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**Management applications of modern control theory.**
*(English)*
Zbl 0343.90001

Studies in Mathematical and Managerial Economics. Vol. 18. Amsterdam - Oxford: North-Holland Publishing Co.; New York: American Elsevier Publishing Co., Inc. xvii, 346 p. Dfl. 95.00; $ 39.75 (1974).

This book provides an intermediate to advanced treatment of optimal control theory including stochastic control theory. In the applications of the theory to areas including inventory theory, marketing, and finance, the authors not only discuss and derive known results, but they extend those results as well. A chapter on the computational aspects of control theory as applied to management is presented. The book is completed with an advanced mathematical review in the areas of probability theory, functional analysis, and both deterministic and stochastic optimal control theory.

The treatment of optimal control theory begins with a chapter providing the main results of the theory which are used in later applications. Those results are applied to to inventory control, the theory of the firm, finance, marketing, natural resource and environment control, and other topics. In particular the models which are developed include the incorporation of nonrandomness in finance models, of empirical studies in marketing models, and of pollution in natural resource and firm models.

The content of this book is important not only to students of quantitative management, but also to students of economics, operations research and applied mathematics. The material summarizes and presents major recent contributions and provides valuable insights of its own. Accordingly, it can be used as a guide to the literature for those students who wish to obtain recent contributions in the applied fields. The book can also be used by applied mathematicians who wish to see new areas of control theory applications.

The treatment of optimal control theory begins with a chapter providing the main results of the theory which are used in later applications. Those results are applied to to inventory control, the theory of the firm, finance, marketing, natural resource and environment control, and other topics. In particular the models which are developed include the incorporation of nonrandomness in finance models, of empirical studies in marketing models, and of pollution in natural resource and firm models.

The content of this book is important not only to students of quantitative management, but also to students of economics, operations research and applied mathematics. The material summarizes and presents major recent contributions and provides valuable insights of its own. Accordingly, it can be used as a guide to the literature for those students who wish to obtain recent contributions in the applied fields. The book can also be used by applied mathematicians who wish to see new areas of control theory applications.

Reviewer: Norman P. Obst (East Lansing, MI)

### MSC:

90-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming |

49-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control |

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

93C95 | Application models in control theory |

93E20 | Optimal stochastic control |

90B05 | Inventory, storage, reservoirs |

90B60 | Marketing, advertising |

91B38 | Production theory, theory of the firm |

91B76 | Environmental economics (natural resource models, harvesting, pollution, etc.) |

60K10 | Applications of renewal theory (reliability, demand theory, etc.) |