Total requirement coefficient

The overall demand coefficient is a variable that plays a role in the planning of lot sizes and the use of resources for goods that are mass-produced in multi-stage production processes. The coefficient also serves, among other things, in the context of business cost unit accounting for cost control in such processes.

Basics

The total requirement coefficient expresses indirectly which input quantity of an upstream production stage is required, taking into account the quantity difference with adding multi-stage division calculation, in order to manufacture a certain quantity of the end product. The output quantity is the quantity of the product that is produced in a usable manner coming from a production step - the quantities given result from the fact that intermediate products between the individual production stages can be temporarily stored in an interim storage facility and this interim storage is made dependent on short-term practical logistical requirements - with the aim of selling the output volume (production output) at the end of the production and sales steps. The amount used, on the other hand, is the amount of preliminary or intermediate product or semi-finished product that must be used as input in a subsequent production step so that a certain output volume is achieved after running through the production step and after accounting for the intermediate storage step.

For the total demand coefficient of the -th production stage as the product of the input coefficients of the production stages with the lower index, we can write: ${\ displaystyle {} J}$

{\ displaystyle \ gamma _ {\ mathrm {J}} = \ prod _ {j = 1} ^ {J-1} {\ varepsilon _ {j}} = \ varepsilon _ {1} \ cdot \ varepsilon _ {2 } \ cdot \ ldots \ cdot \ varepsilon _ {j * -1} \ cdot \ varepsilon _ {j *} \ ldots \ cdot \ varepsilon _ {J-1}}

With

{\ displaystyle \ varepsilon _ {j} = {\ frac {r_ {j}} {x_ {j}}}}

in the simplest case, where the input quantity and the output quantity represent the stage , so that: ${\ displaystyle {} r_ {j}}$ ${\ displaystyle {} x_ {j}}$ ${\ displaystyle {} j}$

{\ displaystyle \ gamma _ {\ mathrm {J}} = \ prod _ {j = 1} ^ {J-1} {\ frac {r_ {j}} {x_ {j}}} = {\ frac {r_ {1}} {x_ {1}}} \ cdot {\ frac {r_ {2}} {x_ {2}}} \ cdot \ ldots \ cdot {\ frac {r_ {j * -1}} {x_ { j * -1}}} \ cdot {\ frac {r_ {j *}} {x_ {j *}}} \ ldots \ cdot {\ frac {r_ {J-1}} {x_ {J-1}} }}

with the respective production stage (taking into account any downstream process stages)

{\ displaystyle j = 1,2, \ ldots, j_ {end}}

,

where any value may be within the permissible index variable range . Likewise may be any value within the allowable index for variable area to be. ${\ displaystyle j {*}}$ ${\ displaystyle j {*} = 1,2, \ ldots, J-1}$ ${\ displaystyle J}$ ${\ displaystyle J = 1,2, \ ldots, j_ {end}}$

If there is no intermediate storage of the intermediate product behind the exit of the -th stage and in front of the entrance of the -th stage, then the output of the -th stage becomes the direct input of the -th stage: ${\ displaystyle (j {*} - 1)}$ ${\ displaystyle j {*}}$ ${\ displaystyle (j {*} - 1)}$ ${\ displaystyle j {*}}$

{\ displaystyle x_ {j * -1} = r_ {j *}}

.

These terms can then be truncated from the total fraction for the total demand coefficient.

In the event that the rejects produced, which arise in the individual production stages, are to be taken into account, a corrected input coefficient is inserted into the product of the input coefficients to determine the overall coefficient. In addition to the quotient of the input and output quantity, the corrected input coefficient also takes into account a reject coefficient : ${\ displaystyle \ varepsilon _ {j_ {korr}}}$ ${\ displaystyle \ alpha _ {j}}$

{\ displaystyle \ varepsilon _ {j} = \ varepsilon _ {j_ {korr}} = {\ frac {r_ {j}} {x_ {j}}} \ cdot \ alpha _ {j} = {\ frac {r_ {j}} {x_ {j}}} \ cdot {\ frac {x_ {j}} {x_ {j_ {usable}}}}}

.

From a business point of view, the input coefficients are nothing more than production coefficients .

Calculation example

For a four-stage production process with downstream sales ( = 5), the determination of the overall requirement coefficient could look something like this: ${\ displaystyle j_ {end}}$

index	Production stage	Use amount	Application rate	Use coefficient	Total requirement coefficient
j = 5	1st stage (preproduct processing)	${\ displaystyle {} r_ {5}}$ = 165,165 ME	${\ displaystyle {} x_ {5}}$ = 127,050 ME	${\ displaystyle \ varepsilon _ {5}}$ = 1.3	${\ displaystyle \ gamma _ {5}}$ = 2.541
j = 4	2nd stage (1st intermediate product processing)	${\ displaystyle {} r_ {4}}$ = 127,050 ME	${\ displaystyle {} x_ {4}}$ = 82,500 ME	${\ displaystyle \ varepsilon _ {4}}$ = 1.54	${\ displaystyle \ gamma _ {4}}$ = 1.65
j = 3	3rd stage (2nd intermediate product processing)	${\ displaystyle {} r_ {3}}$ = 82,500 ME	${\ displaystyle {} x_ {3}}$ = 55,000 ME	${\ displaystyle \ varepsilon _ {3}}$ = 1.5	${\ displaystyle \ gamma _ {3}}$ = 1.1
j = 2	4th stage (end product manufacture)	${\ displaystyle {} r_ {2}}$ = 55,000 ME	${\ displaystyle {} x_ {2}}$ = 50,000 ME	${\ displaystyle \ varepsilon _ {2}}$ = 1.1	${\ displaystyle \ gamma _ {2}}$ = 1.0
j = 1	distribution	${\ displaystyle {} r_ {1}}$ = 50,000 ME	${\ displaystyle {} x_ {1}}$ = 50,000 ME	${\ displaystyle \ varepsilon _ {1}}$ = 1.0	${\ displaystyle \ gamma _ {1}}$ has no numerical value

Practical calculation of the total requirement coefficient

Method: Successive multiplication of all application coefficients of the higher-numbered levels.
The total requirement coefficient of level 2 is obtained by successively multiplying the input coefficients of the following levels 3, 4 and "sales" to: 1.65 = 1.0 (sales) * 1.1 (level 4) * 1.5 (level 3).
The input and output quantities are usually given in units of measure (ME), in the case of mass-produced goods, for example, in kilograms or in tons or the like.

literature

KLR. Data center

Individual evidence

↑ Andreas Schmidt: Cost accounting: Basics of full cost, contribution margin and plan cost accounting as well as cost management. 7th, update u. supplementary edition, Kohlhammer, Stuttgart 2014, ISBN 978-3-17-024889-2 , pp. 120f.
^ Günter Fandel: Part requirement calculation in multi-stage production. In: WiSt - Wirtschaftswwissenschaftliches Studium ( ISSN 0340-1650 ) Vol. 9, H. 10, pp. 449–456, 498–500, Oct. 1980, in particular on p. 454.

[1] Andreas Schmidt: Cost accounting: Basics of full cost, contribution margin and plan cost accounting as well as cost management. 7th, update u. supplementary edition, Kohlhammer, Stuttgart 2014, ISBN 978-3-17-024889-2 , pp. 120f.

[2] Günter Fandel: Part requirement calculation in multi-stage production. In: WiSt - Wirtschaftswwissenschaftliches Studium ( ISSN 0340-1650 ) Vol. 9, H. 10, pp. 449–456, 498–500, Oct. 1980, in particular on p. 454.