清華大學工業(yè)工程系運籌學課件(ppt)(文件)
【正文】 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 are changed Righthand side of each constraint is still nonnegative Changing the column of a nonbasic variable xj or adding a new variable xj Changes the coefficient for xj in row 0 and xj’s constraint column in optimal tableau The coefficient of xj in row 0 is still nonnegative Next 26 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China Sensitivity Analysis When More Than One Parameter Is Changed: The 100% Rule ? 1. The 100% Rule for Changing Objective Function Coefficients Case 1: All variable who’s objective function coefficients are changed have nonzero reduced costs in the optimal row 0 Case 2: At least one variable whose objective function coefficient is changed has a reduced cost of zero 27 Author:Zhang Zhihai, Dept. of Industrial Engineering, Tsinghua University, 100084, Beijing, China ? If and only if the objective function coefficient for each variable remains wi
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