Contract - Semi-continuous variables

#include <xpress.hpp>
#include <stdexcept>  // For throwing exceptions

using namespace xpress;
using namespace xpress::objects;
using xpress::objects::utils::sum;

/* Shows the use of a matrix of variables (i.e. x[i][j]) and different ways to specify contraints*/

/* Contract Allocation example. Given a number of districts, we have to produce enough
 * of a certain resource to fulfill all contracts. Each district has a maximum amount of
 * resource they can produce. Minimize costs to fulfill contracts.
 */

const int NDISTRICT = 6;  // Number of districts
const int NCONTRACT = 10; // Number of contracts

const std::vector<double> output = { 50, 40, 10, 20, 70, 50 };  // Max. output per district
const std::vector<double> cost   = { 50, 20, 25, 30, 45, 40 };  // Cost per unit per district
// Required volume of resources by contracts:
const std::vector<double> volume = { 20, 10, 30, 15, 20, 30, 10, 50, 10, 20 };


int main() {
    try {
        // Create a problem instance with verbose messages printed to Console
        XpressProblem prob;
        prob.callbacks.addMessageCallback(XpressProblem::console);

        /* VARIABLES */

        // Variables indicating whether a project is chosen
        std::vector<std::vector<Variable>> x = prob.addVariables(NDISTRICT, NCONTRACT)
                .withType(ColumnType::Binary)
                .withName("x_d%d_c%d")
                .toArray();

        // Quantities allocated to contractors
        std::vector<std::vector<Variable>> q = prob.addVariables(NDISTRICT, NCONTRACT)
                        .withType(ColumnType::SemiContinuous)
                        .withUB([&](int d, int){ return output[d]; })
                        .withLimit(5)
                        .withName("q_d%d_c%d")
                        .toArray();

        /* CONSTRAINTS */

        // "Size": Produce the required volume of resource for each contract
        // for all c in [0,NCONTRACT]
        //      sum(d in [0,NDISTRICT]) q[d][c] >= volume[c]
        prob.addConstraints(NCONTRACT, [&](int c) {
            SumExpression coveredVolume = sum(NDISTRICT, [&](int d) { return q[d][c]; });
            return coveredVolume.geq(volume[c]).setName("Size_" + std::to_string(c));
        });

        // "Min": at least 2 districts per contract
        // for all c in [0,NCONTRACT]
        //      sum(d in [0,NDISTRICT]) x[d][c] >= 2
        prob.addConstraints(NCONTRACT, [&](int c) {
            LinExpression districtsPerContract = LinExpression::create();
            for (int d=0; d<NDISTRICT; d++) {
                districtsPerContract.addTerm(x[d][c]);
            }
            return districtsPerContract.geq(2.0).setName("Min_" + std::to_string(c));
        });

        // Do not exceed max. output
        // for all d in [0,NDISTRICT]
        //      sum(c in [0,NCONTRACT]) q[d][c] <= output[d]
        prob.addConstraints(NDISTRICT, [&](int d) {
            return (sum(q[d]) <= output[d]).setName("Output_" + std::to_string(d));
        });

        // If a contract is allocated to a district, then at least 1 unit is allocated to it
        // for all d in [0,NDISTRICT[
        //      for all c in [0,NCONTRACT[
        //           x[d][c] <= q[d][c]
        prob.addConstraints(NDISTRICT, NCONTRACT, [&](int d, int c) {
            return x[d][c].leq(q[d][c]).setName("XQ_" + std::to_string(d) + "_" + std::to_string(c));
        });

        /* OBJECTIVE */

        LinExpression obj = LinExpression::create();
        for (int c=0; c<NCONTRACT; c++) {
            for (int d=0; d<NDISTRICT; d++) {
                obj.addTerm(q[d][c], cost[d]);
            }
        }
        prob.setObjective(obj, ObjSense::Minimize);

        /* SOLVE & PRINT */

        prob.writeProb("Contract.lp", "l");
        prob.optimize();

        // Check the solution status
        if (prob.attributes.getSolStatus() != SolStatus::Optimal && prob.attributes.getSolStatus() != SolStatus::Feasible) {
            std::ostringstream oss; oss << prob.attributes.getSolStatus(); // Convert xpress::SolStatus to String
            throw std::runtime_error("Optimization failed with status " + oss.str());
        }

        // Print the solution
        std::vector<double> sol = prob.getSolution();
        std::cout << "*** Solution ***" << std::endl;
        std::cout << "Objective value: " << prob.attributes.getObjVal() << std::endl;
        for (std::vector<Variable> q_d : q) {
            for (Variable q_dc : q_d) {
                if (q_dc.getValue(sol) > 0.0) {
                    std::cout << q_dc.getName() << ": " << q_dc.getValue(sol) << ", ";
                }
            }
            std::cout << std::endl;
        }
        return 0;
    }
    catch (std::exception& e) {
        std::cout << "Exception: " << e.what() << std::endl;
        return -1;
    }
}