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Workforce1.java
/* Copyright 2022, 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. */ import gurobi.*; public class Workforce1 { 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.Status.UNBOUNDED) { System.out.println("The model cannot be solved " + "because it is unbounded"); return; } if (status == GRB.Status.OPTIMAL) { System.out.println("The optimal objective is " + model.get(GRB.DoubleAttr.ObjVal)); return; } if (status != GRB.Status.INF_OR_UNBD && status != GRB.Status.INFEASIBLE ){ System.out.println("Optimization was stopped with status " + status); return; } // Compute IIS System.out.println("The model is infeasible; computing IIS"); model.computeIIS(); System.out.println("\nThe following constraint(s) " + "cannot be satisfied:"); for (GRBConstr c : model.getConstrs()) { if (c.get(GRB.IntAttr.IISConstr) == 1) { System.out.println(c.get(GRB.StringAttr.ConstrName)); } } // Dispose of model and environment model.dispose(); env.dispose(); } catch (GRBException e) { System.out.println("Error code: " + e.getErrorCode() + ". " + e.getMessage()); } } }