workforce1_cs.cs
/* Copyright 2019, Gurobi Optimization, LLC */ /* Assign workers to shifts; each worker may or may not be available on a particular day. If the problem cannot be solved, use IIS to find a set of conflicting constraints. Note that there may be additional conflicts besides what is reported via IIS. */ using System; using Gurobi; class workforce1_cs { static void Main() { try { // Sample data // Sets of days and workers string[] Shifts = new string[] { "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6", "Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13", "Sun14" }; string[] Workers = new string[] { "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu" }; 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 }; // Amount each worker is paid to work one shift double[] pay = new double[] { 10, 12, 10, 8, 8, 9, 11 }; // 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. Since an assignment model always produces integer // solutions, we use continuous variables and solve as an LP. 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], pay[w], GRB.CONTINUOUS, Workers[w] + "." + Shifts[s]); } } // The objective is to minimize the total pay costs model.ModelSense = GRB.MINIMIZE; // Constraint: assign exactly shiftRequirements[s] workers // to each shift s for (int s = 0; s < nShifts; ++s) { GRBLinExpr lhs = 0.0; for (int w = 0; w < nWorkers; ++w) lhs.AddTerm(1.0, x[w, s]); model.AddConstr(lhs == shiftRequirements[s], Shifts[s]); } // Optimize model.Optimize(); int status = model.Status; if (status == GRB.Status.UNBOUNDED) { Console.WriteLine("The model cannot be solved " + "because it is unbounded"); return; } if (status == GRB.Status.OPTIMAL) { Console.WriteLine("The optimal objective is " + model.ObjVal); return; } if ((status != GRB.Status.INF_OR_UNBD) && (status != GRB.Status.INFEASIBLE)) { Console.WriteLine("Optimization was stopped with status " + status); return; } // Do IIS Console.WriteLine("The model is infeasible; computing IIS"); model.ComputeIIS(); Console.WriteLine("\nThe following constraint(s) " + "cannot be satisfied:"); foreach (GRBConstr c in model.GetConstrs()) { if (c.IISConstr == 1) { Console.WriteLine(c.ConstrName); } } // Dispose of model and env model.Dispose(); env.Dispose(); } catch (GRBException e) { Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message); } } }
