Quantitative Planning and Control

Essays in Honor of William Wager Cooper on the Occasion of His 65th Birthday

Yuji Ijiri, Andrew B. Whinston

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780123704504
• eBook ISBN: 9781483259369
• Topic: Business
• Subtopic: Management
• Index: Business

Quantitative Planning and Control: Essays in Honor of William Wager Cooper on the Occasion of His 65th Birthday features a collection of papers prepared by students and associates of William Wager Cooper to honor him on the occasion of his sixty-fifth birthday. The book centers on the theme of Quantitative Planning and Control, the theme to which much of Professor Cooper's research effort has been devoted. The theme covers diverse fields of inquiry as reflected in the articles in this book, which are organized in four parts: (1) mathematical programming and decision models; (2) economic development and firm growth; (3) manpower planning and design; and (4) accounting and control. At the core of all of the articles in this book lies a belief that analytical approaches can help solve all managerial problems, a philosophy that is deeply rooted in Professor Cooper's thinking. This book demonstrates how this fundamental view on management can be reflected in dealing with problems in various fields of management. In particular, the book focuses on three main areas of application of this view, economic development, manpower planning, and accounting and control, along with the subject of developing tools that are necessary for solving managerial problems analytically.

Part I

MATHEMATICAL PROGRAMMING AND DECISION MODELS

Outline

Chapter 1: Gradient States for Some Dualities with the C2 Extremal Principle

Chapter 2: Branch and Round: An Enumerative Algorithm for Integer Programs

Chapter 3: A Minimax Procedure for a Class of Stochastic Programs

Chapter 4: A Linguistic Model for 3-D Constructions

Chapter 5: Decision-Making with Multiple Objectives—Some Analytic Approaches

1

Gradient States for Some Dualities with the C² Extremal Principle ^†

A. CHARNES, CENTER FOR CYBERNETIC STUDIES, GRADUATE SCHOOL OF BUSINESS, UNIVERSITY OF COLORADO, BOULDER, COLORADO

L. SEIFORD, FACULTY OF ADMINISTRATIVE STUDIES, YORK UNIVERSITY, DOWNSVIEW, ONTARIO, CANADA

Publisher Summary

Charnes and Cooper developed the duality state characterizations for constrained problems involving the information theoretic functional in the primal and an unconstrained functional in the dual problem. The unconstrained problem involved only exponential and linear functions. This chapter discusses functions that are convex and differentiable on an open convex set in finite dimensional Euclidean space. It reviews the influence of properties of the range of the gradient mapping and of the decoupling equality system on the possible duality states for the dual problem obtained via the extremal principle for dualities. The C² extremal principle for dualities is an approach to derive dual optimization problems with proper duality inequality that simplifies and generalizes the Fenchel–Rockafellar scheme. The derivation is accomplished in two stages. The first is the achievement of the dualit...

Table of contents

• Cover image
• Title page
• Table of Contents
• Inside Front Cover
• Copyright
• List of Contributors
• Preface
• A Yankee from Chicago
• Adventures in Invention
• The Great Teacher
• Part I: MATHEMATICAL PROGRAMMING AND DECISION MODELS
• Part II: ECONOMIC AND FIRM GROWTH
• Part III: MANPOWER PLANNING AND DESIGN
• Part IV: ACCOUNTING AND CONTROL
• Appendix: Bibliography of the Works of William Wager Cooper