Concept of production system and production process. Technological process and technological set

Ministry of Education and Science of the Russian Federation

Novgorod State University named after Yaroslav the Wise

Abstract on the discipline:

Management

Completed by student gr.6061 zo

Makarova S.V.

Accepted by Suchkov A.V.

Veliky Novgorod

1. PRODUCTION PROCESS AND ITS ELEMENTS.

The basis of the production and economic activity of the enterprise is the production process, which is a set of interconnected labor processes and natural processes aimed at producing certain types of products.
The organization of the production process consists of combining people, tools and objects of labor into a single process for the production of material goods, as well as ensuring a rational combination in space and time of basic, auxiliary and service processes.

Production processes at enterprises are detailed by content (process, stage, operation, element) and place of implementation (enterprise, processing unit, workshop, department, section, unit).
The many production processes occurring in an enterprise constitute the total production process. The production process of each individual type of product of an enterprise is called private production process. In turn, in a private production process, partial production processes can be distinguished as complete and technologically isolated elements of a private production process, which are not primary elements of the production process (it is, as a rule, carried out by workers of different specialties using equipment for various purposes).
Should be considered as a primary element of the production process technological operation- a technologically homogeneous part of the production process, performed at one workplace. Technologically isolated partial processes represent stages of the production process.
Partial production processes can be classified according to several criteria:

For intended purpose;

The nature of the course over time;

The method of influencing the subject of work;

The nature of the labor used.
Processes are distinguished by purpose main, auxiliary and servicing.
Basic production processes - processes of converting raw materials and materials into finished products, which is the main, core
products for this enterprise. These processes are determined by the manufacturing technology of this type of product (preparation of raw materials, chemical synthesis, mixing of raw materials, packaging and packaging of products).
Auxiliary production processes are aimed at manufacturing products or performing services to ensure the normal flow of basic production processes. Such production processes have their own objects of labor, different from the objects of labor of the main production processes. As a rule, they are carried out in parallel with the main production processes (repair, packaging, tool management).
Attendants production processes ensure the creation of normal conditions for the occurrence of main and auxiliary production processes. They do not have their own subject of labor and, as a rule, proceed sequentially with the main and auxiliary processes, interspersed with them (transportation of raw materials and finished products, their storage, quality control).
The main production processes in the main workshops (areas) of the enterprise form its main production. Auxiliary and servicing production processes, respectively, in auxiliary and servicing workshops form an auxiliary facility.
The different roles of production processes in the overall production process determine the differences in the management mechanisms of different types of production units. At the same time, the classification of partial production processes according to their intended purpose can only be carried out in relation to a specific private process.
The combination of main, auxiliary, servicing and other processes in a certain sequence forms the structure of the production process.
The main production process represents the process of production of the main products, which includes natural processes, technological and work processes, as well as interoperational maintenance.
A natural process is a process that leads to a change in the properties and composition of the object of labor, but occurs without human intervention (for example, in the manufacture of certain types of chemical products).

Natural production processes can be considered as necessary technological breaks between operations (cooling, drying, aging, etc.)
Technological the process is a set of processes as a result of which all the necessary changes occur in the subject of labor, i.e. it turns into a finished product.
Auxiliary operations contribute to the performance of main operations (transportation, control, product sorting, etc.).
Work process - a set of all work processes (main and auxiliary operations).
The structure of the production process changes under the influence of the technology of the equipment used, division of labor, production organization, etc.
Interoperative monitoring - breaks provided for by the technological process.
According to the nature of the course of time, they distinguish continuous And periodic production processes. In continuous processes there are no interruptions in the production process. Production maintenance operations are carried out simultaneously or in parallel with the main operations. In periodic processes, the execution of main and service operations occurs sequentially, due to which the main production process is interrupted in time.
According to the method of influence on the subject of labor, they are distinguished mechanical, physical, chemical, biological and other types of production processes.
According to the nature of the labor used, production processes are classified into automated, mechanized and manual.

The principles of organizing the production process represent the starting points on the basis of which the construction, operation and development of the production process are carried out.

There are the following principles for organizing the production process:
differentiation - division of the production process into separate parts (processes, operations, stages) and their assignment to the relevant divisions of the enterprise;
combination - combining all or part of different processes for the production of certain types of products within one site, workshop or production;
concentration - the concentration of certain production operations for the manufacture of technologically homogeneous products or the performance of functionally homogeneous work at individual workplaces, areas, workshops or production facilities of the enterprise;
specialization - assigning to each workplace and each department a strictly limited range of works, operations, parts and products;
universalization - production of parts and products wide range or performing dissimilar production operations at each workplace or production unit;
proportionality - a combination of individual elements of the production process, which is expressed in their certain quantitative relationship with each other;
parallelism - simultaneous processing of different parts of one batch for a given operation at several workplaces, etc.;
directness - the implementation of all stages and operations of the production process in conditions of the shortest path through the object of labor from beginning to end;
rhythmicity - repetition through established periods of time of all individual production processes and a single process for the production of a certain type of product.
The above principles of production organization in practice do not operate in isolation from each other; they are closely intertwined in each production process. The principles of production organization develop unevenly - in one period or another, one or another principle comes to the fore or acquires secondary importance.
If the spatial combination of elements of the production process and all its varieties is implemented on the basis of the formation of the production structure of the enterprise and its divisions, the organization of production processes in time is expressed in the establishment of the order of execution of individual logistics operations, the rational combination of execution time various types works, determining calendar and planning standards for the movement of objects of labor.
The basis for building an effective production logistics system is a production schedule, formed based on the task of meeting consumer demand and answering the questions: who, what, where, when and in what quantity will produce (produce). The production schedule makes it possible to establish volumetric and time characteristics of material flows differentiated for each structural production unit.
The methods used to create a production schedule depend on the type of production, as well as the characteristics of demand and parameters of orders: single, small-scale, serial, large-scale, mass.
The characteristics of the type of production are complemented by the characteristics of the production cycle - this is the period of time between the beginning and end of the production process in relation to a specific product within the logistics system (enterprise).
The production cycle consists of working time and break time during the manufacture of products.
In turn, the working period consists of the main technological time, the time for carrying out transport and control operations and the picking time.
The time of breaks is divided into the time of inter-operational, inter-site and other breaks.
The duration of the production cycle largely depends on the characteristics of the movement material flow, which can be serial, parallel, parallel-serial.
In addition, the duration of the production cycle is also influenced by the forms of technological specialization of production units, the system of organization of the production processes themselves, the progressiveness of the technology used and the level of unification of manufactured products.
The production cycle also includes waiting time - this is the interval from the moment an order is received until the start of its execution, to minimize which it is important to initially determine the optimal batch of products - a batch at which the costs per product are minimal.
To solve the problem of choosing the optimal batch, it is generally accepted that the cost of production consists of direct manufacturing costs, costs of storing inventory and costs of equipment changeover and downtime when changing batches.
In practice, the optimal batch is often determined by direct counting, but when creating logistics systems, it is more effective to use mathematical programming methods.
In all areas of activity, but especially in production logistics, a system of norms and standards is of utmost importance. It includes both aggregated and detailed standards for the consumption of materials, energy, equipment use, etc.

2. Methods for solving the transport problem.

Transport problem (classical)- a problem about the optimal plan for transporting a homogeneous product from homogeneous points of availability to homogeneous points of consumption on homogeneous vehicles (predetermined quantity) with static data and a linear approach (these are the main conditions of the problem).

For the classical transport problem, two types of problems are distinguished: the cost criterion (achieving a minimum of transportation costs) or distances and the time criterion (a minimum of time is spent on transportation).

History of the search for solution methods

The problem was first formalized by a French mathematician Gaspard Monge V 1781 year . The main advance was made in the fields during Great Patriotic War Soviet mathematician and economist Leonid Kantorovich . That's why this problem is sometimes called Monge-Kantorovich transport problem.

Let's consider an economy with l goods. For a particular firm, it is natural to consider some of these goods as factors of production and some as output products. It should be noted that this division is rather arbitrary, since the company has sufficient freedom in choosing the range of products produced and the cost structure. When describing technology, we will distinguish between output and costs, representing the latter as output with a minus sign. For the convenience of presenting technology, products that are neither consumed nor produced by the company will be classified as its output, and the volume of production of these products will be considered equal to 0. In principle, a situation in which a product produced by a company is also consumed by it in the production process cannot be excluded. In this case, we will consider only the net output of this product, i.e. its output minus costs.

Let the number of factors of production be equal to n, and the number of types of output equal to m, so that l = m + n. Let us denote the cost vector (by absolute value) through r Rn + , and output volumes through y Rm + . We will call the vector (−r, yo ) vector of net issues. The set of all technologically feasible vectors of net outputs y = (−r, yo ) is technological set Y. Thus, in the case under consideration, any technological set is a subset of Rn − × Rm +.

This description of production is general in nature. At the same time, it is possible not to adhere to a strict division of goods into products and factors of production: the same good can be spent with one technology, and produced with another. In this case, Y Rl.

Let us describe the properties of technological sets, in terms of which specific classes of technologies are usually described.

1. Non-emptiness

The technological set Y is non-empty.

This property means the fundamental possibility of carrying out production activities.

2. Closedness

The technological set Y is closed.

This property is rather technical; it means that the technological set contains its boundary, and the limit of any sequence of technologically feasible net output vectors is also a technologically feasible net output vector.

3. Freedom to spend:

if y Y and y0 6 y, then y0 Y.

This property can be interpreted as the ability to produce the same amount of output, but at greater cost, or less output at the same cost.

4. No “cornucopia” (“no free lunch”)

if y Y and y > 0, then y = 0.

This property means that to produce a product in a positive quantity, costs are required in a non-zero volume.

Rice. 4.1. Technological variety with increasing returns to scale.

5. Non-increasing returns to scale:

if y Y and y0 = λy, where 0< λ < 1, тогда y0 Y.

This property is sometimes called (not entirely accurately) diminishing returns to scale. In the case of two goods, where one is expended and the other is produced, diminishing returns mean that the (maximum possible) average productivity of the input does not increase. If in an hour you can solve, at best, 5 similar problems in microeconomics, then in two hours, under conditions of diminishing returns, you could not solve more than 10 such problems.

50. Non-decreasing returns to scale:

if y Y and y0 = λy, where λ > 1, then y0 Y.

In the case of two goods, where one is expended and the other is produced, increasing returns mean that the (maximum possible) average productivity of the input does not decrease.

500. Constant returns to scale is a situation when the technological set satisfies conditions 5 and 50 simultaneously, i.e.

if y Y and y0 = λy0 , then y0 Y λ > 0.

Geometrically, constant returns to scale mean that Y is a cone (possibly not containing 0).

In the case of two goods, where one is input and the other is produced, constant output means that the average productivity of the input does not change as output changes.

Rice. 4.2. Convex technology set with diminishing returns to scale

The convexity property means the ability to “mix” technologies in any proportion.

7. Irreversibility

if y Y and y 6= 0, then (−y) / Y.

Let's say you can produce 5 bearings from a kilogram of steel. Irreversibility means that it is impossible to produce a kilogram of steel from 5 bearings.

8. Additivity.

if y Y and y0 Y , then y + y0 Y.

The property of additivity means the ability to combine technologies.

9. Acceptability of inactivity:

Theorem 44:

1) From the non-increasing returns to scale and additivity of the technological set, its convexity follows.

2) Non-increasing returns to scale follow from the convexity of the technological set and the permissibility of inactivity. (The converse is not always true: with non-increasing returns, the technology may be non-convex, see Fig. 4.3 .)

3) The technological set has the properties of additivity and non-increasing

returns to scale if and only if it is a convex cone.

Rice. 4.3. A non-convex technological set with non-increasing returns to scale.

Not all eligible technologies are equally important from an economic point of view. Among the permissible ones, special ones stand out efficient technologies. An admissible technology y is usually called effective if there is no other (different from it) admissible technology y0 such that y0 > y. Obviously, this definition of efficiency implicitly implies that all goods are in some sense desirable. Effective technologies constitute efficient frontier technological set. Under certain conditions, it becomes possible to use the effective frontier in the analysis instead of the entire technological set. In this case, it is important that for any admissible technology y there is an effective technology y0 such that y0 > y. In order for this condition to be met, it is required that the technological set be closed, and that within the technological set it is impossible to increase the output of one good indefinitely without reducing the output of other goods. It can be shown that if technological

Rice. 4.4. Efficient technology set boundary

set has the property of freedom of expenditure, then the effective boundary uniquely defines the corresponding technological set.

Introductory and intermediate courses, when describing the behavior of a producer, are based on the representation of his production set through a production function. A relevant question is under what conditions on the production set such a representation is possible. Although it is possible to give a broader definition of the production function, hereinafter we will only talk about “single-product” technologies, i.e. m = 1.

Let R be the projection of the technological set Y onto the space of cost vectors, i.e.

R = ( r Rn | yo R: (−r, yo ) Y ) .

Definition 37:

The function f(·) : R 7→R is called production function, representing technology Y, if for each r R the value f(r) is the value of the following problem:

yo → max

(−r, yo) Y.

Note that any point on the effective boundary of the technological set has the form (−r, f(r)). The converse is true if f(r) is an increasing function. In this case, yo = f(r) is the effective frontier equation.

The following theorem gives the conditions under which a technological set can be represented??? production function.

Theorem 45:

Let for a technological set Y R × (−R) for any r R the set

F (r) = ( yo | (−r, yo ) Y )

closed and bounded from above. Then Y can be represented by a production function.

Note: The fulfillment of the conditions of this statement can be guaranteed, for example, if the set Y is closed and has the properties of non-increasing returns to scale and the absence of a cornucopia.

Theorem 46:

Let the set Y be closed and have the properties of non-increasing returns to scale and the absence of a cornucopia. Then for any r R the set

F (r) = ( yo | (−r, yo ) Y )

closed and bounded from above.

Proof: The closedness of the sets F (r) follows directly from the closedness of Y. Let us show that F (r) are bounded from above. Let this not be so and for some r R there is

There exists an infinitely increasing sequence (yn) such that yn F (r). Then, due to non-increasing returns to scale (−r/yn , 1) Y . Therefore (due to closure), (0, 1) Y , which contradicts the absence of a cornucopia.

Note also that if the technological set Y satisfies the free spending hypothesis, and there is a production function f(·) representing it, then the set Y is described by the following relation:

Y = ( (−r, yo ) | yo 6 f(r), r R ) .

Let us now establish some relationships between the properties of the technological set and the production function representing it.

Theorem 47:

Let the technological set Y be such that for all r R the production function f(·) is defined. Then the following is true.

1) If the set Y is convex, then the function f(·) is concave.

2) If the set Y satisfies the free spending hypothesis, then the converse is also true, i.e., if the function f(·) is concave, then the set Y is convex.

3) If Y is convex, then f(·) is continuous on the interior of the set R.

4) If the set Y has the property of freedom of spending, then the function f(·) does not decrease.

5) If Y has the property of not having a cornucopia, then f(0) 6 0.

6) If the set Y has the property of allowing inactivity, then f(0) > 0.

Proof: (1) Let r0 , r00 R. Then (−r0 , f(r0 )) Y and (−r00 , f(r00 )) Y , and

(−αr0 − (1 − α)r00 , αf(r0 ) + (1 − α)f(r00 )) Y α ,

since the set Y is convex. Then, by definition of the production function

αf(r0 ) + (1 − α)f(r00 ) 6 f(αr0 + (1 − α)r00 ),

which means f(·) is concave.

(2) Since the set Y has the property of free spending, the set Y (up to the sign of the cost vector) coincides with its subgraph. And the subgraph of a concave function is a convex set.

(3) The fact to be proved follows from the fact that a concave function is continuous internally.

the size of its domain of definition.

(4) Let r 00 > r0 (r0 , r00 R). Since (−r0 , f(r0 )) Y , then by the property of freedom of spending (−r00 , f(r0 )) Y . Hence, by the definition of the production function, f(r00) > f(r0), that is, f(·) does not decrease.

(5) The inequality f(0) > 0 contradicts the assumption of the absence of a cornucopia. So f(0) 6 0.

(6) By the assumption of the admissibility of inactivity (0, 0) Y . So, by definition

Assuming the existence of a production function, the properties of a technology can be described directly in terms of this function. Let us demonstrate this using the example of the so-called elasticity of scale.

Let the production function be differentiable. At point r, where f(r) > 0, we define

local elasticity of scale e(r) as:

If at some point e(r) is equal to 1, then it is considered that at this point constant returns to scale, if more than 1 then increasing returns, less - diminishing returns to scale. The above definition can be rewritten as follows:

P ∂f(r) e(r) = i ∂r i r i .

Theorem 48:

Let the technological set Y be described by the production function f(·) and

V at point r we have e(r) > 0. Then the following is true:

1) If the technological set Y has the property of diminishing returns to scale, then e(r) 6 1.

2) If the technological set Y has the property of increasing returns to scale, then e(r) > 1.

3) If Y has the property of constant returns to scale, then e(r) = 1.

Proof: (1) Consider the sequence (λn ) (0< λn < 1), такую что λn → 1. Тогда (−λn r, λn f(r)) Y , откуда следует, что f(λn r) >λn f(r). Let us rewrite this inequality as:

Technological sets Y can be specified in the form implicit production functions g(·). By definition, a function g(·) is called an implicit production function if technology y belongs to technological set Y if and only if g(y) >

Note that such a function can always be found. For example, a suitable function is such that g(y) = 1 for y Y and g(y) = −1 for y / Y . Note, however, that this function is not differentiable. Generally speaking, not every technological set can be described by one differentiable implicit production function, and such technological sets are not something exceptional. In particular, the technological sets considered in initial microeconomics courses are often such that their description requires two (or more) inequalities with differentiable functions, since it is necessary to take into account additional restrictions on the non-negativity of factors of production. To account for such restrictions, one can use vector implicit

Let us continue our study of models of balanced economic growth at a more general level and move on to models of economic well-being that are close to them. The latter, like growth models, belong to normative models.

When we talk about the welfare economy, we mean its development when all consumers uniformly reach the maximum of their utility. However, in practice, such an ideal situation occurs quite rarely, since the well-being of some is often achieved at the expense of the deterioration of the condition of others. Therefore, it is more realistic to talk about a level of distribution of goods when no consumer can increase his well-being without infringing on the interests of other consumers.

If, along the trajectory of equilibrium growth, no consumer, like no producer, can purchase more without additional costs (no profit in equilibrium), then when the economy develops along the trajectory of such “welfare”, no consumer can become richer without becoming poorer at the same time another.

From the previous section it follows that taking into account temporary factors in mathematical models of the economy helps to discover a completely logical connection between economic processes and the natural growth of production and consumer capabilities. Under linear models, under certain assumptions, the rate of such growth is equal to the percentage of capital and the corresponding process of economic expansion is characterized by a balanced increase in the intensity of production of all products and a balanced decrease in their prices. In this section, we will formulate a general dynamic model of production, covering the previously discussed linear models as special cases, and study the issues of balanced growth in it.

The generality of the model considered here is that the production process is described not through the production function in general, and the linear production function (as in the Leontief and Neumann models) in particular, but using the so-called technological set.

Technological set(let's denote it by the symbol ) - this is the set of economic transformations when production of products at costs is technologically possible if and only if . The pair is called production process, therefore the set represents the set of all production processes possible with a given technology. For example, in the Leontiev model the technological set j-th industry has the form where is gross output j-th product, and - j th column of the technology matrix A. Therefore, the technological set in Leontiev’s model as a whole is and in the Neumann model -

The production process, generally speaking, may contain products that are both consumed and released (for example, fuels and lubricants, flour, meat, etc.). In economic and mathematical models, for greater generality, it is often assumed that each product can be both consumed and produced (for example, in the Leontiev and Neumann models). In this case the vectors x And y have the same dimension and their corresponding components represent the same products.

Let be the expended volume i-th product, and is its output volume. Then the difference is called net release in progress . Therefore, instead of the production process, the vector of net output is often considered, characterizing this difference as flow(or intensity), i.e. the amount of net output per unit of time. In this case, the technological set is understood as the set of all possible pure outputs. and the vector is called process with thread.

Let us list some properties of the technological set, which are a reflection of the fundamental laws of production.

Different production processes can be compared in terms of both efficiency and profitability.

A process is said to be more efficient than a process if , . The process is called effective, unless it contains more efficient processes than .

Let be a price vector. They say the process more profitable than the process if the value is not less than the value .

These two options for natural and cost assessment of processes turn out to be virtually equivalent.

Theorem 6.1. Let be a technological set. Then a) if, given the price vector, the process maximizes profit on the set, then it is an efficient process; b) if u is convex and efficient in the process, then there is a price vector such that profit reaches a maximum at

Let us determine the structure of the technological set for those models that take into account the time factor. Let's consider a planning period with discrete points Let per year (i.e. at the beginning planning period) the economy is characterized by a stock of goods In this case, the economy is said to be in a state of . By the end of the period, the economy reaches a different state, which is predetermined by the previous state. In this case, they say that the production process has been implemented where is a given technological set. Here the vector is considered as costs incurred at the beginning of the period, and as the output corresponding to these costs, produced with a time lag of one year. At the next stages of production we have etc. In this way it is carried out dynamics of economic development. Such economic movement is self-sustaining, since products in the system are reproduced without any influx from the outside.

The finite sequence of vectors is called acceptable economic trajectory(described by the technological set Z) on a time interval if each pair of its two consecutive members belongs to the set Z, i.e.

Let us denote by the set of all admissible trajectories on the interval corresponding to the initial state

Let The trajectory is said to be more efficient than if the Trajectory is called effective trajectory, if does not contain a more efficient trajectory than . The trajectory is called more profitable than if

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With the help of technological sets, production processes that are carried out by the production system are modeled. Each system has inputs and outputs:

The production process is presented as a process of unambiguous transformation of production factors into production products within a given time interval. During this time interval, factors completely disappear and products appear.

With such modeling - the transformation of factors into products - the role of the internal structure is completely hidden production system, its organization and production management methods.

Observers have access to information about the state of the system inputs and outputs. These states are determined, on the one hand, by a point in the space of goods and factors, and on the other, the state of outputs is determined by a point in the space of outputs.

Space models include many space factors, many space parameters, and many available technologies.

Technology is a technical way of converting factors of production into products.

A technological process is an ordered set of two vectors, where is the vector of production factors and is the vector of products. Process is the simplest model of space, which is defined from a number of elements:

Thus, the technological process is described by a set of (n+m) numbers: .

For example, let’s take a computer of type A and , that is, one computer is produced, then this technological process is described 7+1=8 numbers.

In the practice of modeling real production systems, the hypothesis of linear technologies is used as a first approximation.

Linearity of technologies implies an increase in products V with increasing sets of factors U.

Let's consider the main properties of technological processes:

1. Similarity.

The technological process is similar, i.e. ~ if the condition is met: , which means that this is the same technological process, but proceeding with intensity:

For such processes, the system of equalities is fulfilled:

Similar processes lie on the same line of production technology.

2. Difference.

Different technological processes lie on different rays and cannot be converted into each other by multiplying by a positive number.

3. Composite technological processes.

A process is called composite if there exist and , that .

A process that is not compound is called basic.

The ray passing through the origin in the direction of the base process is called the base ray. Each base beam corresponds to a base technology, and all points on the base beam reflect similar technological processes.

By definition, a basic technological process cannot be expressed through a linear combination of other technological processes.

In the positive octant, you can place a hyperplane that cuts off unit segments from each coordinate.

This allows you to visualize production technologies.

We will show possible intersections of the hyperplane with technological rays.

1) The only technology available is basic.

2) The emergence of new additional basic technology.

3) Linear combination of two basic technologies.

4) Third additional basic technology.

5) The possibility of forming technologies lying inside the triangular area.

6) Two triangular areas with six basic technologies.

7) Combining technologies - a convex hexagon.

8) The case with an infinite number of basic technologies is possible.

In these graphic images, all internal and boundary points, with the exception of the vertices, reflect the constituent technological processes, and the set of all technological processes is called the technological set Z.

Technological sets have the following properties:

1. Not realizing the cornucopia.

(Ø, V)Z, hence, V= Ø.

(Ø, Ø) Z means inaction.

2. The technological set is convex, and processes whose rays lie on the boundary of this set can mix with each other.

3. The technological set is limited from above due to limited economic resources.

4. The technological set is closed, and effective technologies lie on the border of this set.

A specific property of technological sets is the existence of ineffective processes.

If , then any technological processes are possible that satisfy the condition (for factors) (for products).

Exists ( ,Ø) Z, which means the complete destruction of factors of production. No products arise in it at all.

The technological process is more efficient than if and/or.

PRODUCTION FUNCTION.

Mathematical description efficient process can be converted into a production function by aggregating the factors of production, as well as aggregating the products of production into a single product.