Mathematical methods of organizing and planning production. English translation by Robert W. Campbell and W. H. Marlow.

*(English)*Zbl 0995.90532From the editor’s introduction: This is the English translation of the famous 1939 article by L. V. Kantorovich, originally published in Russian.

The author of the work “Mathematical Methods of Organizing and Planning Production”, Professor L. V. Kantorovich, is an eminent authority in the field of mathematics. This work is interesting from a purely mathematical point of view since it presents an original method, going beyond the limits of classical mathematical analysis, for solving extremal problems. On the other hand, this work also provides an application of mathematical methods to questions of organizing production which merits the serious attention of workers in different branches of industry.

The work which is here presented was discussed at a meeting of the Mathematics Section of the Institute of Mathematics and Mechanics of the Leningrad State University, and was highly praised by mathematicians. In addition, a special meeting of industrial workers was called by the Directorate of the University at which the other aspect of the work – its practical application – was discussed. The industrial workers unanimously evinced great interest in the work and expressed a desire to see it published in the near future.

The basic part of the present monograph reproduces the contents of the report given at the meetings mentioned above. It includes a presentation of the mathematical problems and an indication of those questions of organization anld planlning in the fields of industry, construction, transportation and agriculture which lead to the formulation of these problems. The exposition is illustrated by several specific numerical examples. A lack of time and the fact that the author is a mathematician rather than someone concerned with industrial production, did not permit an increase in the number of these examples or an attempt to make these examples as real and up-to-date as they might be. We believe that, in spite of this, such examples will be extremely useful to the reader for they show the circumstances in which the mathematical methods are applicable and also the effectiveness of their application.

Three appendices to the work contain an exposition and the foundations of the process of solving the indicated extremal problems by the method of the author.

We hope that this monograph will play a very useful role in the development of our socialist industry.

Contents: Editor’s Foreword (A. R. Marchenko); Introduction;

I. The Distribution of the Processing of Items by Machines Giving the Maximum Output Under the Condition of Completeness (Formulation of the Basic Mathematical Problems).

II. Organization of Production in Such a Way as to Guarantee the Maximum Fulfillment of the Plan Under Conditions of a Given Product Mix.

III. Optimal Utilization of Machinery.

IV. Minimization of Scrap.

V. Maximum Utilization of a Complex Raw Material.

VI. Most Rational Utilization of Fuel.

VII. Optimum Fulfillment of a Construction Plan with Given Construction Materials.

VIII. Optimum Distribution of Arable Land.

IX. Best Plan of Freight Shipments.

Conclusion; Appendix 1. Method of Resolving Multipliers; Appendix 2. Solution of Problem A for a Complex Case (The problem of the Plywood Trust). Appendix 3. Theoretical Supplement (Proof of Existence of the Resolving Multipliers).

The author of the work “Mathematical Methods of Organizing and Planning Production”, Professor L. V. Kantorovich, is an eminent authority in the field of mathematics. This work is interesting from a purely mathematical point of view since it presents an original method, going beyond the limits of classical mathematical analysis, for solving extremal problems. On the other hand, this work also provides an application of mathematical methods to questions of organizing production which merits the serious attention of workers in different branches of industry.

The work which is here presented was discussed at a meeting of the Mathematics Section of the Institute of Mathematics and Mechanics of the Leningrad State University, and was highly praised by mathematicians. In addition, a special meeting of industrial workers was called by the Directorate of the University at which the other aspect of the work – its practical application – was discussed. The industrial workers unanimously evinced great interest in the work and expressed a desire to see it published in the near future.

The basic part of the present monograph reproduces the contents of the report given at the meetings mentioned above. It includes a presentation of the mathematical problems and an indication of those questions of organization anld planlning in the fields of industry, construction, transportation and agriculture which lead to the formulation of these problems. The exposition is illustrated by several specific numerical examples. A lack of time and the fact that the author is a mathematician rather than someone concerned with industrial production, did not permit an increase in the number of these examples or an attempt to make these examples as real and up-to-date as they might be. We believe that, in spite of this, such examples will be extremely useful to the reader for they show the circumstances in which the mathematical methods are applicable and also the effectiveness of their application.

Three appendices to the work contain an exposition and the foundations of the process of solving the indicated extremal problems by the method of the author.

We hope that this monograph will play a very useful role in the development of our socialist industry.

Contents: Editor’s Foreword (A. R. Marchenko); Introduction;

I. The Distribution of the Processing of Items by Machines Giving the Maximum Output Under the Condition of Completeness (Formulation of the Basic Mathematical Problems).

II. Organization of Production in Such a Way as to Guarantee the Maximum Fulfillment of the Plan Under Conditions of a Given Product Mix.

III. Optimal Utilization of Machinery.

IV. Minimization of Scrap.

V. Maximum Utilization of a Complex Raw Material.

VI. Most Rational Utilization of Fuel.

VII. Optimum Fulfillment of a Construction Plan with Given Construction Materials.

VIII. Optimum Distribution of Arable Land.

IX. Best Plan of Freight Shipments.

Conclusion; Appendix 1. Method of Resolving Multipliers; Appendix 2. Solution of Problem A for a Complex Case (The problem of the Plywood Trust). Appendix 3. Theoretical Supplement (Proof of Existence of the Resolving Multipliers).

##### MSC:

90B30 | Production models |