BASIC PRINCIPLES OF THE DESIGN AND OPERATION OF ASUP-TOMSK

Yu. N. Efimov, V. I. Kizev, V. I. Nevraev, F. I. Peregudov,
P. A. Sedelnikov

(Presented by the scientific seminar of the Computer Engineering Department of the Scientific Research Institute of AEM)

The continuously increasing difficulties of managing modern industrial enterprises make it necessary to develop automated control systems. Built on a scientific basis and successfully combining the experience and knowledge of managers with the great capabilities of modern computing equipment, automated enterprise control systems represent a qualitative leap in the organization of production management.

The authors have developed one variant of an automated enterprise control system (ASUP-Tomsk), applicable under conditions of large-batch, batch, and small-batch production. The proposed system differs fundamentally from other ASUP systems [1, 2] having the same field of application in its method of forming the operational calendar plan and, accordingly, in all the other issues associated with calendar planning. It should also be noted that the main ideas of ASUP-Tomsk, based on graph theory and set-theoretic representations, in principle exclude the possibility of “manual calculation” and require the use of electronic computers (ECMs).

Beginning in September 1968, the developed system underwent experimental testing at one of the enterprises in the city of Tomsk. For products planned by the ECM, within two months the enterprise entered a rhythm of supplying parts from its own production. With the continuous increase of the directive commodity plan and an unchanged number of workers, the rhythm of output improved and the volume of work in progress was significantly reduced. The calendar plan and its technical-economic indicators encompass and synchronize the activity of all divisions of the enterprise in the interests of producing marketable products. Since October 1969, for the first time all marketable production, and since January 1970 also the material and technical supply of the enterprise, have been transferred to machine planning.

Two years’ experience in operating individual blocks of the system has shown its high efficiency, especially for planning products that are complex in design. The possibility of phased implementation of ASUP (by product), the simplicity of the methodology for preparing products for transfer to machine planning and control, the provision of end-to-end accounting of balances, and the minimization of work in progress—these are the distinctive qualities of the proposed system and serve as a guarantee of its successful implementation and operation.

In developing ASUP-Tomsk, the “Ural-11B” computer was used; however, the system can be oriented toward the use of any modern general-purpose electronic computer. Since the organization of the computing process depends on the specific type of computer employed (word length, size of main memory, composition of external devices), the article does not present flowcharts of particular programs. The article also does not discuss questions connected with the forms of input, output, and control documents, since they must take into account both the characteristics of the computer and the specifics of the particular enterprise.

Principal Functions of the System

In the planning mode, ASUP-Tomsk performs the following planning-and-calculation functions, coordinating the activity of the various divisions of the enterprise.

1. Calculation of an operational calendar production plan on the basis of directive plans for the output of commodity products and with allowance for the current state of production. The calendar plan generated by the system synchronizes the work of all divisions of the enterprise, which guarantees rhythmic fulfillment of the directive plan with a minimal level of work in process.

2. Normative calculation of the technical-and-economic indicators of the output plan for each division of the enterprise in terms of labor input, wage fund, and the cost of the resources needed for its implementation (materials, purchased components).

3. Normative calculation of the planned requirement for material resources in accordance with the calendar launch plan of each division separately for two time periods. On the basis of the planned requirement in the first period, the current material-and-technical provision of production is checked. The second period characterizes the prospective requirement for resources and makes it possible to submit the necessary requisitions in good time.

4. Calculation of detailed standards for the cost of materials and purchased components for each division of the enterprise, as well as compilation of a costing of normative prime cost for all elements of the product design.

5. Calculation of the volume of work in process in value terms, in accordance with the inventory balances.

6. Compilation of a statement of kitting according to the consolidated specification, and vice versa. The kitting statement may be distributed by the addresses of the kitting sections.

7. Formation of a plan for preparing the production of a product, or of individual elements of its design, coordinated respectively with the output plan for the lead batch of this product or with the calendar plan of current production.

In the control mode, when ASUP operates on operational-dispatch reports, in addition to the functions set forth above, the following accounting-and-regulating functions are performed:

1. Compilation of reports on the actual fulfillment of the plan by individual divisions and by the enterprise as a whole.

2. Accounting for the movement of material assets on the scale of the enterprise and control of their consumption by means of planned limitation of the use of resources at all stages of production.

3. Calculation of the planned volume of work in process in value terms by divisions and for the enterprise as a whole.

4. Regular monitoring of the fulfillment of the operational calendar plan in order to detect instances of lagging in good time.

5. Statistical study of the duration of the production cycle of an accepted batch of parts in order to correct its initial value.

The listed set of tasks is solved by the system in an interrelated manner and requires a minimal amount of initial information.

Production Model.

Operational Calendar Planning

The compilation of an operational calendar plan that synchronizes the activity of all divisions of the enterprise in the interests of fulfilling the plan for the output of marketable products within the established time periods, while simultaneously providing the necessary proportional backlogs, is one of the central tasks of any ASUP.

To solve this problem on a computer it is necessary to develop an economic-mathematical model, that is, to describe formally the process being planned. It is obvious that increasing the set of production states distinguished by the model leads to an increase in the volume of information required to describe it. In constructing an automated control system, the level of the production state distinguished by the model must be chosen on the basis of a reasonable compromise between the informational value of the output (control) data and the volume, reliability, and cost of collecting and processing the corresponding input information, as well as the capabilities of the computers currently being produced serially. In principle, it is possible to create models that distinguish the state of production both down to the level of the inter-shop route of each structural element of the product or down to the level of its intra-shop route by sections, and down to the level of an individual technological operation.

In the ASUP being described, a model has been adopted that distinguishes only the inter-shop route of parts, assemblies, instruments, etc., as individual structural elements of a marketable product. This model is represented in the form of a finite directed graph, which makes it possible to use the mathematical apparatus effectively for its analysis. We shall give a more complete description of the network production model proposed by us, as well as a stricter mathematical formulation of the operational calendar planning problem within the framework of this model.

Each marketable product of the enterprise, in accordance with its design and technological documentation, is represented by a finite directed graph \(G=(IU)\) without circuits, containing \(|I|\) vertices and \(|U|\) arcs [3]. The vertices (products) \(i \in I\) of the graph are the marketable products themselves, as well as all elements of their structure (parts, subassemblies, assemblies, instruments, etc.). To each arc \((ij)\in U\) there is assigned a parameter \(r_{ij}\), which has the meaning of the consumption rate of product \(i\) per unit of product \(j\).

In the proposed production model, the enterprise is represented by two sets of divisions \(Y=\{y\}\) and \(X=\{x\}\), respectively producing products \(i\) (shops) and issuing into work products that are the initial items for the production of each product \(i\) (warehouses, kitting sections). To each vertex (product) \(i\in I\) of the graph \(G\) there correspond the following data:

\(m_i\) — manufacturing batch of product \(i\);

\(Y_i\) — technological route of product \(i\);

\(T_i\) — duration of the production cycle for manufacturing a batch of product \(i\) in division \(y\in Y\);

\(x_i\) — address of the division issuing into work products that are initial items for the production of product \(i\);

\(\Delta_i\) — stock of finished product \(i\) at time \(t_0\), corresponding to the beginning of the planned period;

\(\sigma_i^y\) — quantity of product \(i\) that, at time \(t_0\), is in the process of production in division \(y\in Y_i\);

\(H_{i\Theta}^{y}\) is the norm of expenditure of a resource of type \(\Theta\), consumed by subdivision \(y \in Y_i\) in producing product \(i\).

To each subdivision \(y \in Y_i\) one may assign the number \(k_i = k(i,y)\)—the ordinal number of subdivision \(y\) in \(Y_i\).

\[ K_i = 1, 2, \ldots, k_i^{y}, \ldots, n_i . \]

Then, in the expressions considered below, the current subdivision in \(Y_i\) may be denoted by \(y_k\).

For each vertex \(i \in I\) (including commercial products), a directive output plan may be specified in the form of a discrete function \(P_i^{\mathrm{d}}(t)\).

On the basis of the data listed above, it is required to transform the directive plans \(P_i^{\mathrm{d}}(t)\) into particular plans for launching \(P_i^{\mathrm{zu}}(t)\) and output \(P_i^{\mathrm{vu}}(t)\) for all vertices (products) \(i \in I\), with their distribution among the addresses of subdivisions \(y\).

For simplicity of the subsequent reasoning, let \(n_i = 1\).

In view of the discreteness of the function \(P_i^{\mathrm{d}}(t)\), the function \(P_i^{\mathrm{z}}(t)\) is also discrete and can be represented by a finite set of pairs ordered by increasing \(t\):

\[ P_i^{\mathrm{z}}(t) = \{q_{i\lambda}^{\mathrm{z}},\ t_{i\lambda}\}_{\lambda = 1,\mu_i}, \]

where

\(q_{i\lambda}^{\mathrm{z}}\) is the quantity of product \(i\) launched into production at time \(t\);

\(\mu_i\) is the number of elements of the launch plan.

The values of the elements of the launch plan for product \(i\) are determined by the consumption plan \(P_i^{\mathrm{p}}(t)\) for this product, which is also represented by a finite set of pairs:

\[ P_i^{\mathrm{p}}(t) = \{q_{i\lambda}^{\mathrm{p}},\ t_{i\lambda}^{\mathrm{p}}\}_{\lambda = \overline{1,\nu}}, \]

where

\(q_{i\lambda}^{\mathrm{p}}\) is the quantity of product \(i\) consumed at time \(t_\lambda\);

\(\nu_i\) is the number of elements of the consumption plan.

It is obvious that for the enterprise’s commercial products

\[ P_i^{\mathrm{p}}(t) = P_i^{\mathrm{d}}(t). \]

The dependence between \(P_i^{\mathrm{z}}(t)\) and \(P_i^{\mathrm{p}}(t)\) is determined by the relation

\[ P_i^{\mathrm{z}}(t) \ge P_i^{\mathrm{p}}(t + T_i) - (\Delta_i + \sigma_i), \]

which expresses the basic principle of maintaining the synchronous operation of all subdivisions of the enterprise. To satisfy this relation, it is necessary to launch product \(i\) in the amount \(q_i^{\mathrm{z}}\lambda = \chi_i\lambda \cdot m_i\) (\(\chi_i\lambda\) is a positive integer) at those times \((t_i^{\mathrm{p}}\lambda - T_i)\) when its available quantity becomes less than the planned consumption over the time period \(T_i\) required for its production.

It is obvious that, over an infinite time interval, the output plan for any product \(P_i^{\mathrm{vu}}(t)\) in each subdivision \(y\) exceeds its launch plan \(P_i^{\mathrm{zu}}(t)\) by the amount \(\sigma_i^y\). Therefore, in order to preserve the time distribution of the output of that part of product \(i\) which, at time \(t_0\), is in production, a conditional launch plan is formed:

\[ P_i(t) = m_i \cdot E \left[ \frac{ P_i^{\mathrm{p}}\left(t + \sum_{k_j=1}^{n_i} T_i^{y_k}\right) - \Delta_i }{ m_i } \right], \]

where \(E[d]\) is the least integer not less than the argument \(d\).

In turn, the planned consumption of product \(i \in I\) may be determined by the following relation:

\[ P_i^{\mathrm{п}}(t)=P^{q_i}(t)+\sum_{j\in\Gamma_1}\left[P_i(t)-\sum_{k_j=1}^{n_i}\sigma_j^{y_k}\right]\cdot r_{ij}. \]

As is evident from the relations given above, the conditional launch plan is a recurrent function, which necessitates the sequential recalculation of plans, beginning with commercial products and ending with parts. To make such a recalculation possible, it is necessary first to order the topology of the graph by layers, for example by the method of [4].

The time required to calculate plans on a computer depends substantially on the method of specifying the graph.

When analyzing the graph in the form \(G=(I,\Gamma^{-1})\), it becomes necessary to store a large number of partial consumption plans for vertices \(i\in\Gamma^{-1} I_1\), but \(i\in I_1\) (\(I_1\) is the set of graph vertices examined at some fixed stage of the computational process). The number of stored partial consumption plans is determined by the topology of the graph and changes during the computation. It should also be noted that the number of elements is not the same, and that the form in which consumption plans are written is cumbersome. All this leads to irrational use of the computer’s main and external memory, complicates the storage and retrieval of plans, and, consequently, increases computation time.

When analyzing the graph in the form \(G=(I,\Gamma)\), it is necessary to store only the conditional launch plans. Since in them the size of the one-time order \(q_{ij}\) is a multiple of the batch \(m_i\), one may write:

\[ P_i(t)=m_i\cdot x_i(t), \]

where \(x_i\) is a quantity characterizing the quantity being launched, and its location (position) in \(P_i(t)\) is the launch time. Let us assume that no more than one batch \(m_i\) is launched at the same time. In this case it is sufficient to record only the fact of launch itself, which requires one binary digit. This form of notation is quite compact, which makes it possible to make it of fixed length. It follows from this that representing the graph in the form \(G=(I,\Gamma)\) is more convenient for implementing algorithms for its analysis. In this connection, if the graph is specified in the form \(G=(I,\Gamma^{-1})\), it must be brought to the form \(G=(I,\Gamma)\), using, for example, the algorithm of [5].

On the basis of the obtained conditional launch plans it is not difficult to form calendar launch–output plans for the complete set of products \(i\in I^y\) that are to be processed in a specified time interval, where \(I_y\in I\) is the nomenclature of subdivision \(y\in Y\).

The launch plan of product \(i\) in subdivision \(y^*\) is determined as follows:

\[ P_i^{\mathrm{з}y^*}(t) = P_i\left( t-\sum_{k_i=1}^{k^{y^*}}T_i^{y_k}+T_i^{y^*} \right) - \sum_{k_i=i^{y^*}}^{n_i}\sigma_i^{y_k}. \]

The output plan, respectively, is equal to:

\[ P_i^{\mathrm{в}y^*}(t) = P_i\left( t-\sum_{k_i=1}^{k^{y^*}}T_i^{y_k} \right) - \left( \sum_{k_i=k_i^{y^*}}^{n_i}\sigma_i^{y_k}-\sigma_i^{y^*} \right). \]

In the proposed model it is assumed that, in the production of any product \(i\in I\), all structural elements included in it are consumed by the first shop along the technological route. Then, for the purposes of kitting, one may use the calendar launch plans of the first shops for the complete set of products \(i\in I_x\), where \(I_x\in I\) is the nomenclature of products kitted by subdivision \(x\).

\[ P_i^{x}(t)=P_i(t)-\sum_{k_i=1}^{n_i}\sigma_i^{y_k}. \]

It should be noted that, according to the proposed algorithm, the conditional launch plan is formed taking into account not only the enterprise’s own balances, but also the balances of products that enter into the direct transitive closure of the graph \(G\) for vertex \(i\), i.e., an end-to-end accounting of balances is carried out.

It may be asserted that the algorithm ensures rhythmic operation of the enterprise’s producing subdivisions at a level of work in process close to the minimum.

It must be borne in mind that the correctness of forming calendar plans can be ensured only if the directive plan for product output \(P_i^{\mathrm{d}}(t)\) is specified over a time interval no shorter than the duration of the production cycle for manufacturing this product as a whole (beginning with parts), plus the duration of the planned period. The duration of the production cycle for manufacturing an item is equal to:

\[ T_i^{\mathrm{c}}=\max_{i\in I} T_i^{\mathrm{c}}, \]

where the values \(T_i^{\mathrm{c}}\) for the vertices of the graph ordered by layers are computed by the following recurrence formula:

\[ T_i^{\mathrm{c}}=\sum_{k_i=1}^{n_i} T_i^{y_k}+\max_{j\in \Gamma_i} T_j^{\mathrm{c}}. \]

Sometimes there arises a need for the joint calculation of several items, especially in the case of significant intersections of their topologies. However, design and technological documentation, as a rule, is compiled separately for each item. In this case the topologies of the product networks are “stitched together” on the basis of certain formal graph-transformation procedures [5].

It should also be noted that the design documentation may contain such elements of the product structure whose production process, within the proposed model, is not controlled at the enterprise. To exclude uncontrolled vertices, the graph is reduced according to the algorithm [6]. If the uncontrolled item is subdivision \(y\in Y_i\), then it should not be included among the parameters of the network model for production of the item.

Since the proposed calculation algorithm performs end-to-end accounting of balances, the accuracy of calculating calendar launch-output plans depends largely on the reliability of information about the current state of production. In the planning mode, when the size of the product balances \(i\in I\) available at the enterprise is determined as a result of an inventory of work in process, precise determination of the value \(\sigma_i^{y}\) presents great difficulties. These difficulties can be overcome only when operating in a control mode that provides accounting for the movement of products among the enterprise’s subdivisions.

In preparing the production of new items, the network model of the item is linked with the model for preparing its production. As a result of the calculation, mutually time-coordinated plans are formed for manufacturing tooling and a pilot batch of items.

Operational planning of material and technical supply

One of the important factors ensuring the normal functioning of the MTS services and, ultimately, the fulfillment by the enterprise

...of planned assignments is the timely determination of the amounts of this enterprise’s need for material resources within a specified time interval, as well as their comparison with the quantities available on hand. The results of such a comparison are the initial data for preparing supply applications, and the amounts of planned resource consumption may be used for the purposes of monitoring their expenditure.

It is obvious that the planned need for resources must be determined on the basis of previously calculated launch plans for all elements of the design of the products manufactured at the enterprise; i.e., the mathematical model of material-and-technical supply (MTS) must be interfaced with the model of operational calendar planning.

In the proposed MTS model, the enterprise is represented by three sets of subdivisions:

\(Y=\{y\}\) — the set of subdivisions (shops) consuming resources;

\(X=\{x\}\) — the set of subdivisions (warehouses) issuing the corresponding resources to the shops;

\(Z=\{z\}\) — the set of subdivisions (MTS groups) concerned with the acquisition of resources.

As a model of resource consumption, a directed graph \(G=(J,\Gamma)\) is used, whose topology reflects the interrelation, determined by design and technological documentation, of materials and purchased products, on the one hand, and parts, assemblies, and instruments, on the other.

The vertices \(i\in J\) of the graph \(G\) are materials and purchased products, while the elements \((j,y)\) of their direct mapping \(\Gamma_i\) are products constituting the network model of the planned product and manufactured in subdivisions \(y\in Y_j\).

The following parameters correspond to each vertex of the graph \(G\):

\(x_i\) — the address of the subdivision issuing resource element \(i\) into work;

\(z_i\) — the group to which resource element \(i\) belongs;

\(c_i\) — the price of resource element \(i\);

\(\Delta_i\) — the balance of resource \(i\) in warehouse \(x_i\);

\(\sigma_i^y\) — the balance of resource \(i\) in the shop warehouse \(y\in\Gamma_i\).

To each arc \(i,(j,y)\) of the graph \(G\) there is assigned a parameter \(r_{ij}^y\), having the meaning of the consumption norm of resource element \(i\) per unit of product \(j\), manufactured in subdivision \(y\in Y_j\).

On the basis of the MTS model described above and of the previously calculated conditional launch plans \(P_j(t)\), we determine the planned consumption of each resource element \(i\in J\) in the time interval according to the formula:

\[ Q_i=\sum_{(j,y)\in\Gamma_i}\sum_{t=t_a}^{t_\beta} \left[ P_j\left(t-\sum_{k_j=1}^{k_j^y}T_j^{yk}+T_j^y\right) - \sum_{k_j=k_j^y}^{n_j}\sigma_j^{yk} \right]\cdot r_{ij}^y, \]

The amount of planned consumption of resource element \(i\) by subdivision \(y^*\) in the time interval \([t_1,t_2]\) is determined by the following expression:

\[ Q_i^{y^*}= \sum_{(j,y^*)\in\Gamma_i}\sum_{t=t_1}^{t_2} \left[ P_j\left(t-\sum_{k_j=1}^{k_j^{y^*}}T_j^{yk}+T_j^{y^*}\right) - \sum_{k_j=k_j^{y^*}}^{n_j}\sigma_j^{yk} \right]\cdot r_{ij}^y. \]

Let us note that end-to-end accounting of balances when calculating conditional launch plans makes it possible to increase the accuracy of calculating the planned need for resources in a specified time interval.

The calculated \(Q_i^y\) and the values of resource balances \(\sigma_i^y\) in the corresponding shop warehouses are the basis for forming limit-

requisition statements for the full set of resource elements \(i \in I^{xy}\), issued to the addresses of warehouses \(x \in Y\) with distribution by the addresses of shops \(y \in Y\).

To form shortage statements for the full set of resource elements \(i \in I_z\), distributed by groups \(z \in Z\), data are used on the available balances of resources in factory and shop warehouses,

\[ \Delta_i + \sum_{y \in I_i} \delta_i^y \]

and on planned requirements in the time intervals \([t_1, t_2]\) and \([t_2+1, t_3]\). The time interval \([t_1, t_2]\) is the current planned period, and \([t_2+1, t_3]\) is the next planned period, which determines the shortage forecast.

Data on the prices of resource elements \(c_i\) and their consumption rates per unit of product \((j, y^*)\) are used to calculate the cost \(H_j^{y^*}\) of the resources consumed by subdivision \(y^* \in Y_j\) per unit of each product \(j\):

\[ H_j^{y^*} = \sum_{i \in (j,-1)^{y^*}} c_i \cdot r_{i,j}^{y^*}. \]

The results of such a calculation are used for purposes of techno-economic planning.

Data on resource balances are also used to determine their value.

Since the design and technological documentation available at the enterprise is compiled by products, while it is desirable to obtain data on material and technical supply for the enterprise as a whole, all calculations are performed by products, and the results are summed.

Since, for calculating planned requirements, it is more convenient to specify the topology of the graph in the form \(G = (J, \Gamma^{-1})\), then, if it is necessary to change the way it is represented, the algorithm [5] can be used.

In the case when models of production of products are “stitched together,” the network models of material and technical supply are subjected to the same procedure.

Techno-economic Planning

For planned-economic calculations, techno-economic standards are used, entered directly into the production model (labor and wage standards), as well as standards calculated on the basis of the model of material and technical supply (the cost of materials and purchased items). All the listed standards for each product are determined as a whole for the subdivision participating in the production of this product. The normative techno-economic calculations cover the following series of independent tasks: calculation of the techno-economic indicators of the production schedule for each subdivision and for the enterprise as a whole for a given planning period; calculation of the distribution of resource costs per unit of marketable product by manufacturing subdivisions; calculation of the normative cost for each structural element and for the product as a whole; calculation of the volume of work in progress for individual subdivisions and for the enterprise as a whole.

The calculation of the techno-economic indicators of the production schedule is reduced to forming a consolidated (by nomenclature) plan of material and labor costs for the product separately for each type of resource in a given time interval. The consolidated plan of a subdivision for any type of cost is determined by the expression:

\[ \Pi_{\theta}^{y^*} = \sum_{t=t_1}^{t} \sum_{i \in I_{y^*}} P_i^{by^*}(t) \cdot H_{i\theta}^{y^*}. \]

The consolidated plan of the enterprise for each type of cost \(\Theta\) is determined by the relation:

\[ \Pi_{\Theta}=\sum_{y\in Y}\Pi^{y\Theta}. \]

The calculation of the expenditures of subdivisions \(y\in Y\) per unit of product is performed as follows. First, the consumption norm of each product \(i\in I\) per unit of product is determined from the following recurrence relation:

\[ r_{iИ}=\sum_{i\in \Gamma_i} r_{ij}\cdot r_{jИ}, \]

where \(r_{jИ}\) is the consumption norm of product \(j\) per unit of product. Then a direct calculation is made of each type of expenditure of subdivision \(y^*\):

\[ c_{\Theta}^{y^*}=\sum_{i\in I_{y^*}} r_{iИ}\cdot H_{\Theta}^{y^*}. \]

The cost of each product \(i\in I\) by standard cost items is determined as the sum of the individual types of expenditures, which, in turn, are found from the following recurrence relation:

\[ c_{i\Theta}=\sum_{i\in \Gamma_{j-1}} c_{i\Theta}\cdot r_{ij}+\sum_{k_j=1}^{n_j} H_{j\Theta}^{y_k}, \]

where \(c_{i\Theta}\) is the magnitude of cost item \(\Theta\) in the standard cost.

The calculation of the volume of work in progress can be divided into two parts according to the types of work in progress \(\Delta_i\) and \(\sigma_i^y\).

Determining the volume of stocks of finished products by types of expenditure presents no difficulty and is carried out by the formula:

\[ M_{\Theta}=\sum_{i\in I}\Delta_i\cdot c_{i\Theta}. \]

An exact calculation of the volume of work in progress, \(\sigma_i^y\), corresponding to products that are in the production stage, cannot be performed. This is due to the fact that, in the adopted model, the actual stage of the production process of a product within a subdivision is not recorded. Therefore, we shall assume that some types of resource are consumed immediately, while others are consumed uniformly over a period of time equal to the duration of the production cycle for manufacturing product \(T_i^y\). Then the calculation of the volume of work in progress \(\sigma_i^{y^*}\) for each subdivision \(y^*\), by the types of expenditures introduced into the product immediately (the cost of materials and component parts), can be performed by the formula:

\[ M_{\Theta}^{y^*}=\sum_{i\in I_{y^*}}\sigma_i^{y^*} \left( c_{i\Theta}-\sum_{k_i=k_{y^*}}^{n_i} H_{i\Theta}^{y_k}+ \Pi_{i\Theta}^{y^*} \right). \]

For calculating expenditures that increase continuously in the production process (for example, wages), let us assume that the entire set of work in progress is at the average stage of completion. Then

\[ M_{\Theta}^{y^*}=\sum_{i\in I_{y^*}}\sigma_i^{y^*} \left( c_{i\Theta}-\sum_{k_i=k_{y^*}}^{n_i} H_{i\Theta}^{y_k}+ \frac{1}{2}H_{i\Theta}^{y^*} \right). \]

As is evident from the foregoing, the proposed methodology for techno-economic calculations requires the introduction into the production model of a small amount of additional information (only labor and wage standards) and makes it possible to perform calculations with a sufficient degree of accuracy.

Organization of the System’s Information Support

The preparation of permanent information arrays needed for introducing an automated control system into the practice of enterprise planning is a labor-intensive process and must be organized with due regard for the established forms of documents and for the particular distribution of functions among subdivisions within the enterprise’s organizational structure. To improve the reliability of the source information and to simplify the task of preparing it, the ASUP-Tomsk production model adopted parameters that characterize only the given item in the product composition; parameters whose preparation requires studying the structural interrelationship or technological sequence of different products are entirely absent. The latter include, for example, lead time \[1\].

The information needed for the operation of ASUP-Tomsk consists of arrays for which, in the enterprise structure, there are corresponding subdivisions responsible for their reliability.

The information array on the topology (TI) of the product network model is created on the basis of a consolidated specification or of summary specifications for the complete list of drawings of the given product. The array of parameters of the elements of the product design (MPI) contains the following information for each product making up the item: code, decimal designation, technological route, production batch, and number of the completing section.

After the computer has checked the one-to-one correspondence of codes in TI and MPI, statements are formed for each subdivision, over its full nomenclature, to present information on production-cycle durations, labor-consumption standards, and wages.

The procedure described for preparing the source information makes it possible to transfer to machine planning a product with a composition of 1,000 item names within one month.

Information on the topology (TR) of the MTO network model is formed in separate arrays for each product, for each type of resource consumed (materials, component parts). Information on the parameters of resource elements (MPR) is formed as separate arrays for each type of resource on the scale of the enterprise. The MPR for each type of resource contains the following data for each element of its nomenclature: code, designation, unit of measure, price, group, storage warehouse.

With the aid of the computer, the one-to-one correspondence of the TR, MPR, and TI codes is checked, as well as the addresses of subdivisions in TR and MPI.

It should be noted that the arrays listed above have documentary representation at the enterprise, which simplifies the initial collection of the required volume of information. Program checking of the correspondence between certain arrays makes it possible to identify a number of logical errors and to ensure their rigid coordination.

Organization of the Computing Process

It is obvious that the tasks solved by an ASUP are complex and many-sided. Therefore it is fundamentally impossible to develop a single universal program that solves all the tasks listed above. There is no doubt that the mathematical support of an ASUP must include a set of programs ordered according to the principle of continuity of input and output information. However, if one follows the path of creating small programs, the number of such programs, as well as the instructions and other guiding materials for them, will be considerable. The development of large programs is also not expedient because of

that, given the limited capabilities of modern computers, this leads to a sharp increase in the ratio of “exchange” time to “computing” time and, consequently, to a decrease in speed. Evidently, there is always an optimal universality of programs, which depends both on the specifics of the problem being solved and the efficiency of the computational method, and on the characteristics of the computer being used.

As already indicated, the algorithms proposed in ASUP-Tomsk are implemented on the Ural-11B computer. Taking into account the above considerations, the entire computational process is divided into approximately 40 programs, united by means of a dispatcher program (D). All programs can be divided into the following groups:

a) input with preliminary processing;
b) control programs;
c) calculation programs;
d) output to the ACPU;
e) transformations of network models;
f) combined programs (including the functions of several groups).

Each program has from 1 to 8 modifications:

a) with checking or without checking;
b) analysis of TI or TR;
c) analysis of the graph in the form \(G=(I,\Gamma)\) or \(G=(I,\Gamma^{-1})\).

All programs, taking modifications into account, are assigned pseudocodes (PK), consisting of the program number (P) and the modification number (M). According to P, the dispatcher calls the required program from the NML into the NF, and according to M it sets the operating mode. The dispatcher program ensures both the execution of an individual PK specified by the operator from the computer control console and the execution of a group of PKs recorded in the pseudocode table (TPK).

In general, D consists of a constant (C) and a variable (XZ) part. C contains the dispatcher program itself, the TPK, and global constants. XZ is the characteristic of a particular order (product), which contains information on the location and sizes of the arrays belonging to this order. This information is entered into XZ by programs that form the corresponding arrays. D makes it possible, by the order number specified by the operator from the control console, to call the corresponding XZ, while the state of the previous XZ is recorded on ML. This makes it possible to interrupt the processing of an order at any stage of the computations and then continue from the interrupted stage. The calling of XZ is also permitted to certain global programs by means of a special call to D.

The functions of D also include preliminary distribution of ML among the arrays of a single order.

The development of the dispatcher program made it possible to greatly simplify and accelerate the performance of the calculations provided for by the automated control system, and also to reduce to a minimum the number of errors inevitably made by the operator.

In conclusion, let us note that all algorithms executed by ASUP-Tomsk in the planning mode have been fully tested and implemented at the enterprise under conditions in which other planning methods are excluded. Experience has shown that the proposed algorithms are sufficiently effective and cover all the principal planning tasks of the enterprise. Without substantial changes, these algorithms can be widely used at machine-building enterprises of various profiles.

The algorithms executed by the system in the control mode are still at the development stage.

Of particular interest are optimization problems, which may

can be solved within the framework of the proposed economic-mathematical model. For example, the problem of selecting a variant of an enterprise’s commodity plan given specified resource availability; drawing up an optimal schedule for processing products in each particular subdivision with the aim of strictly fulfilling the calculated launch-output plans; planning the production of enterprises interconnected by cooperative deliveries (the network model has circuits), and others.

Apparently, it is also expedient to study the dependence of the possible degree of detail of network models of individual products on the means of computer technology employed. The programs developed for the Ural-11B computer make it possible to analyze network models of products containing no more than 4095 vertices.

The authors hope that the basic principles of the design and operation of ASUP-Tomsk may find application in the development of automated control systems both for enterprises and for an industry.

REFERENCES

1. A. E. Perel’man. Automated system of operational planning and production control. Moscow, 1968.

2. Automated system of operational control for the Barnaul Radio Plant (ASU-Barnaul). Novosibirsk, 1969.

3. K. Berge. Graph Theory and Its Applications. Moscow, Foreign Literature Publishing House, 1962.

4. Yu. N. Efimov. Algorithm for finding the order function of a network graph. Izv. TPI, vol. 168, 1969.

5. Yu. N. Efimov, P. A. Sedel’nikov. On an algorithm for transforming the form of representation of a graph. (This collection).

6. V. I. Kizev, Yu. N. Efimov, V. I. Nevraev, P. A. Sedel’nikov. On an algorithm for coarsening a graph. Izv. TPI, vol. 223 (in press).