The book was motivated by Prof Mashelkar¿s slogan of ¿innovations for more¿, which has hurled Indiäs talent for science and innovation to the international arena. Such innovations have become the cornerstone of modern development that strives for ¿ultra-low-cost designs¿ to cater for increased global population, amidst abject poverty. Some innovations have direct consequences on wellbeing of mankind and others reach them indirectly, yet they all are intended to make life better and easier. This book uncovers some innovations developed by the authors in Mathematics of OR dealing with linear and integer optimization. In the case of linear optimization, some mathematical tools exist that can help to identify optimality of a given solution, but for integer programs, establishing optimality is more challenging, and to find an ordered optimal solution, can be computationally hard. This book has attempted to deal with some of these problems in an innovative way. Students, researchers and practitioners in OR, production and system engineering, management, quantitative economics, computing systems analysis, applied mathematics and statistics, will find this book of great value.