Sensitivity analysis: a method to study and analyze the sensitivity of the state or output change of a system (or model) to the change of system parameters or surrounding conditions. Sensitivity analysis is often used in optimization methods to study the stability of the optimal solution when the original data is inaccurate or changes. Through sensitivity analysis, we can also decide which parameters have great influence on the system or model. Therefore, sensitivity analysis is very important in almost all operational research methods and in evaluating various schemes.
For linear programming problems:
Here max stands for maximum, s.t. stands for constraint, x is objective function, and xj is decision variable. It is generally assumed that aij, bi and cj are known constants. But in fact, these parameters are often estimated or predicted data, so there are errors. At the same time, in the actual process, these parameters will change to varying degrees. For example, the linear programming problem of product collocation, cj in the objective function is generally related to market conditions and other factors. When market conditions and other factors change, cj will also change. The aij in the constraint conditions changes with the change of process conditions and other factors, while the value of bi is related to the ability of the enterprise and other factors. The problem of sensitivity analysis in linear programming is: when one or more of these data changes, what will happen to the optimal solution? In other words, the optimal solution will not change when these data change in a large range.