational entities. With their help, the elements of the system “organisational economic entities” are analysed in detail. Graph is a set of reciprocal inter-conditioned activities that have a beginning and a end. Each activity is assigned specific financial resources material, human and technological. For these reasons each activity has a cost and requires execution time. Depending on the execution time of each activity in the graph we obtain finally the total duration of the process, a complex of activities represented by the graph. The essence of each graph refers to the calculation of the size of the critical path in the graph, based on the graph theory. In the graph theory, a specific situation is the graphic transport networks, which are preponderant in econometric models. For any manager, the calculation of the critical paths and of the Hamiltonian roads and circuits in a graph leads to taking optimal decisions.

Queuing string theory beginning at problems occurred in practice on telecommunications processes, processes of transport services, processes gas stations. Based on the content of this theory have been developed for decision models in organizational management. This is because any production process also involves an undesirable consumption of production means, resources, performers and time which cannot be removed entirely. For this reason, some econometric models based on the queuing string theory have been elaborated and have the following variables: the consumers, queuing string, service stations. Such variables must be optimised by establishing the optimal level of some parameters, such as: arrivals in the system, service time, intensity of traffic, etc. The econometric models used in this case may be: model with a single service station and limited queuing string and respectively model wherein the queuing string is unlimited; model with several service stations and arrival from a finite population and respectively model with the arrival from an infinite population; model with a service station and arrivals from a finite population.

The game is a competitive process that occurs between several players by certain rules and is used very often in the management of organisational entities. The representation of any game is always done by a matrix that is much used in the decision-making process, regardless of the conditions in which managers take the decision. Organizational entities activity is performed in a dynamic environment which requires the managers to make timely decisions in short intervals. Managers do not always know the conditions and factors that influence decisions which they are to take. The managers are not aware of the consequences of decisions to take regarding the future activity organizational entities. Therefore the purpose of any goal of any manager is to optimise the decisions. Depending on the conditions in which decisions will be made and their consequences in game theory have developed a series of models that contain mathematical format, considering that decisions are made and the consequences of those decisions. Between the best known such methods are: the Wald method, Laplace method, method of multiple criteria decision tree, Electre method, graphical representation method, etc. Strategic management uses very much for making decisions based on multi-criteria optimization models.

Any production process involves consumption of resources, material resources is very important. Consumption of these resources require a financial effort and not always is a rhythmic consumption. He is conditioned by technology execution of each product. Material resources must exist in every moment of the production flow. For this organizational entity must have supplied. Their supply consumes financial, human resources and time. For this reason they must be well dimensioned. A similar situation is also the occasion of obtain finished products and selling them to the beneficiaries. Thus there are organizational entities that delivers products based on the orders of their beneficiaries or have them stored in stock and then deliver them to beneficiaries. From these circumstances decisions regarding supply-sales activities are subject stock management. This involves the adoption of some managerial decisions regarding the supply-sale activity using econometric models. Such models use specific econometric equations, namely stochastic equations. Solving such equations is based on the calculation of the inverse matrix. There is a group of models consisting of classical stochastic models, such as those with fixed period and constant demand; those with fixed period and the possibility of stock outage; those for a single product, etc. The heuristic stochastic models are also used, such as the ABC model, etc.

The development of current science and technology causes broad changes in the evolution of fixed assets. Thus, it is required for fixed assets to be affected as little as possible by physical wear and obsolescence. Depending on the degree of development and improvement of production of fixed assets, organisational entities must adopt appropriate decisions for maintaining or replacing the fixed assets they have. For this they must take into account the stage fixed assets are at which they have and the level of expenses incurred by upgrading the existing ones or by replacing them with new ones. The amount of losses must also be taken into account if physically worn or obsolete fixed assets are still in operation. The main problem of establishing equipment replacement decisions rules under specific conditions is to find decision variables that minimize total incurred costs over a planning horizon. Basically, the rules differ depending on what type of production type is used. For a batch production organization the suitable criterion is built on the principle of economies of scale. Proposed econometric models in this chapter are focused on a multiple machine replacement problem in flexible manufacturing cells with several machines for parts’ processing, and industrial robots for manipulation and transportation of manufactured objects. Firstly, models for a simple case multiple machine replacement problems are presented. Subsequently, the more complicated case is considered where technological improvement is taken into account.

The objective of any organizational entity is achievement of the products at a cost of production that enable them to get a larger profit. Price and cost must always be in favor of the organizational entity that finally obtain the desired profit to enable them, such keep them on the market and its development. In this context, the matrix calculus is essential in the use of econometrics by the management of production costs in general and of the production unit cost in particular. Such a calculation is based on using the inverse matrix of the cost. Applying the econometric model of the production cost is done within an organisational entity wherein the achievement of the production is conditioned by a certain operational management of the industrial production. The econometric model takes into account the matrix calculus applied for establishing the primary expenses by product. Then we move on to actually designing the mathematical model for the primary consumptions by departments and operations, for the primary expenses and primary consumptions by products, for the unit prices of the primary input components, for estimating the structure of the direct and indirect primary expenses and finally for estimating the unit cost by product.

Under the conditions of a globalised market, organisational entities must used econometric models regarding the preparation of budgets in general and of those by production functions in particular. Under these conditions, the budget is a managerial tool, and budgeting becomes a systemic management technique for achieving the proposed managerial objectives. The models cover several types of budgets, namely: general or partial budgets; fixed or flexible budgets; budgets by departments; budgets by products, projects or item. At the level of the organisational entity, econometric models are developed concerning the general budget, the production budget, the budget of the commercial activity, budget of investments, budget of the research-development budget, the treasury budget. The model regarding the budget of production unit budget has certain specificity. The drawing up of production costs budgets, implies drawing up the following budgets: raw materials and direct materials expenditures budget; expenditure budget of direct wages, the contribution to the social insurances and the afferent social protection; direct expenses budget for electric power in motor purposes; technological fuel direct expenditures budget; the budget of direct expenditures with the fixed means’ redemption; indirect manufacturing costs budget; the general budget of manufacturing costs; unitary costs budget per product.

In the organisational management, quality management occupies an important place in general and total quality management in particular. Such a concept is the essence of modelling the production quality. The most common models used for this are those based on the Taguchi technique regarding the continuous improvement of the quality of production and products. The variables taken into account are: “loss of quality” function; starting point of quality; ensuring the quality in production; verification of total quality, etc. Based on these variables, the function of the loss of quality must be optimised under the conditions of complying with some criteria such as: optimisation criteria; target criteria regarding the quality content, criteria to maximise the quality efficiency. Under these conditions, the econometric models are used particularly in the field of total quality management. In terms of econometrics, both the quality and non-quality products can be measured. This is because econometric models are developed separately for their product quality and non-quality. Such models contains an objective function to be optimized in terms of a set of restrictions for quality and nonquality.