workforce5_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。第二优化允许高达降解第一个目标的10％的较小的值和2 * /使用系统;使用Gurobi;类workforce5_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”， “托比”};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 }, { 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 GRBEnv env = new GRBEnv(); // Create initial model GRBModel model = new GRBModel(env); model.ModelName = "workforce5_cs"; // 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. 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, string.Format("{0}.{1}", 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, string.Format("{0}Slack", Shifts[s])); } // 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, string.Format("{0}TotShifts", Workers[w])); } 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, GRB.EQUAL, shiftRequirements[s], Shifts[s]); } // Constraint: set totSlack equal to the total slack lhs = new GRBLinExpr(); lhs.AddTerm(-1.0, totSlack); for (int s = 0; s < nShifts; ++s) { lhs.AddTerm(1.0, slacks[s]); } model.AddConstr(lhs, GRB.EQUAL, 0, "totSlack"); // Constraint: compute the total number of shifts for each worker for (int w = 0; w < nWorkers; ++w) { lhs = new GRBLinExpr(); lhs.AddTerm(-1.0, totShifts[w]); for (int s = 0; s < nShifts; ++s) { lhs.AddTerm(1.0, x[w,s]); } model.AddConstr(lhs, GRB.EQUAL, 0, string.Format("totShifts{0}", Workers[w])); } // 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, GRB.INFINITY, "minShift"); model.AddGenConstrMax(maxShift, totShifts, -GRB.INFINITY, "maxShift"); // Set global sense for ALL objectives model.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_cs.lp"); // Optimize int status = solveAndPrint(model, totSlack, nWorkers, Workers, totShifts); if (status != GRB.Status.OPTIMAL) return; // Dispose of model and environment model.Dispose(); env.Dispose(); } catch (GRBException e) { Console.WriteLine("Error code: {0}. {1}", 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 {0}", status); return status; } // Print total slack and the number of shifts worked for each worker Console.WriteLine("\nTotal slack required: {0}", totSlack.X); for (int w = 0; w < nWorkers; ++w) { Console.WriteLine("{0} worked {1} shifts", Workers[w], totShifts[w].X); } Console.WriteLine("\n"); return status; } }
