Sensitivity Analysis

Consider the Linear Programming Problem

               Maximize   Z = Σⁿ_j=1  c_jx_j ,

               Subject to

                                   Σⁿ_j=1   a_ijx_j   ≤   b_i                            for   i = 1, 2, 3 ..... m          

               and                              x_j    ≥     0                            for   j = 1, 2, 3,.0..... n

or in the matrix notation

                Maximize      Z    =   cx

                subject to     Ax  ≤    b

                and                x  ≥   0.

Sensitivity Analysis involves investigating  the effect on the optimal solution of making changes in the values of the model parameters (the a_ij , b_i  and c_j ).

Procedure for Sensitivity Analysis

We are having an optimal solution of a LP model with specified values for  a_ij , b_i  and c_j  parameters.

To initiate sensitivity analysis one or more of the parameters now is changed.

After making the changes, let  a`<sub>ij</sub> , b`_i   and  c`_j  denote the values of the various parameters. Thus, in matrix notation,

                    b  →  b`   ,    c  → c`    ,  A  →  A`,

with these changed parameters we try to find out the changes in the optimal solution for investigation.