For more than a decade, scientists from many different fields and countries haTe come together for the annual Optimization Days in Montreal to share their newest research results. This event is, in turn, hosted by various Departments of the four Universities in Montreal, viz. Concordia University, McGill University, Universite de Montreal and Universite du Quebec a. Montreal. In 1986, the Optimization Days were hosted by the Ecole des Hautes Etudes Commerciales, the Business School affiliated with Universite de Montreal. In that year, for the first time, it was attempted to produce a collection of papers presented at that conference. The result is this volume. Its contents are divided into the following six sections: Mathematics of Operations Research and Global Optimization Linear and Combinatorial Programming Tours, Locations and Scheduling Dynamic Programming and Game Theory Control Theory Economic Models Each of the contributions in this volume has been refereed. This task was made easy by the many helping hands in the form of colleagues from Canada, Italy, Poland, U. S. A., Britain and The Netherlands. We wish to express our sincere thanks to themj without their help this volume could not have been completed. Additional thanks are due to our students Linda Mimeault and Ernest Leung and to Mrs. Halina Monkiewicz who typed the entire manuscript. Montreal, Canada H. A. Eiselt and G. Pederzoli October 1987 TABLE OF OONTENTS FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -. . . . . . . . . . . . m I. MATHEMATICS OF OPERATIONS RESEARCH AND GLOBAL OPTIMIZATION Matrix Differential Equations and LyapunoT Transformations . . . . . . . . . . . . . . . . . . . . . . . . . .