The problem of dual interpretation after converting GAMS tutorial to ratio constraints into linear constraints

Ratio constraints of GAMS tutorial into dual interpretation after Linear constraints

The 'ratio constraints' that commonly Appear in blending and refining problems. Problem of dual interpretation after ratio constraints is converted into linear constraints ____________________________________________ Y (I, j)/q (j) = l =. 26; Is equivalent Y (I, j)-. 25 * q (j) = l = 0.01 * q (j ); ____________________________________________ 2.10.2. TRANSFORMATION AND DISPLAY OF OPTIMAL VALUES (This section can be skipped on first reading if desired .) After the optimizer is called via the solve statement, the values it computes for the primal And dual variables are placed in the database in the. l and. m fields. We can then read These results and transform and display them with GAMS statements. For example, in the transportation problem,. Suppose we wish to know the percentage Each market's demand that is filled by each plant. After the solve statement, we wowould Enter Parameter pctx (I, j) Perc of market J's demand filled by plant I; Pctx (I, j) = 100.0 * X. L (I, j)/B (j ); Display pctx; Appending these commands to the original transportation problem input results in Following output: Pctx percent of market J's demand filled by plant I New-York Chicago Topeka Seattle 15.385 100.000 San-Diego 84.615 100.000 For an example involving marginal, we briefly consider the 'ratio constraints' that commonly Appear in blending and refining problems. These linear programming models are concerned With determining the optimal amount of each of several available raw materials to put Each of several desired finished products. Let y (I, j) be the variable for the number Tons of product j produced. Suppose the 'ratio constraint' is that no product can consist More than 25 percent of one ingredient, that is, Y (I, j)/q (j) = l =. 25; For all I, j. To keep the model linear, the constraint is written Ratio (I, j) .. y (I, j)-. 25 * q (j) = l = 0.0; Rather than explicitly as a ratio. The problem here is that ratio. m (I, j), the marginal value associated with the linear Form of the constraint, has no intrinsic meaning. At optimality, it tells us by at most how Much we can benefit from relaxing the linear constraint Y (I, j)-. 25 * q (j) = l = 1.0; Unfortunately, this relaxed constraint has no realistic significance. The constraint we are Interested in relaxing (or tightening) is the nonlinear form of the ration constraint. Example, we wowould like to know the marginal benefit arising from changing the ratio Constraint Y (I, j)/Q (j) = L =. 26; We can in fact obtain the desired marginals by entering the following transformation on Undesired marginals: Parameter Amr (I, j) Appropriate marginal for ratio constraint; Amr (I, j) = ratio. m (I, j) * 0.01 * q. L (j ); Display AMR; Notice that the assignment statement for AMR Accesses both. M and. l records from Database. The idea behind the transformation is to notice that Y (I, j)/Q (j) = L =. 26; Is equivalent Y (I, j)-. 25 * q (j) = L = 0.01 * q (j );