ILOG CPLEX 11.0 User's Manual

in demand; in terms of this model, the demand should meet the supply as well. Those ideasare represented as constraints added to the model, like this:for(i = 0; i < nbSupply; i++) { // supply must meet demandmodel.add(IloSum(x[i]) == supply[i]);}for(j = 0; j < nbDemand; j++) { // demand must meet supplyIloExpr v(env);for(i = 0; i < nbSupply; i++)v += x[i][j];model.add(v == demand[j]);v.end();}Checking Convexity and ConcavityTo illustrate the ideas of convex and concave piecewise linear functions, two tables of coststhat vary according to the quantity of cars shipped were introduced in the problemdescription. To accommodate those two tables in the model, the following lines are added.if (convex) {for(i = 0; i < nbSupply; i++){for(j = 0; j < nbDemand; j++){model.add(y[i][j] == IloPiecewiseLinear(x[i][j],IloNumArray(env, 2, 200.0, 400.0),IloNumArray(env, 3, 30.0, 80.0, 130.0),0.0, 0.0));}}}else{for(i = 0; i < nbSupply; i++){for(j = 0; j < nbDemand; j++){model.add(y[i][j] == IloPiecewiseLinear(x[i][j],IloNumArray(env, 2, 200.0, 400.0),IloNumArray(env, 3, 120.0, 80.0, 50.0),0.0, 0.0));}}}Adding an ObjectiveThe objective is to minimize costs of supplying cars from factories to showrooms, It is addedto the model in these lines:IloExpr obj(env);for(i = 0; i < nbSupply; i++){obj += IloSum(y[i]);}model.add(IloMinimize(env, obj));obj.end();346 ILOG CPLEX 11.0 — USER’ S MANUAL