Workforce3.java
/* 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, relax the model to determine which constraints cannot be satisfied, and how much they need to be relaxed. */ import gurobi.*; public class Workforce3 { public static void main(String[] args) { 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.set(GRB.StringAttr.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.set(GRB.IntAttr.ModelSense, GRB.MINIMIZE); // Constraint: assign exactly shiftRequirements[s] workers // to each shift s for (int s = 0; s < nShifts; ++s) { GRBLinExpr lhs = new GRBLinExpr(); for (int w = 0; w < nWorkers; ++w) { lhs.addTerm(1.0, x[w][s]); } model.addConstr(lhs, GRB.EQUAL, shiftRequirements[s], Shifts[s]); } // Optimize model.optimize(); int status = model.get(GRB.IntAttr.Status); if (status == GRB.UNBOUNDED) { System.out.println("The model cannot be solved " + "because it is unbounded"); return; } if (status == GRB.OPTIMAL) { System.out.println("The optimal objective is " + model.get(GRB.DoubleAttr.ObjVal)); return; } if (status != GRB.INF_OR_UNBD && status != GRB.INFEASIBLE ) { System.out.println("Optimization was stopped with status " + status); return; } // Relax the constraints to make the model feasible System.out.println("The model is infeasible; relaxing the constraints"); int orignumvars = model.get(GRB.IntAttr.NumVars); model.feasRelax(0, false, false, true); model.optimize(); status = model.get(GRB.IntAttr.Status); if (status == GRB.INF_OR_UNBD || status == GRB.INFEASIBLE || status == GRB.UNBOUNDED ) { System.out.println("The relaxed model cannot be solved " + "because it is infeasible or unbounded"); return; } if (status != GRB.OPTIMAL) { System.out.println("Optimization was stopped with status " + status); return; } System.out.println("\nSlack values:"); GRBVar[] vars = model.getVars(); for (int i = orignumvars; i < model.get(GRB.IntAttr.NumVars); ++i) { GRBVar sv = vars[i]; if (sv.get(GRB.DoubleAttr.X) > 1e-6) { System.out.println(sv.get(GRB.StringAttr.VarName) + " = " + sv.get(GRB.DoubleAttr.X)); } } // Dispose of model and environment model.dispose(); env.dispose(); } catch (GRBException e) { System.out.println("Error code: " + e.getErrorCode() + ". " + e.getMessage()); } } }
