Heinen production function

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The production function according to Heinen , as a production function of type C is known, in the economic production theory a production function , which on the Gutenberg production function builds (type B). In contrast to this, it assumes that factor consumption changes over time and differentiates in production between the start-up phase, the processing phase, the braking phase and the idling phase.

Consumption and load functions

Edmund Heinen differentiates between the technical consumption function and the economic consumption function . The technical consumption function creates a connection between the factor consumption and the technical power output of a unit (e.g. a machine ). The economic consumption function establishes relationships between factor consumption and the output quantity created (finished products). A load function indicates a relationship between the current performance of a unit and its determinants, which depend on the specific individual case. The instantaneous power is shown as the derivative dA / dt of work A over time.

Elementary combinations

An elementary combination is a production process with a clear connection between the technical and economic performance of a unit. Heinen categorizes elementary combinations according to the three dimensions

  • Factor input relationship (limitational / substitutional)
  • Variability of the application rate (fixed / variable) and
  • Dependence of the number of repetitions on the amount of end product (primary, secondary and tertiary elementary combinations)

Limitation and substitutional factor input relationships

In the case of substitutional factor input relationships, a certain number of products can be created using various factor combinations. Often, for example, man hours and machine hours can be exchanged (substituted) within a certain area. With limited operational relationships, only a certain combination is possible, for example the combination of exactly four table legs and exactly one top to make a table.

Output fixes and output variable elementary combinations

If an elementary combination leads to the same output set with each repetition, it is an output-fixed elementary combination. In the other case an output variable. According to Heinen, output-fixed limitationale elementary combinations are of great importance in industry .

Accordingly, there are four types of loading functions. With output-fixed limitational elementary combinations they only depend on the time: to

dA / dt = f (t)

The load on the unit over time is recorded.

With output variables, limitational elementary combinations, the realized output o is itself an independent variable:

dA / dt = f (t, o)

With output-fixed, substitutional elementary combinations, load isoquants can be formed. In the chemical industry in particular, different combinations of temperature and pressure often lead to the same output quantity. The load isoquant of one unit (e.g. furnace) then depends not only on the time but also on the performance of the other unit (e.g. compressor):

dA 1 / dt = f (dA 2 / dt, t)

Output variable, substitutional elementary combinations consequently lead to a load function that also depends on the output:

dA 1 / dt = f (dA 2 / dt, t, o)

Primary, secondary and tertiary elementary combinations

The repetition of the elementary combinations is usually necessary to produce a certain amount of end products. Heinen distinguishes between

  • primary elementary combinations that cause work progress on the products. Their repetition immediately increases the amount of output produced.
  • Secondary elementary combinations , the repetition of which is only loosely related to the output. This includes setup processes as well as starting and braking processes.
  • Tertiary elementary combinations either depend indirectly on the output via other quantities or do not depend on the output at all. For example, maintenance and cleaning work.

In the case of primary elementary combinations, the required repetitions w can be determined simply by dividing the required amount of end or intermediate products by the output amount of the elementary combination. The necessary repetitions of the secondary elementary combination result from dividing the number of primary repetitions by the edition size (lot size).

See also

literature

  • Edmund Heinen: Business cost theory , 6th edition, Gabler, Wiesbaden, 1983.

Individual evidence

  1. ↑ Christian Brecher (Ed.): Integrative Production Technology for High-Wage Countries , Springer, Berlin, 2011, p. 47.
  2. ^ Hans Corsten, Ralf Gössinger: Production economy . Oldenburg, Munich, 12th edition, 2009. p. 102
  3. ↑ Jürgen Bloech, Wolfgang Lücke: Manufacturing management in Franz Xaver Bea, Erwin Dichtl, Marcel Schweitzer: General Business Administration, Volume 3: performance process. Gustav Fischer Verlag, Stuttgart, 1991, p. 92.