Workforce5_c ++。CPP
/ *版权所有2018年，Gurobi狗万app足彩优化，LLC * / / *分配工人轮班;每个工人可能会或可能无法使用在特定的一天。我们采用多目标优化求解模型。最高优先级的目标最小化的松弛的总和（即，未覆盖的移位的总数）。次要目的最小化的最大值和移位的最小数目之间的差的工作的所有工人。第二优化允许高达10％和2 * /＃包括较小的值“gurobi_c ++小时。”降解第一物镜的#include使用命名空间std ;INT solveAndPrint（GRBModel＆模型，GRBVar＆totSlack，INT nWorkers，字符串*工人，GRBVar * totShifts）掷（GRBException）;诠释主（INT的argc，字符* argv的[]）{GRBEnv * ENV = 0;GRBVar ** X = 0;GRBVar *松弛= 0; GRBVar *totShifts = 0; int xCt = 0; int s, w; try { // Sample data const int nShifts = 14; const int nWorkers = 8; // Sets of days and workers string Shifts[] = { "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6", "Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13", "Sun14" }; string Workers[] = { "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu", "Tobi" }; // Number of workers required for each shift double shiftRequirements[] = { 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 }; // Worker availability: 0 if the worker is unavailable for a shift double availability[][14] = { { 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 }, { 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 }, { 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 }, { 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 }, { 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 }, { 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 }, { 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1 }, { 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; // Create environment env = new GRBEnv("workforce5_c++.log"); // Create initial model GRBModel model = GRBModel(*env); model.set(GRB_StringAttr_ModelName, "workforce5_c++"); // Initialize assignment decision variables: // x[w][s] == 1 if worker w is assigned to shift s. // This is no longer a pure assignment model, so we must // use binary variables. x = new GRBVar*[nWorkers]; for (w = 0; w < nWorkers; w++) { x[w] = model.addVars(nShifts, GRB_BINARY); xCt++; for (s = 0; s < nShifts; s++) { ostringstream vname; vname << Workers[w] << "." << Shifts[s]; x[w][s].set(GRB_DoubleAttr_UB, availability[w][s]); x[w][s].set(GRB_StringAttr_VarName, vname.str()); } } // Initialize slack decision variables slacks = model.addVars(nShifts); for (s = 0; s < nShifts; s++) { ostringstream vname; vname << Shifts[s] << "Slack"; slacks[s].set(GRB_StringAttr_VarName, vname.str()); } // Variable to represent the total slack GRBVar totSlack = model.addVar(0, GRB_INFINITY, 0, GRB_CONTINUOUS, "totSlack"); // Initialize variables to count the total shifts worked by each worker totShifts = model.addVars(nWorkers); for (w = 0; w < nWorkers; w++) { ostringstream vname; vname << Workers[w] << "TotShifts"; totShifts[w].set(GRB_StringAttr_VarName, vname.str()); } GRBLinExpr lhs; // Constraint: assign exactly shiftRequirements[s] workers // to each shift s, plus the slack for (s = 0; s < nShifts; s++) { lhs = 0; lhs += slacks[s]; for (w = 0; w < nWorkers; w++) { lhs += x[w][s]; } model.addConstr(lhs == shiftRequirements[s], Shifts[s]); } // Constraint: set totSlack column equal to the total slack lhs = 0; for (s = 0; s < nShifts; s++) { lhs += slacks[s]; } model.addConstr(lhs == totSlack, "totSlack"); // Constraint: compute the total number of shifts for each worker for (w = 0; w < nWorkers; w++) { lhs = 0; for (s = 0; s < nShifts; s++) { lhs += x[w][s]; } ostringstream vname; vname << "totShifts" << Workers[w]; model.addConstr(lhs == totShifts[w], vname.str()); } // Constraint: set minShift/maxShift variable to less <=/>= to the // number of shifts among all workers GRBVar minShift = model.addVar(0, GRB_INFINITY, 0, GRB_CONTINUOUS, "minShift"); GRBVar maxShift = model.addVar(0, GRB_INFINITY, 0, GRB_CONTINUOUS, "maxShift"); model.addGenConstrMin(minShift, totShifts, nWorkers, GRB_INFINITY, "minShift"); model.addGenConstrMax(maxShift, totShifts, nWorkers, -GRB_INFINITY, "maxShift"); // Set global sense for ALL objectives model.set(GRB_IntAttr_ModelSense, GRB_MINIMIZE); // Set primary objective model.setObjectiveN(totSlack, 0, 2, 1.0, 2.0, 0.1, "TotalSlack"); // Set secondary objective model.setObjectiveN(maxShift - minShift, 1, 1, 1.0, 0, 0, "Fairness"); // Save problem model.write("workforce5_c++.lp"); // Optimize int status = solveAndPrint(model, totSlack, nWorkers, Workers, totShifts); // Delete local variables if (status != GRB_OPTIMAL) return 1; } catch (GRBException e){ cout << "Error code = " << e.getErrorCode() << endl; cout << e.getMessage() << endl; } catch (...) { cout << "Exception during optimization" << endl; } for (s = 0; s < xCt; s++) delete[] x[s]; delete[] x; delete[] slacks; delete[] totShifts; delete env; return 0; } int solveAndPrint(GRBModel& model, GRBVar& totSlack, int nWorkers, string* Workers, GRBVar* totShifts) throw(GRBException) { model.optimize(); int status = model.get(GRB_IntAttr_Status); if ((status == GRB_INF_OR_UNBD) || (status == GRB_INFEASIBLE) || (status == GRB_UNBOUNDED) ) { cout << "The model cannot be solved " << "because it is infeasible or unbounded" << endl; return status; } if (status != GRB_OPTIMAL) { cout << "Optimization was stopped with status " << status << endl; return status; } // Print total slack and the number of shifts worked for each worker cout << endl << "Total slack required: " << totSlack.get(GRB_DoubleAttr_X) << endl; for (int w = 0; w < nWorkers; ++w) { cout << Workers[w] << " worked " << totShifts[w].get(GRB_DoubleAttr_X) << " shifts" << endl; } cout << endl; return status; }
