MODELING IN DEVELOPMENT OF ORGANIZATIONAL AND PRODUCTION SYSTEMS
The effectiveness of the ASOIU depends significantly on the quality of the models on the basis of which the management process is implemented. Because of the complexity of the control object, it is decomposed into separate parts, that is, functional subsystems are distinguished, including such as technical and economic planning, technical preparation of production, operational management of production, etc. [25, 29, 34, 52] .
The simulation object.
Consider one of the functional tasks of the subsystem of operational control of the main production. As an example of such a task, you can result in the task "Calculation of the plan for the delivery and receipt of parts in natural expression".
The decision of this task on the computer completely allows you to automate the receipt of information on the calculation of delivery plans and details in kind by shops for the year, broken down by quarter and month in enterprises with a sub-planning system. Plans for the delivery and receipt of parts are calculated for all shop-manufacturers and shops-consumers of the enterprise according to the technological route. The basis of these plans is a detailed plan for the need for detail in the commodity output, adjusted for the magnitude of the plan for changing the reserves and compensating for unavoidable in-house losses.
At enterprises with a discrete nature of production (for example, large-scale and mass instrumentation and machine building), the process of the movement of products (parts, assemblies) consists of blanking, machining and assembly stages (Figure 10.7). Usually the procurement and assembly stages are detrimental -
Fig. 10.7. Structural diagram of the movement of products in the process of discrete production
Minimized processes, and the mechano-processing industry has a stochastic nature. In fact, the machining units of production are some kind of cybernetic system of the "black box" type, the input of which receives the stream of blanks, and the output has a stream of batches of finished parts. The number of standard parts in the lot and the release time are random values. To smooth the stochasticity and make the flow of parts of the parts arriving at the assembly, a rhythmic character in advance before the beginning of the planning period, parts are fixed.
stockpiles means various kinds of blanks, purchased component parts, finished parts, etc., located at different stages of the production process in order to ensure the smooth running of the work at its various stages. Usually allocate the following reserves: negotiable, representing the stocks of parts, complex products, etc., which arise due to incomplete coordination of the time of work on individual lines or workplaces; insurance (reserve), which are reserves designed to localize unforeseen interruptions and failures in order to prevent them from spreading further along the direction of the technological route.
In order to determine the optimal size of the parts in the functional subsystem of the operational management of the main production of the company's automated control systems, the corresponding task is solved, based on a model based on an analytical or simulation approach.
A fragment of the production process showing the interaction of the workshop 1 (machining) and the workshop 2 (assembly) through the working and insurance reserves, is presented in the form of a structural diagram (Figure 10.8). In the production process, the following situations are possible: a) normal, when the parts from shop 1 enter the negotiating reserve (link /), and from the backlog - to the assembly (link 5); in the insurance department there is a full stock of parts; b) emergency, when parts from shop 1 do not arrive, the backlog is consumed, and the assembly in shop 2 is provided only at the expense of insurance reserve (communication 4): c) simple, when there is no flow of parts
Fig. 10.8. Structural scheme of interaction between machining and assembly shops
from the shop 1, and stocks of parts in the working and insurance reserves are exhausted, ie, shop 2 is idle; d) transitional, when there are parts in the backlog and it is replenished from the shop 1 (link 7), the details go to the assembly (link 5), and in addition, the insurance fund is being completed (communication 2).
Formalization of the process of modeling object functioning. The process of entering and consuming parts in the workshop 2 can be formalized as a Q-scheme (Figure 10.9). Here I is the source; К - the channel; H - drive.
Thus, the process of procurement of products for assembly (parts, purchased component parts) can be represented as a source (I), issuing a deterministic flow of purchased components and a stochastic stream of batches of parts for assembly. In we will assume that the deterministic flow of purchased components is missing, since in the general case it can be considered as a special case of a stochastic flow. Then at the output AND there will be a flow of parts for processing, which is described as the number of units of parts q in a batch, each of which arrives through Q hours.
The machining process in the machining workshop 1 can be represented in the form of a channel K, with a processing time p sub об об = = const and the time of the inter-operative queuing Q Mn = var, the time of the channel maintenance is Q 1 = Qo6 + Qmu, by the channel K A as well as two drives: and H 2 ,
and as a result of the loss from the marriage qt the number of parts produced q l is random.
The parts after processing are fed to the storage tank x , whose capacity L i corresponds to the nominal value of the parts in the turnaround L = Z o 6 . When the nominal value L v is reached, the details enter the storage tank H 2 , corresponding to the insurance department (if it needs replenishment). When the storage tank H 2 is filled, i.e., reaches the value L 2 , the valve at its input is blocked, with the initial value L t in the drive for the planned period is equal to the value of one batch of parts released from the channel K 1e and the required value of the insurance reserve L 2 = Z C 7 must be evaluated as a result of the solution of the problem.
The process of assembling products in assembly shop 2 can be represented in the form of the channel K 2 , consuming ^ 2 parts in time intervals Q 2 = = const. If there are not enough details in the back-up stock (drive H x ), the need for assembly is filled from the insurance reserve (drive H 2 ) by unlocking the corresponding valve at the output H 2 .
If there are not enough details in the working and insurance grounds, the assembly section, ie the channel K 2 , is idle until the moment it comes from the channel K 1 the required number of parts.
In order to be able to select the desired value of the backlog L l , we determine the probability of the downtime of the assembly site (channel K 2 ) as a function of L 2 , that is, the probability P ^.
Thus, this model is a two-phase Q-scheme with two parallel queues in the second phase of maintenance and with the presence of locks. At the same time, the flows of receipts and services are both deterministic and stochastic. Taking into account the foregoing, it is impossible to obtain the probability P "p analytically by an explicit method, so we will use the simulation method on a computer.
Fig. 10.9. Representation of a production fragment in the form of a Q-scheme
For the model of the production process under consideration, there are two output streams in the form of ( 1-schemes : the flow of processed products & pound; 2 and the defective parts flow b.
Let's represent the variables and equations of the model in the following form: endogenous variable: Рцр - the probability of layup of shop 2; exogenous variables: (2 - the time interval between running parts lots in shop 1; d - the size of batches of parts entering the processing in shop 1; 0 1 sub> = bob + + cm n - time interval -
Fig. 10.10. The enlarged scheme of modeling algorithm of a fragment of manufacture
me between the release of parts from the shop 1, where Ол - a constant processing time; Q MJ 1 is the time of the inter-operative straining; q l = q-qt is the number of parts produced by the workshop 1, where q 6 = qF 6 - the number of defective parts; F 6 - the proportion of defective parts that is considered to be uniformly distributed in the interval (0, Ft); Q 2 - the time interval between the start of parts in shop 2; q 2 - the number of parts in the batch for shop 2; Z CT - insurance reserve, whose value at the beginning of the year Zero; Zo6 - a backlog, whose value at the beginning of the year Zo6oi model equation
where F г - the annual fund of time; T ni is the downtime of shop 2 due to lack of parts. For the simulation interval (0, T) we take the annual time fund T = r = 4080 h.
The integrated scheme of the modeling algorithm of the production fragment at the level of solving the problem of determining the insurance reserve, i.e., the interaction between the machining (shop 1) and the assembly shop (shop 2), is shown in Fig. 10.10.
The results of the simulation in the form of the POPP/(QT) D * m * dependence of the various values of the start are shown in Fig. 10.11.
Fig. 10.11. The result of modeling the production fragment
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