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A Generalized Multi-Stage Input-Output Model and Some Derived Equivalent Systems.

John E. Butterworth¹; Bendt A. Sigloch²

¹ Assistant Professor, The University of British Columbia 1 · ² The University of British Columbia 2

A general input-output model has been constructed of which all possible alternative forms are special cases. It was shown that one of two alternative sets of assumptions is necessary to assure the existence and feasibility of a solution to the problems of determining the unknown input for a given output, and that of determining the unknown output for a given input. Methods for the transformation of one specific realization of the model into another were developed, together with a technique for the translation of a problem stated in physical terms into one of dollar transactions. The methods were illustrated by a specific example. Finally, some well-known special models were used to illustrate the generality of the representation. It remains to be shown in another context, for example that of a particular real system, that the algebraic transformations have more than purely technical or computational significance. It may suffice here to point out that the levels of the input-output model may easily be identified with cost or profit centers, divisions or plants, in which case the transformations applied to the basic model may be chosen to supply the transfers and aggregations desired for planning, budgeting and control purposes. It is hoped that the overall model will provide a useful tool for the integration of extant material, a standardization of output model may easily be identified with cost or profit centers, divisions or plants, in which case the transformations applied to the basic model may be chosen to supply the transfers and aggregations desired for planning, budgeting and control purposes. It is hoped that the overall model will provide a useful tool for the integration of extant material, a standardization of notation and a basis for simplifying the process of modelling new situations which lend themselves to input-output analysis. Extension into the more general area of linear programming is obviously possible, and the transformations suggested are...

DOI

10.2308/tar-4503897

Volume

46 (4)

Pages

700-716

Language

en

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