Originally posted by: SalmanKhan

I wanted your help with solving an intertemporal electricity market clearing problem using CPLEX in Java.

A brief description of my problem: I have 5 electricity generators.

1.       Maximum generation capacity is fixed for all time steps.
2.       The price at which they offer electricity is fixed for all time steps

I want to minimize the marginal cost of overall generation against demand. My code is as follows:

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import ilog.concert.*;
import ilog.cplex.*;

public class LPex1 {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        model1();
    }

    public static void model1() {         
       
        double marginalCostGasPlant = 90.67;
        double marginalCostNuclearPlant = 40.98;
        double marginalCostCoalPlant = 50.44;
        double marginalCostWindPlant = 10.53;
        double marginalCostSolarPlant = 20.54;

        double maxGenerationCapacityGasPlant = 4000;
        double maxGenerationCapacityNuclearPlant = 2800;
        double maxGenerationCapacityCoalPlant = 5000;
        double maxGenerationCapacityWindPlant = 500;
        double maxGenerationCapacitySolarPlant = 1000;
       
        double maxSolarIrradiance = 0.6;
        double maxWindSpeed = 0.7;
       
        double availableWindCapacity = maxGenerationCapacityWindPlant * maxWindSpeed;
        double availableSolarCapacity = maxGenerationCapacitySolarPlant * maxSolarIrradiance;
       
        double totalDemand = 1000;

        System.out.println("Starting optimization model");
        System.out.println("Available wind capacity is: "+availableWindCapacity);
        System.out.println("Available solar capacity is: "+availableSolarCapacity);
       
        double mTotalDemand = totalDemand;

        try {
            IloCplex cplex1 = new IloCplex();

            // defining variables

            IloNumVar generationCapacityGasPlant = cplex1.numVar(0, maxGenerationCapacityGasPlant,
                    "generationCapacityGasPlant");
            IloNumVar generationCapacityNuclearPlant = cplex1.numVar(0, maxGenerationCapacityNuclearPlant,
                    "generationCapacityNuclearPlant");
            IloNumVar generationCapacityCoalPlant = cplex1.numVar(0, maxGenerationCapacityCoalPlant,
                    "generationCapacityCoalPlant");
            IloNumVar generationCapacityWindPlant = cplex1.numVar(0, availableWindCapacity,
                    "generationCapacityWindPlant");
            IloNumVar generationCapacitySolarPlant = cplex1.numVar(0, availableSolarCapacity,
                    "generationCapacitySolarPlant");

            // defining expressions

            IloLinearNumExpr objective1 = cplex1.linearNumExpr();
            objective1.addTerm(marginalCostWindPlant, generationCapacityWindPlant);
            objective1.addTerm(marginalCostSolarPlant, generationCapacitySolarPlant);
            objective1.addTerm(marginalCostGasPlant, generationCapacityGasPlant);
            objective1.addTerm(marginalCostNuclearPlant, generationCapacityNuclearPlant);
            objective1.addTerm(marginalCostCoalPlant, generationCapacityCoalPlant);

            // defining objective

            cplex1.addMinimize(objective1);

            // defining constraints

            IloLinearNumExpr constraint1 = cplex1.linearNumExpr();
            constraint1.addTerm(1, generationCapacityWindPlant);
            constraint1.addTerm(1, generationCapacitySolarPlant);
            constraint1.addTerm(1, generationCapacityGasPlant);
            constraint1.addTerm(1, generationCapacityNuclearPlant);
            constraint1.addTerm(1, generationCapacityCoalPlant);

            cplex1.addEq(constraint1, mTotalDemand);

            cplex1.addGe(maxGenerationCapacityGasPlant, generationCapacityGasPlant);
            cplex1.addGe(maxGenerationCapacityNuclearPlant, generationCapacityNuclearPlant);
            cplex1.addGe(maxGenerationCapacityCoalPlant, generationCapacityCoalPlant);
            cplex1.addGe(availableWindCapacity, generationCapacityWindPlant);
            cplex1.addGe(availableSolarCapacity, generationCapacitySolarPlant);

            cplex1.setParam(IloCplex.IntParam.Simplex.Display, 0);

            // solve

            if (cplex1.solve()) {
                System.out.println("Objective = " + cplex1.getObjValue());
                System.out.println("Objective = " + cplex1.getStatus());

                System.out.println("generationCapacityGasPlant = " + cplex1.getValue(generationCapacityGasPlant));
                System.out.println("generationCapacityNuclearPlant = " + cplex1.getValue(generationCapacityNuclearPlant));
                System.out.println("generationCapacityCoalPlant = " + cplex1.getValue(generationCapacityCoalPlant));
                System.out.println("generationCapacityWindPlant =  " + cplex1.getValue(generationCapacityWindPlant));
                System.out.println("generationCapacitySolarPlant =  " + cplex1.getValue(generationCapacitySolarPlant));
                System.out.println("TotalGeneration =  " + cplex1.getValue(constraint1));

            } else {
                System.out.println("Something went wrong");
            }

            cplex1.end();

        } catch (IloException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
     }
}

This is for just one time step. I want to clear the market for multiple time steps. For that I would need to minimize a whole matrix with many linearNumExpr rather then just one. I would really appreciate if you can help me out here. I am looking into the addminimize function but it doesn't take matrices or arrays as input. Further more, how can I assign linear num exprs to matrix locations?

 Thanks

I think we resolved the issues offline. Please come back if you still have trouble.