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**Linear programming and network flows.**
*(English)*
Zbl 1060.90688

New York, NY: John Wiley & Sons. x, 565 p. (1977).

This book may be used as a textbook for a course in the fundamentals of the simplex method for advanced undergraduates or first year graduate students in the fields of industrial engineering, operations research, quantitative management, or engineering. The emphasis is on the theory and mechanics of applying the simplex method to the solution of linear programs, and to the special cases of network flows and transportation problems. The style will appeal to engineering oriented students; the instructor who is designing a linear programming course for a mathematics department would do well to look elsewhere for a textbook.

Pertinent results from linear algebra and convex analysis are summarized at the beginning of the book. Beginning with Chapter III, the chapter headings are: The simplex method, Starting solution and convergence, Special simplex forms and optimality conditions, Duality and sensitivity, The decomposition principle, The transportation and assignment problems, Minimal cost network flows, The out-of-kilter algorithm, Maximal flow shortest path and Multicommodity flow problems. Each chapter has about fifty drill problems, with solutions available in a separate manual. Not included is any discussion of computer related aspects of linear programs such as data handling, the nature of codes, numerical problems, or the LU algorithm used with modern codes. Nor is there any detailed discussion of the actual scope of present applications. Two pages on integer programming (the cutting plane algorithm) are included, but linear approximations for convex programs are not.

Pertinent results from linear algebra and convex analysis are summarized at the beginning of the book. Beginning with Chapter III, the chapter headings are: The simplex method, Starting solution and convergence, Special simplex forms and optimality conditions, Duality and sensitivity, The decomposition principle, The transportation and assignment problems, Minimal cost network flows, The out-of-kilter algorithm, Maximal flow shortest path and Multicommodity flow problems. Each chapter has about fifty drill problems, with solutions available in a separate manual. Not included is any discussion of computer related aspects of linear programs such as data handling, the nature of codes, numerical problems, or the LU algorithm used with modern codes. Nor is there any detailed discussion of the actual scope of present applications. Two pages on integer programming (the cutting plane algorithm) are included, but linear approximations for convex programs are not.

Reviewer: A. C. Williams (MR 56#2346)