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Appendix I
The present book is a monograph on a new subject: it represents the research of the authors and development of a theory ab nuouo, both in scope and content, as well as in details of mathematical theory per se. The subject is new, and it is not easy to give either a complete reference list or a historical account. If we were to confine the listings to immediate references used, the list would be too short and would hardly reflect the importance of the subject. If we were to list the references concerned in general with the hierarchies and largescale systems of the kind considered in this book, the list would be too long. We shall steer a middle course and therefore briefly mention related, especially theoretical, work in general, and then mention specificreferences in connection with the material presented in different chapters. GENERAL BACKGROUND
Our broad objective was to initiate a theory of multilevel decision-making systems, i.e., systems with organizational-type structures. Our first motivation stems from the area of automation and control of complex industrial systems. In this respect, the multivariable control theory can be viewed as an immediate predecessor of the current work; in particular, the present book is a follow-up to [29] in the natural evaluation of a long-term concern with the problem of large-scale systems control. Our second motivation comes from Organization Research. The VonNeuman-Morgenstern theory of games concerned with competitive situations and the more recent Marshak-Radner theory of teams concerned with cooperative situations, are dealing with single-level systems, while our concern is with the multilevel systems. We share, of course, the methodology with these theories :we are interested in the mathematical theory of organizational structure with all benefits and limitations entailed. 283
284
Appendix I
Last, but not least, we were motivated by the problems of control and communications, in general, whether biological, social, or man-made. In this respect, the theory is in the spirit of cybernetics in Wiener’s sense and in the spirit of general systems theory presented in [30] and [31]. CHAPTER I
Only a handful of papers or books are explicitly cited. The literature here is really extensive, and no attempt is made to review it. CHAPTER II
Conceptualization is based on the framework reported in [32] and in an earlier publication [33] (which represents the first publication of the Systems Research Center, Case Western Reserve University, and the source for much of the further research ideas). More recent accounts are given in [34] and [35]. Concepts of multilayer hierarchies are based on [21] and [36]. Much of the motivation for the study of multilevel systems in industrial automation is provided by the pioneering paper [37]. Hierarchical arrangement of the solution algorithms for complex problems can also be found in [20] and [26]. CHAPTER In
Formalization is performed in the approach to mathematical theory of general systems as reported in [30], [31], and [38]. Formalization of multiechelon hierarchy is from [39] and 1401. CHAPTERS IV AND V
Coordination principles are first reported explicitly in [41] and [42], although the idea originated in [32] and was used in the research presented in Chapters V and VI. The coordinability concepts are those from [42] and
WI. CHAPTER VI
The particular development here is based on [44] and [45]. However, the concept of interaction decoupling from [32] has been investigated in detail in a more specific simplified context of static optimization in [46] and [47].
Appendix I
285
This was further pursued in [48] and [49], and an attempt was made to generalize the approach to dynamic systems in [50] and [51] (although the basic results for dynamic systems were already reported in 1401) and partial differential equations in [52]. However, the framework of functional analysis and the concept of interaction operators introduced in [44] help resolve much earlier confusion, indicate the generality of the interaction balance principle, and show the irrelevance of such incidental similarities as, e.g., the fact that linear zero-sum modification generated by the interaction operator leads to an overall apparent performance, which is of the so-called Lagrangian form (quadratic modification can be derived just as easily as the linear one!) CHAPTER W
Development here shows clearly the applicability of the coordination principles to programming problems. No attempt is made to relate this to other decompositions, except that of Dantzig-Wolf [53], since at one stage of development, confusion was introduced on that point. It would be of interest, of course, to compare the decompositionsresulting from the coordination principles with other, particularly nonlinear-type decompositions. The interaction-estimation principle also seems worth investigating, for the integer programming problems. CHAPTER VIII
Material here is primarily based on [54]and [55]. The satisfaction approach used by decision units in the system is from [36], [56], and [57] and was motivated by early studies on the sensitivity of optimal control, [48] and
WI.
Our broad objective was to initiate a theory of multilevel decision-making systems, i.e., systems with organizational-type structures. Our first motivation stems from the area of automation and control of complex industrial systems. In this respect, the multivariable control theory can be viewed as an immediate predecessor of the current work; in particular, the present book is a follow-up to [29] in the natural evaluation of a long-term concern with the problem of large-scale systems control. Our second motivation comes from Organization Research. The VonNeuman-Morgenstern theory of games concerned with competitive situations and the more recent Marshak-Radner theory of teams concerned with cooperative situations, are dealing with single-level systems, while our concern is with the multilevel systems. We share, of course, the methodology with these theories :we are interested in the mathematical theory of organizational structure with all benefits and limitations entailed. 283
284
Appendix I
Last, but not least, we were motivated by the problems of control and communications, in general, whether biological, social, or man-made. In this respect, the theory is in the spirit of cybernetics in Wiener’s sense and in the spirit of general systems theory presented in [30] and [31]. CHAPTER I
Only a handful of papers or books are explicitly cited. The literature here is really extensive, and no attempt is made to review it. CHAPTER II
Conceptualization is based on the framework reported in [32] and in an earlier publication [33] (which represents the first publication of the Systems Research Center, Case Western Reserve University, and the source for much of the further research ideas). More recent accounts are given in [34] and [35]. Concepts of multilayer hierarchies are based on [21] and [36]. Much of the motivation for the study of multilevel systems in industrial automation is provided by the pioneering paper [37]. Hierarchical arrangement of the solution algorithms for complex problems can also be found in [20] and [26]. CHAPTER In
Formalization is performed in the approach to mathematical theory of general systems as reported in [30], [31], and [38]. Formalization of multiechelon hierarchy is from [39] and 1401. CHAPTERS IV AND V
Coordination principles are first reported explicitly in [41] and [42], although the idea originated in [32] and was used in the research presented in Chapters V and VI. The coordinability concepts are those from [42] and
WI. CHAPTER VI
The particular development here is based on [44] and [45]. However, the concept of interaction decoupling from [32] has been investigated in detail in a more specific simplified context of static optimization in [46] and [47].
Appendix I
285
This was further pursued in [48] and [49], and an attempt was made to generalize the approach to dynamic systems in [50] and [51] (although the basic results for dynamic systems were already reported in 1401) and partial differential equations in [52]. However, the framework of functional analysis and the concept of interaction operators introduced in [44] help resolve much earlier confusion, indicate the generality of the interaction balance principle, and show the irrelevance of such incidental similarities as, e.g., the fact that linear zero-sum modification generated by the interaction operator leads to an overall apparent performance, which is of the so-called Lagrangian form (quadratic modification can be derived just as easily as the linear one!) CHAPTER W
Development here shows clearly the applicability of the coordination principles to programming problems. No attempt is made to relate this to other decompositions, except that of Dantzig-Wolf [53], since at one stage of development, confusion was introduced on that point. It would be of interest, of course, to compare the decompositionsresulting from the coordination principles with other, particularly nonlinear-type decompositions. The interaction-estimation principle also seems worth investigating, for the integer programming problems. CHAPTER VIII
Material here is primarily based on [54]and [55]. The satisfaction approach used by decision units in the system is from [36], [56], and [57] and was motivated by early studies on the sensitivity of optimal control, [48] and
WI.