Postoptimal Analyses, Parametric Programming, and Related Topics (repost)

For some considerable time, linear programming has been one of the methods of operations research which has been widely known and much applied in Germany too, both in the literature ofthe subject and in practice. Its applications range from production planning through finance planning and from optimization of traffic networks through urban planning. The literature of linear programming includes textbooks of a strictly mathematical nature as weil as programmed textbooks for those with no previous knowledge of mathematics. An objection frequently heard to more extensive dissemination of the theories of linear programming in the practical field has been that data wh ich are available in practice are at once too inexact and too unreliable to provide the basis for the application of "exact" procedures like linear programming. This problem is the starting point of the present volume. The inexactitude and unreliability of existing data often cannot be disputed. Using conventional planning methods, the determination of the effects of these inaccuracies is frequently very difficult, if not impossible. In most cases, this is, however, possible using sensitivity analysis in the widest sense (i.e., including postoptimal analysis and parametric programming), and the amount of effort involved is reasonable. My colleague, Professor Gal has been involved in research in this field for many years. His decision to undertake the writing of an introduction to and interpretation of the area of linear programming which enables us to make statements on the possible effects of data changes, data inaccuracies, and decision changes on operational and other problems is, therefore, to be welcomed.
Sensitivity analysis, as interpreted in the present volume, has been seen by experts - correctly, in my opinion - as the bridge between pure dissemination of information and decision making. There is, thus, ample justification for including a volume on such an important subject in the "Operations Research" series. As the present volume is likely to interest both hose working in linear programming and research mathematicians, the chapters have been written primarily with practical application in mind, and an abridged mathematical version has been appended to each of them. It is hoped that this will increase the usefulness of the volume for a wide range of readers.