Linear Programming for Optimization

Linear programs are widely used to model real life problems using linear equations and inequalities. There are some decision variables, an objective function and some constraints. Solving linear program means finding such values of decision variables that optimizes the objective function (either maximizes or minimizes depending on the requirement) within identified constraints. None of the constraints should be violated with the solution because such solution cannot be implemented (infeasible solution). The optimum solution is the best one under given constraints.

It is possible that there is no such solution that satisfies all the constraints. It means that the identified problem has no feasible solution. So, either relax some of the constraints or increase resources. It is possible that there are many feasible solutions and one of them gives the best value for the objective function. In some special cases, there may be multiple optimal solutions. These concepts you cannot learn by learning Linear Programming through features of some software/tool.

Solving a linear program requires lots of computation. Hence, there are tools/ software that can do all these computations for you. They can provide the results in various report forms that can be easy to interpret. So, it may be useful to learn such tool/ software once you are comfortable with the concepts of Linear Programming in Optimization.

Can you learn Linear Programming for Optimization by learning the features of such software/ tool? Do you become better expert of this technique by learning more of such tools/ software? Learning Industry is flooded with such courses that focus on such tool/software. That only creates market for such tools. Success/ progress of you as an expert of Linear Programming is heavily restricted if you learn the topic by learning through such courses focusing on tools.

Suppose, the organization using Liner Programming for Optimization gets additional fund. Where they should allocate this to have best impact on the objective function? Suppose, availability of some resource is adversely impacted due to political adversity in that area. How to handle that to avoid adverse impact on objective function? These are not solving a linear program, but are related to deep understanding and usage of concepts involving linear programming and optimization. There could be plenty of such situations where one has to go beyond computation. This understanding doesn't come through courses focusing on tools/ software.

This course doesn't talk about any software or tool. It should not. But, it takes you deep into the concepts in intuitive way. This is a must if you want to get the thrill of using Linear Programming and Optimization.

This course aims at making you comfortable with the most important optimization technique - Linear Programming. It starts with the concept of linear, takes you through linear program formulation, brings you at ease with graphical method for optimization and sensitivity, dives into simplex method to get to the nuances of optimization, prepares you to take advantage of duality and also discusses various special situations that can help you in becoming smart user of this technique.