workforce5_c + + . cpp
/ *版权所有2021，Gurobi优狗万app足彩化，LLC * / / *分配工人转移;每个工人都可能或可能无法在特定日期上使用。我们使用多目标优化来解决模型。最高优先级目标最小化了松弛的总和（即，未发现的转移总数）。二级目标最大限度地减少了所有工人之间工作的最大和最小班次之间的差异。允许第二优化将第一个目标降低到较小的值为10％和2 * / #include“gurobi_c ++。h”#include 使用命名空间std;int solveandprint（grbmodel＆model，grbvar＆totslack，int nworkers，string * work，grbvar * totshifts）;int main（int argc，char * argv []）{grbenv * env = 0;grbvar ** x = 0;grbvar * slacks = 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) { 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; }
