The subject “Linear Programming” forms a part of “Operations Research” which deals with systematic study of system of operations. This term was first introduced by Mc-Closky and Trefthenin 1939. This subject came in existence during World War II.

Chapter 1 is an introductory chapter and gives a briefhistorical backgroundand latest research work done in the fieldof linear programming problems with bounded variables and importance of sensitivity analysis.It also describes the dual simplex method for linear programming with bounded variables.

Chapter 2 deals with basic sensitivity analysis in linear programming with bounded variables.There are seven basic types of changes in the data, like, change in cost vector or requirement vector, addition or deletion of a constraint, addition or deletion of a variable and change in the coefficient matrix. All these aspects have been discussed in details in Chapter 2 along with numerical problems.

Chapter 3 deals with positive sensitivity in linear programming problems with bounded variables. In this chapter, we have discussed some propertiesof PSA, the relationship between PSA and sensitivity analysis using optimal basesand the relationship between PSA and sensitivity analysis using optimal partition.

The book entitled Linear Programming with Bounded Variables: Sensitivity Analysis 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.

Dr. Kalpana Dahiyacompleted her M.Sc. (Mathematics) in 2002and 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. Herresearch area included manylinear 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.