Chapter 1 is an introductory chapter on linear fractional problems and gives a brief historical backgroundand latest research work done in this fieldand importance of linear fractional programming in real life problems.It also describes the simplex method for linear fractional programming with bounded variables.

Chapter 2 deals with development of various valid-cuts, like, Dantzig, Gomory and edge truncating cut for integer fractional programming with bounded variables. Various proof have been included in this chapter.

Chapter 3 deals integer linear fractional programming problems with bounded variables. Sometimes the optimal solution is not ofpractical interest due to certain limitations. In such situations, one is interestedin ranking the integer feasible solutions in decreasing order of values of objectivefunction and from the exhaustive list of various integer solutions with distinct valuesof objective function. Various cuts have been developed for ranking of integer feasible solutions of linear fractional programming with bounded variables.

Chapter 4 deals with constrained integer linear fractional programming problems with bounded variables which involves scanning of all alternate integer feasible solutions of the problem.

The book entitled Integer FractionalProgramming with Bounded Variables has been written to serve suitable text/reference book for master students, research students of Mathematics (Operations Research) and Management whose courses of studies include some or all the topics treated here.The subject “fractional Programming” is a very important topic in Mathematical Programming Problems.

Dr. Kalpana Dahiya completed her M.Sc. (Mathematics) in 2002 and Ph.D. (Mathematics) in 2008 with specialization in Operations Research from Department of Mathematics, Panjab University, Chandigarh, India. She is currently Assistant Professor at University Institute of Engineering and Technology, Panjab University, Chandigarh, India. She has a total teaching experience of 8 years (undergraduate and postgraduate) and research experience of 11 years. Her research area included many linear and linear fractional programming problems, transportation and assignment problems, nonlinear programming, bi-criterion optimization problem. She has published 13 research papers in international journals like European Journal of Operational Research, Computational Optimization and Applications and Opsearch.