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Coping with complexity: Perspectives for economics, management and social sciences
138
EuropeanJournal of OperationalResearch21 (1985) 138-145 North-Holland
Book Reviews Hans W. GOT'FINGER Coping with Comp|exi~: Perspectives. for Economics, Mar~ge~,nen| and Social Sciences Volume 33 m: Theo~T and Decision Library, Reidel, Dordrecht, 1~83, xv + 224 pages, Dfl.100.O0 Complexity is a wonderful concept. It adds status to hummn activity by its presence and denies it by its absence. After all, anything that is not complex ,must be t;Svial or staightforward and hence rarely leads to a Nobel Prize or a Rolls Royce. Of course, such a universally useful concept is bound to mean different things,; to different people. An economis~ is bothered by l:he complexity of a macroeconomic model. An operations researcher worries about the complexity of a production planning proNem. An engineer complains about the complexity of a nuclear reactor. The question arises if there is an abstract zontext in which they are :alking about essentially the sanae thing. Hans Gottinger, ~ge author of this book, seems to think that the answer is affirmative. More specifically, he thinks that the appropriate abstract setting is pro~ided by the algebraic theory of finite state machines. !n the second chapter of the book, he summarizes this abstract mathematical theory which culminates in the so-called g~rohn-Rhodes prime decomposition theorem. The 39 pages of this chapter are filled densely with mathematical notation. The rest of the book is almost completely free of mathematical symbolism. The author suggests that readers might want to slip quickly through the second chapter in a first reading. TNs I found to be excellent advice. The book as a whole can cerlairdy not be fat~lted for lack of ambition. The author draws his examOperational Researchers w;slm,g to review books and publashers wishing to have ne~, books reviewed flease contact C. ~. Titam~s, Eindhocen Unwersilv of Technology. P.O. Box 5t3, 5600 M B Eindl~oven, N efherlonds, Tel. 31- 40- 4 73601
ples from all over the scientific literature, ranging from the problem of a monkey who has to figure out how to reach a bunch of bananas, to issues of urban design and macroeconomic policy. But although there is a genuine attempt to find the common finite machine traits in all these appearan~s of complexity, I did not find myself convinced of the utility of this framework. The imposition of mathematical structure can only be justified if the subsequent application of mathematical analysis to the structure produces a surprising insight that is not readily available through common sense reasoning. Viewed in this light, the elaborate mathematics of finite state machines yield a very limited pay-off in the rest of the book. I am not even convinced that the general theory of complexity that the author is searching for so valiantly really exists. I regard complexity as a property of some problem solving procedure. Hence, the complexity of a structure can only be sensibly defined if the problem posed by the structure is articulated and if a set of potential problem solving procedures is defined. The complexity of the structure could then perhaps be related to that of the simplest possible procedure. But any useful definition of procedural complexity will depend on the resources that the procedure draws upon, and these will vary widely across the sciences. Computer scientists have perhaps been most successful in analyzing procedural complexity, if only because the introduction of a computer as a mechanical device to implement the procedure introduces a certain objectivity to the measurement of complexity. The area that I am most famifiar with, concrete computational complexity theory, provides many fine examples of the useful insight; that a properly specified complexity analysis can provide° The author deals with this area too (albeit briefly) and in doing so demonstrates that he i~; aware of what is going on (although there are a few annoying errors of fact)° I am less competent to jvdge how well he does in the many other areas that he draws his examples from. His attempts at a
0377-2217/85/$3.30 © 1985, ElsevierSciencePublishersB.V. (North-Holland)
Book Reviews
synthesis, however, could and should have been presented in a more convincing and accessible manner. The Editorial Board of Theory and Decision Library, in which this book appears, should take partial responsibility for a presentation that leaves much to be desired in terms o f lucidity and organization.
A.H.G. RINNOOY KAN Sloan School of Management Cambridge, MA 02139, U.S.A. N.K. KAMBO
Mathematical Programming Techniques Affiliated East-West Press PVT, 104 Nirmal Tower, 26 Barakhamba Road, New Delhi, 1984, 719 pages, RS57.00 (India) Nirmal Singh Kambo, Professor of Mathematics at the Indian Institute of Technology, New Delhi, India makes two claims about this book. Firstly it "presents the concepts, techniqaes and applications of mathematical programming", and secondly "it equips the reader with the ability to apply the techniques to both theoretical and realworld problems". Professor Kambo succeeds admirably with the first objective, but falls short on providing a comprehensive text for the modeller and implementer. The text is based on undergraduate and postgraduate courses and certainly for the student about to make a decision on whether to pursue algorithmic development or formulation and modelling implementation, it provides a comprehensive intermediate level coverage of MP theory supported with numerous examples of a broad range of applications. Pre-requisite mathematical knowledge, the book claims, is only an elementary knowledge of calculus, linear algebra and probability theory. This is an understatement. Professor Kambo's book would be a useful supporting text for applied courses at an intermediate level in these branches of mathematics! However, almost to appease lapsed mathematicians like myself, a most useful Appendix is included of mathematical preliminaries, being a concise rexdew of "~hc basic definitions, notations and relations that are used in treating sets, vector spaces, matrices functiot~s etc. I found this section invaluable.
139
The Preface claims no pretensions to exhaustiveness. Professor Kambo is too modest. The treatment of MP theory is exhaustive in its breadth if not in depth. Chapter 1 is a well balanced and structured introduction of mathematical programming (MP). In a mere twenty pages, the book packs an impressive but succinct coverage of the broad range of MP with more than a dozen small, but illustrative examples of different (linear, quadratic, integer, etc.) problem types in a variety of settings. Good for both the theorist and the practician. Chapter 2 provides a fairly detailed summary of convex sets and functions and their relevance in optimization theory. Almost exclusively for the theorist. Chapter 3 provides a traditional but well presented expose of LP theory and the simplex algorithmic approach, and, as throughout the book, illustrates all aspects with appropriate examples, as well as stud,rot exercises (solutions, but not worked answers are provided). Duality and its particular relevance to the theoretical computational aspects of LP is usefully explored in Chapter 4. The reader is also introduced to post-optimality which is presented witb refreshing clarity and depth. Chapter 5 introduces Transportation, and Assignment problem types, and their application using more examples, and explores the alternative solution approaches. Revised Simplex, Decomposition, Upper Bounding, Branch and Bound, and Pure Integer are all covered more than adequately in Chapter 6 "Methods for Special Linear Programs and Integer Programming". The second half of the book, covering another 400 pages would best be categorised as advanced MP topics for the postgraduate academic student, for it is here that the management student would lose interest. Chapters 7 to 15 cover in some considerable depth a wide range of advanced, but mainly theoretical associated topics (including Convexity, Unconstrained and Transformation Optimization Techniques, Kuhn-Tucker. Geometric, Stochastic Programming, etc.) The book concludes with a short but lighter paced introduction to Game Theo~,. In summary, Professor Kambo has produced a well structured and iogically ordered course in MP techniques which should serCe well the course needs
EuropeanJournal of OperationalResearch21 (1985) 138-145 North-Holland
Book Reviews Hans W. GOT'FINGER Coping with Comp|exi~: Perspectives. for Economics, Mar~ge~,nen| and Social Sciences Volume 33 m: Theo~T and Decision Library, Reidel, Dordrecht, 1~83, xv + 224 pages, Dfl.100.O0 Complexity is a wonderful concept. It adds status to hummn activity by its presence and denies it by its absence. After all, anything that is not complex ,must be t;Svial or staightforward and hence rarely leads to a Nobel Prize or a Rolls Royce. Of course, such a universally useful concept is bound to mean different things,; to different people. An economis~ is bothered by l:he complexity of a macroeconomic model. An operations researcher worries about the complexity of a production planning proNem. An engineer complains about the complexity of a nuclear reactor. The question arises if there is an abstract zontext in which they are :alking about essentially the sanae thing. Hans Gottinger, ~ge author of this book, seems to think that the answer is affirmative. More specifically, he thinks that the appropriate abstract setting is pro~ided by the algebraic theory of finite state machines. !n the second chapter of the book, he summarizes this abstract mathematical theory which culminates in the so-called g~rohn-Rhodes prime decomposition theorem. The 39 pages of this chapter are filled densely with mathematical notation. The rest of the book is almost completely free of mathematical symbolism. The author suggests that readers might want to slip quickly through the second chapter in a first reading. TNs I found to be excellent advice. The book as a whole can cerlairdy not be fat~lted for lack of ambition. The author draws his examOperational Researchers w;slm,g to review books and publashers wishing to have ne~, books reviewed flease contact C. ~. Titam~s, Eindhocen Unwersilv of Technology. P.O. Box 5t3, 5600 M B Eindl~oven, N efherlonds, Tel. 31- 40- 4 73601
ples from all over the scientific literature, ranging from the problem of a monkey who has to figure out how to reach a bunch of bananas, to issues of urban design and macroeconomic policy. But although there is a genuine attempt to find the common finite machine traits in all these appearan~s of complexity, I did not find myself convinced of the utility of this framework. The imposition of mathematical structure can only be justified if the subsequent application of mathematical analysis to the structure produces a surprising insight that is not readily available through common sense reasoning. Viewed in this light, the elaborate mathematics of finite state machines yield a very limited pay-off in the rest of the book. I am not even convinced that the general theory of complexity that the author is searching for so valiantly really exists. I regard complexity as a property of some problem solving procedure. Hence, the complexity of a structure can only be sensibly defined if the problem posed by the structure is articulated and if a set of potential problem solving procedures is defined. The complexity of the structure could then perhaps be related to that of the simplest possible procedure. But any useful definition of procedural complexity will depend on the resources that the procedure draws upon, and these will vary widely across the sciences. Computer scientists have perhaps been most successful in analyzing procedural complexity, if only because the introduction of a computer as a mechanical device to implement the procedure introduces a certain objectivity to the measurement of complexity. The area that I am most famifiar with, concrete computational complexity theory, provides many fine examples of the useful insight; that a properly specified complexity analysis can provide° The author deals with this area too (albeit briefly) and in doing so demonstrates that he i~; aware of what is going on (although there are a few annoying errors of fact)° I am less competent to jvdge how well he does in the many other areas that he draws his examples from. His attempts at a
0377-2217/85/$3.30 © 1985, ElsevierSciencePublishersB.V. (North-Holland)
Book Reviews
synthesis, however, could and should have been presented in a more convincing and accessible manner. The Editorial Board of Theory and Decision Library, in which this book appears, should take partial responsibility for a presentation that leaves much to be desired in terms o f lucidity and organization.
A.H.G. RINNOOY KAN Sloan School of Management Cambridge, MA 02139, U.S.A. N.K. KAMBO
Mathematical Programming Techniques Affiliated East-West Press PVT, 104 Nirmal Tower, 26 Barakhamba Road, New Delhi, 1984, 719 pages, RS57.00 (India) Nirmal Singh Kambo, Professor of Mathematics at the Indian Institute of Technology, New Delhi, India makes two claims about this book. Firstly it "presents the concepts, techniqaes and applications of mathematical programming", and secondly "it equips the reader with the ability to apply the techniques to both theoretical and realworld problems". Professor Kambo succeeds admirably with the first objective, but falls short on providing a comprehensive text for the modeller and implementer. The text is based on undergraduate and postgraduate courses and certainly for the student about to make a decision on whether to pursue algorithmic development or formulation and modelling implementation, it provides a comprehensive intermediate level coverage of MP theory supported with numerous examples of a broad range of applications. Pre-requisite mathematical knowledge, the book claims, is only an elementary knowledge of calculus, linear algebra and probability theory. This is an understatement. Professor Kambo's book would be a useful supporting text for applied courses at an intermediate level in these branches of mathematics! However, almost to appease lapsed mathematicians like myself, a most useful Appendix is included of mathematical preliminaries, being a concise rexdew of "~hc basic definitions, notations and relations that are used in treating sets, vector spaces, matrices functiot~s etc. I found this section invaluable.
139
The Preface claims no pretensions to exhaustiveness. Professor Kambo is too modest. The treatment of MP theory is exhaustive in its breadth if not in depth. Chapter 1 is a well balanced and structured introduction of mathematical programming (MP). In a mere twenty pages, the book packs an impressive but succinct coverage of the broad range of MP with more than a dozen small, but illustrative examples of different (linear, quadratic, integer, etc.) problem types in a variety of settings. Good for both the theorist and the practician. Chapter 2 provides a fairly detailed summary of convex sets and functions and their relevance in optimization theory. Almost exclusively for the theorist. Chapter 3 provides a traditional but well presented expose of LP theory and the simplex algorithmic approach, and, as throughout the book, illustrates all aspects with appropriate examples, as well as stud,rot exercises (solutions, but not worked answers are provided). Duality and its particular relevance to the theoretical computational aspects of LP is usefully explored in Chapter 4. The reader is also introduced to post-optimality which is presented witb refreshing clarity and depth. Chapter 5 introduces Transportation, and Assignment problem types, and their application using more examples, and explores the alternative solution approaches. Revised Simplex, Decomposition, Upper Bounding, Branch and Bound, and Pure Integer are all covered more than adequately in Chapter 6 "Methods for Special Linear Programs and Integer Programming". The second half of the book, covering another 400 pages would best be categorised as advanced MP topics for the postgraduate academic student, for it is here that the management student would lose interest. Chapters 7 to 15 cover in some considerable depth a wide range of advanced, but mainly theoretical associated topics (including Convexity, Unconstrained and Transformation Optimization Techniques, Kuhn-Tucker. Geometric, Stochastic Programming, etc.) The book concludes with a short but lighter paced introduction to Game Theo~,. In summary, Professor Kambo has produced a well structured and iogically ordered course in MP techniques which should serCe well the course needs