“Production functions” are from textbooks on economics and microeconomic models, which have nothing to do with practice.
Pass the curriculum and forget ... Read about global trends and laugh ...
Consider situations where "production functions" can be practically useful and provide an opportunity to significantly improve planning and management processes.
The problem was simple. There is a shortage of funds. The financial block accumulates (withdraws) funds for payments and allocates very little for the purchase of components. Due to the shortage of components, small-scale production of very expensive products is constantly idle and disrupts order fulfillment times. Less money comes in, the financial block accumulates it again, not letting it go to production. Vicious circle.
The following shows how "production functions" naturally arise in an industrial enterprise. They can be used to find mutually acceptable compromises between the production (industrial) and financial blocks of the company.
In the course of building production functions, the question arises about ways to unify the product line, which leads to a decrease in the costs of spare parts reserves.
The converse is also true: without product line unification, it is difficult to achieve practically useful production functions.
In the Soviet Union, cartridges, shells and Kalashnikov assault rifles were mass-produced from finished products. Everything else was related to non-mass production, even if they were assembled on an assembly line: medium-scale, small-scale and unique.
The problem under consideration is quite urgent due to the fact that the small series is still the basis of the Russian economy.
The question immediately arose about the Customer's data for solving the task: to create a working group, to meet weekly ... Dead end.
Our further research is based solely on data obtained from documents that were submitted to the Board when approving the annual budget.
1. "Production functions" and balancing models
When developing models and production functions, the following parameters were used:
temporary
daysInYEAR - days in a year;
shiftSTAFF - number of employees;
shifts - number of shifts;
hours - hours per shift;
lunchTIME - lunch time (rest);
overTimeHOURS - the number of overtime hours;
production
totalCAPACITY - maximum productivity;
unitCycleTIME - the cycle time for the production of one product;
rejectASSEMBLY - reject during assembly;
stop - the probability of stopping due to a lack of components;
cost
laborHourCOST - hourly rate;
overHeadRATE - overhead;
directCOST - direct costs;
parameters of components
partsVOLUME - volume of components;
priceBUY - price of purchased components;
rejectBUY - marriage of purchased components;
priceOWN - price of self-made components;
rejectOWN - rejects of own components;
discountRANGE - volume discount amount;
partsCoefficientBUY - share of purchases;
partsCoefficientOWN - share of own components;
market
unitPRICE - product selling price;
investment - investments;
missedBENEFIT - lost profit;
unitPRICE is the selling price of one product;
"Production function", determined by production and technological factors
Let us form a production function that determines the non-linear relationship between the number of available sets of components and the probability of stopping due to a lack of components.
The model uses an exponential function with a base base to the extent of the number of available kits The maximum number of sets is calculated, after which the stop value becomes practically zero.
Dynamic version of the picture .
Changing the base value (the first slider) changes the slope / flatness of the graph. The second slider allows you to get the value of the function corresponding to the selected number of components, or, conversely, at the desired value of the function (percentage of 1) to find out the corresponding value of the number of components.
As a result, we get (the second graph) a new stop value, which is achieved when there is a corresponding reserve of the number of components.
Instead of an exponential function, there can be any other function in form or content: empirical, heuristic (expert), algebraic, or piecewise continuous.
The purpose of this production function is to relate the stop value to the number of available parts only based on production and technological factors and available experience.
A model for balancing production and technological feasibility and financial and economic efficiency The
production and technological feasibility dictates the desire to have as many components as possible (taking into account possible marriage). On the other hand, financial and economic efficiency is focused on minimizing the money frozen in components.
The balancing of production and technological feasibility and financial and economic efficiency is based on the dependence of the probability of stopping stop due to a lack of components and the amount of investment required for the reserve of components.
An example of the dependence of profit on the stock of components.
Dynamic variant
Values from 0 to 8 correspond to the amount of spare parts, and values from 26 to 34 correspond to the number of units of production that can be made at the current values of the parameters.
For the same data, the amount of investment required for the purchase of a reserve of components (green) and the cost of servicing the loan (orange) were calculated.
Dynamic Option
Time Cost Module
The figure shows the dependence of the specific values of the paid time (blue) and the time of direct work (brown) depending on the stop values - it runs from 0 to 0.7 with a step of 0.001.
Cost module
Includes assembly and component costs, as well as unit values for payroll, overhead, and direct costs.
Green dotted line - profit depending on the number of manufactured products.
Nonlinear dependency module
Dynamic version
The module allows, depending on the ratio "stop - spare parts reserve", to calculate the necessary investments, reduce scrap for purchased components and components of our own production, a volume discount when purchasing components and the cost of servicing a loan.
Benefits of “production functions”
With the accepted division of labor and cooperation, the heads of structural divisions and company management, based on rich experience, can always justify the current specific situation and propose decisions that need to be made. However, each time the vision of the circumstances and the vector of proposed solutions will be shifted in favor of the fixed specialization of the unit.
The basic principle of industrial cooperation always dictates the expediency of making compromise decisions.
The final compromise solution will most often not be optimal for each specific structural unit, but correct for the entire company as a whole. Therefore, a compromise solution should be clear to all stakeholders and obtained in a clear way, overcoming the barriers of fixed divisional specialization.
Manufacturing functions represent the big picture for the company as a whole, so they are useful in justifying the concessions that need to be made to departments and services to improve the company's overall profitability.
2. Unification of the product line
The unification of the product line is exclusively the task of engineers and technologists. But in the general case, they do not have enough information and the necessary tools to correctly solve the problem of unification. It is required at least to overcome two objective barriers to unification.
The first barrier is determined by the fact that decision making is actually influenced by nonlinear relationships between the factors taken into account and patterns hidden in BigData. The first barrier can be overcome by applying “production functions”.
The second barrier is of a systemic nature and, in order to overcome it, requires a common production and commercial picture. In addition, it is necessary to take into account the accumulated contradictions over the years in the chains of compromise decisions, and not treat it as an unpleasant reality. Adequate tools can help.
First, consider the range of characteristics of the components supplied by cooperation. Then we will cluster the products by identical components.
2.1. Characteristics of components supplied by cooperation
Very often it is possible to either produce components ourselves (for example, if there is a foundry, injection molding machines, etc.), or buy them from third parties. How to proceed and for which groups of components is a good task, but it can only be realized when moving to a certain level of digital control.
For now, consider the dependence of the quantity and price for the same groups of components.
List: item supplied by cooperation - total costs.
The graphs show the dynamics of planned costs by year. The first is cumulative, the second is with the monthly costs of each position less than 150 thousand rubles. (each position is not very expensive), the third one costs more than 150 thousand rubles per month.
"Total items" - how many items are taken into account. "Total" is the total amount attributable to these item items.
There is some logic in the charts.
Now let's look at the graphs for groups of components with a breakdown by the actual assortment. The upper graph is a breakdown by month, the lower one is the cost of the actual assortment.
On the lower graph, the abscissa axis (horizontal) is the numbering of the assortment item in order. Red dot along the vertical (ordinate axis) - total costs for the position indicated along the vertical.
Here are some more graphs.
The given graphs speak of significant reserves in planning procedures and provide material for the priorities of unification, if not existing, then at least newly designed products.
In this case, it is enough to explain the principles underlying procurement and procurement dynamics. Most likely, past workarounds will come to light, which have become permanent, complicating the production process.
2.2. Analysis of the existing level of unification
Analysis of the conformity of components to the type of product allows to identify the existing level of unification. There are 48 + 1 (empty) product groups in the original data.
The data shown is not normalized. Therefore, different spelling of names leads to additional unnecessary difficulties in unification. After normalization, 37 + 1 groups remain. An "empty" group is those components for which no correspondence to the product type is specified.
Taking into account all the group connections, the graph looks as follows - red edge labels correspond to the product name, renumbered green vertices correspond to the product group number.
It is clear that nothing good can be extracted from this "carnival" of connections.
Changing the view of the graph does not make it easier to understand the relationships.
If you single out on the graph only a specific type of product and the composition of the groups it belongs to, then the picture becomes clearer.
The above list of groups allows, if necessary, to localize the unification process only by a specific group. In this case, only the data for the group is displayed. Depending on the goals of unification, the principles of group formation can be changed.
2.3.
Unification tools Unification can be viewed as the dominant competitive advantage of modern manufacturing.
In general, it should:
- solve problems arising from the disproportionate production infrastructure to the volume of production;
- enable regular updates of the product line;
- ensure the implementation of the process of development and production of a product with specified parameters in terms of time, quality, cost and consumer properties.
If the existing problems are fixed, as well as the options for solving production, technological, commercial and financial problems are known, then combinatorial enumeration and evaluation of many possible options becomes the most difficult.
Analyzing known software solutions, General Electric (GE) did not find a solution that could be taken as a basis. Therefore, GE decided to create its own Predix control and communication system. Correctly evaluating existing software systems does not guarantee that Predix will move beyond the corporate boundaries of GE with its original plan to create a manufacturing management standard.
For smaller companies, the situation does not look the best: there are no good software solutions for the integrated management of a manufacturing company, and funds for their own large-scale development are not enough.
"Production functions" allow you to create a financially asymmetric solution. Together with dynamic analytics, production functions can become a superstructure over existing accounting, warehouse and other systems of the company.
The initial tasks for solving through production functions can be two:
- production - fixing the level of product unification and its influence on the required volumes of components and degrees of freedom when assembling products of the required models;
- financial and economic - dynamic analytics on costs and involved production facilities.