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The overall goal of this book is to introduce algorithms for improving the economic posture of a utility company in a restructured power system by promoting cost-effective maintenance schedules. Today, cutting operations and maintenance (O&M) costs and preserving service reliability) are among the top priorities for managers ofutility companies. Preventive maintenance is perhaps the single largest controllable cost ofa utility2 operation. It is perceived that a careful planning and a good coordination among self-interested entities in a restructured power system are essential to achieving an optimal trade-off between the cost ofmaintenance and the service reliability. Traditional maintenance programs in verticall/ integrated utilities relied heavily on time-directed maintenance and manufacturer recommendations. This book offers a logical alternative to traditional electric utility maintenance practices and a basis for maintenance decisions. The book is organized as follows. Chapter I reviews various issues related to the power system operation and presents the role of restructuring in maintenance scheduling. In Chapter II, fundamental topics related to linear and nonlinear systems are reviewed. The duality in linear programming is discussed and integer programming is reviewed. Benders decomposition, Lagrangian relaxation, and Dantzig-Wolfe decomposition are presented. Several examples are given to demonstrate the applications ofdifferent methods. The formulation ofreactive power optimization is discussed which will be used again in Chapter VII.