Finding the value of the deterministic solution:
The same model file can be used. All the demand parameters in the old data file are replaced by their average values, to give a new data file. Solving gives the following:
================================================== CPLEX 6.6.0: CPLEX 6.6.0: optimal solution; objective 225.83335 15 simplex iterations (0 in phase I) ampl: display x; x [*] := business 28.3333 economy 134.167 first 11.6667 ; ampl: display y; y := business midday 28.3333 business morning 28.3333 business weekend 28.3333 economy midday 134.167 economy morning 134.167 economy weekend 134.167 first midday 11.6667 first morning 11.6667 first weekend 11.6667 ; =================================================
Note that 225.833 is the value of the deterministic solution, assuming we can sell the average number of tickets in each scenario.
To calculate the Value of the Stochastic Solution, we need to calculate the objective function value for the following restricted version of y:
y := business midday 10 business morning 28.3333 business weekend 25 economy midday 134.167 economy morning 134.167 economy weekend 134.167 first midday 5 first morning 11.6667 first weekend 10 ;This has objective function value 203.0559.
The value of the stochastic solution is thus 208.3333333 - 203.0559 = 5.277.
=============================================== ===============================================If we force integrality, the solution to the deterministic problem is:
=============================================== CPLEX 6.6.0: CPLEX 6.6.0: optimal integer solution; objective 225 10 MIP simplex iterations 0 branch-and-bound nodes ampl: display x; x [*] := business 28 economy 136 first 11 ; ampl: display y; y := business midday 28 business morning 28 business weekend 28 economy midday 136 economy morning 136 economy weekend 136 first midday 11 first morning 11 first weekend 11 ; ===============================================Restricting y shows that this has objective function value 204 in the stochastic program.
So VSS = 208.3333333 - 204 = 4.33.