workforce4_cs.cs.
/ *版权所有2019，Gurobi优狗万app足彩化，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。我们用帕累托优化对模型进行求解：首先，我们尽量减少松弛的线性和。然后，我们限制了休闲裤的总和，而我们最大限度地减少二次目标，试图平衡工人的工作量。*使用系统/;使用Gurobi;类workforce4_cs {静态无效的主要（）{尝试{//采样数据//天，工人串套[]班次=新的String [] { “MON1”， “Tue2”， “Wed3”， “Thu4”，“Fri5”， “Sat6”， “Sun7”， “MON8”， “Tue9”， “Wed10”， “Thu11”， “Fri12”， “Sat13”， “Sun14”};串[]工人=新的字符串[] { “艾米”， “鲍勃”， “凯西”， “丹”， “ED”， “佛瑞德”， “谷”};INT nShifts = Shifts.Length;INT nWorkers = Workers.Length; // Number of workers required for each shift double[] shiftRequirements = new double[] { 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 = new double[,] { { 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 }, { 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; // Model GRBEnv env = new GRBEnv(); GRBModel model = new GRBModel(env); model.ModelName = "assignment"; // Assignment 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. GRBVar[,] x = new GRBVar[nWorkers, nShifts]; for (int w = 0; w < nWorkers; ++w) { for (int s = 0; s < nShifts; ++s) { x[w,s] = model.AddVar(0, availability[w,s], 0, GRB.BINARY, Workers[w] + "." + Shifts[s]); } } // Slack variables for each shift constraint so that the shifts can // be satisfied GRBVar[] slacks = new GRBVar[nShifts]; for (int s = 0; s < nShifts; ++s) { slacks[s] = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, Shifts[s] + "Slack"); } // Variable to represent the total slack GRBVar totSlack = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "totSlack"); // Variables to count the total shifts worked by each worker GRBVar[] totShifts = new GRBVar[nWorkers]; for (int w = 0; w < nWorkers; ++w) { totShifts[w] = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, Workers[w] + "TotShifts"); } GRBLinExpr lhs; // Constraint: assign exactly shiftRequirements[s] workers // to each shift s, plus the slack for (int s = 0; s < nShifts; ++s) { lhs = new GRBLinExpr(); lhs.AddTerm(1.0, slacks[s]); for (int w = 0; w < nWorkers; ++w) { lhs.AddTerm(1.0, x[w, s]); } model.AddConstr(lhs == shiftRequirements[s], Shifts[s]); } // Constraint: set totSlack equal to the total slack lhs = new GRBLinExpr(); for (int s = 0; s < nShifts; ++s) { lhs.AddTerm(1.0, slacks[s]); } model.AddConstr(lhs == totSlack, "totSlack"); // Constraint: compute the total number of shifts for each worker for (int w = 0; w < nWorkers; ++w) { lhs = new GRBLinExpr(); for (int s = 0; s < nShifts; ++s) { lhs.AddTerm(1.0, x[w, s]); } model.AddConstr(lhs == totShifts[w], "totShifts" + Workers[w]); } // Objective: minimize the total slack model.SetObjective(1.0*totSlack); // Optimize int status = solveAndPrint(model, totSlack, nWorkers, Workers, totShifts); if (status != GRB.Status.OPTIMAL) { return; } // Constrain the slack by setting its upper and lower bounds totSlack.UB = totSlack.X; totSlack.LB = totSlack.X; // Variable to count the average number of shifts worked GRBVar avgShifts = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "avgShifts"); // Variables to count the difference from average for each worker; // note that these variables can take negative values. GRBVar[] diffShifts = new GRBVar[nWorkers]; for (int w = 0; w < nWorkers; ++w) { diffShifts[w] = model.AddVar(-GRB.INFINITY, GRB.INFINITY, 0, GRB.CONTINUOUS, Workers[w] + "Diff"); } // Constraint: compute the average number of shifts worked lhs = new GRBLinExpr(); for (int w = 0; w < nWorkers; ++w) { lhs.AddTerm(1.0, totShifts[w]); } model.AddConstr(lhs == nWorkers * avgShifts, "avgShifts"); // Constraint: compute the difference from the average number of shifts for (int w = 0; w < nWorkers; ++w) { model.AddConstr(totShifts[w] - avgShifts == diffShifts[w], Workers[w] + "Diff"); } // Objective: minimize the sum of the square of the difference from the // average number of shifts worked GRBQuadExpr qobj = new GRBQuadExpr(); for (int w = 0; w < nWorkers; ++w) { qobj.AddTerm(1.0, diffShifts[w], diffShifts[w]); } model.SetObjective(qobj); // Optimize status = solveAndPrint(model, totSlack, nWorkers, Workers, totShifts); if (status != GRB.Status.OPTIMAL) { return; } // Dispose of model and env model.Dispose(); env.Dispose(); } catch (GRBException e) { Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message); } } private static int solveAndPrint(GRBModel model, GRBVar totSlack, int nWorkers, String[] Workers, GRBVar[] totShifts) { model.Optimize(); int status = model.Status; if ((status == GRB.Status.INF_OR_UNBD) || (status == GRB.Status.INFEASIBLE) || (status == GRB.Status.UNBOUNDED)) { Console.WriteLine("The model cannot be solved " + "because it is infeasible or unbounded"); return status; } if (status != GRB.Status.OPTIMAL) { Console.WriteLine("Optimization was stopped with status " + status); return status; } // Print total slack and the number of shifts worked for each worker Console.WriteLine("\nTotal slack required: " + totSlack.X); for (int w = 0; w < nWorkers; ++w) { Console.WriteLine(Workers[w] + " worked " + totShifts[w].X + " shifts"); } Console.WriteLine("\n"); return status; } }
