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Tsinghua University, 100084, Beijing, China bBNBIbBCCNBCRHSXXZmBVNBVBVNBVBV1111001???? ?? ? ? ?32213132121332123211321321321,,0,4868..0203060203060maxssxNBVsxxBVsssxxsxxxsxxxsxxxtsxxxzxxxz??????????????????????? ?TNBVBVbNBCC8,20,48012006,118]0,0,30[],0,20,60[?????????????????????????? ? ? ?? ? ? ?? ?0510,10,50,0,3010,10,350,0,300120061180,20,6011?????????????????????????????????????NBVBVCNBC19 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China bBBVbBCvalu ez BV11?????c2 is changed and BV remains optimal, but the values of decision variables and zvalue remain unchanged 20 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China 40,5 2 ??? c? ? ? ?? ? ? ?? ?10,10,50,0,4010,10,350,0,400120061180,20,6011?????????????????????????????NBVBVCNBCx2 is entering variable 21 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China 2. Changing the Objective Function Coefficient of a basic Variable ?The current basis remain optimal ?The current basis is no longer optimal: 22 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China 3. Changing the RightHand Side of a Constraint ?The current basis remain optimal ?The current basis is no longer optimal =Dual simplex algorithm 23 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China 4. Changing the Column of a Variable ?Basic Variable: ?Nonbasic Variable: ?Remain optimal ?No longer optimal 24 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China 5. Adding a New Activity ?Optimal ?No optimal 25 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China Summary (Max Problem) Change in Initial Problem Effect on Optimal Tableau Current Basis Is Still Optimal If: Changing nonbasic objective function coefficient cj Coefficient of xj in optimal row 0 is changed Coefficient of xj in row 0 for current basis is still nonnegative Changing basic objective function coefficient cj Entire row0 may change Each variable still has a nonnegative coefficient in row 0 Changing righthand side of a constraint Righthand side of constraints and row 0