#!/usr/bin/env python3# Copyright 2025, 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.importgurobipyasgpfromgurobipyimportGRBimportsys# Number of workers required for each shiftshifts,shiftRequirements=gp.multidict({"Mon1":3,"Tue2":2,"Wed3":4,"Thu4":4,"Fri5":5,"Sat6":6,"Sun7":5,"Mon8":2,"Tue9":2,"Wed10":3,"Thu11":4,"Fri12":6,"Sat13":7,"Sun14":5,})# Amount each worker is paid to work one shiftworkers,pay=gp.multidict({"Amy":10,"Bob":12,"Cathy":10,"Dan":8,"Ed":8,"Fred":9,"Gu":11,})# Worker availabilityavailability=gp.tuplelist([("Amy","Tue2"),("Amy","Wed3"),("Amy","Fri5"),("Amy","Sun7"),("Amy","Tue9"),("Amy","Wed10"),("Amy","Thu11"),("Amy","Fri12"),("Amy","Sat13"),("Amy","Sun14"),("Bob","Mon1"),("Bob","Tue2"),("Bob","Fri5"),("Bob","Sat6"),("Bob","Mon8"),("Bob","Thu11"),("Bob","Sat13"),("Cathy","Wed3"),("Cathy","Thu4"),("Cathy","Fri5"),("Cathy","Sun7"),("Cathy","Mon8"),("Cathy","Tue9"),("Cathy","Wed10"),("Cathy","Thu11"),("Cathy","Fri12"),("Cathy","Sat13"),("Cathy","Sun14"),("Dan","Tue2"),("Dan","Wed3"),("Dan","Fri5"),("Dan","Sat6"),("Dan","Mon8"),("Dan","Tue9"),("Dan","Wed10"),("Dan","Thu11"),("Dan","Fri12"),("Dan","Sat13"),("Dan","Sun14"),("Ed","Mon1"),("Ed","Tue2"),("Ed","Wed3"),("Ed","Thu4"),("Ed","Fri5"),("Ed","Sun7"),("Ed","Mon8"),("Ed","Tue9"),("Ed","Thu11"),("Ed","Sat13"),("Ed","Sun14"),("Fred","Mon1"),("Fred","Tue2"),("Fred","Wed3"),("Fred","Sat6"),("Fred","Mon8"),("Fred","Tue9"),("Fred","Fri12"),("Fred","Sat13"),("Fred","Sun14"),("Gu","Mon1"),("Gu","Tue2"),("Gu","Wed3"),("Gu","Fri5"),("Gu","Sat6"),("Gu","Sun7"),("Gu","Mon8"),("Gu","Tue9"),("Gu","Wed10"),("Gu","Thu11"),("Gu","Fri12"),("Gu","Sat13"),("Gu","Sun14"),])# Modelm=gp.Model("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.x=m.addVars(availability,ub=1,name="x")# The objective is to minimize the total pay costsm.setObjective(gp.quicksum(pay[w]*x[w,s]forw,sinavailability),GRB.MINIMIZE)# Constraints: assign exactly shiftRequirements[s] workers to each shift sreqCts=m.addConstrs((x.sum("*",s)==shiftRequirements[s]forsinshifts),"_")# Using Python looping constructs, the preceding statement would be...## reqCts = {}# for s in shifts:#   reqCts[s] = m.addConstr(#        gp.quicksum(x[w,s] for w,s in availability.select('*', s)) ==#        shiftRequirements[s], s)# Save modelm.write("workforce1.lp")# Optimizem.optimize()status=m.Statusifstatus==GRB.UNBOUNDED:print("The model cannot be solved because it is unbounded")sys.exit(0)ifstatus==GRB.OPTIMAL:print(f"The optimal objective is{m.ObjVal:g}")sys.exit(0)ifstatus!=GRB.INF_OR_UNBDandstatus!=GRB.INFEASIBLE:print(f"Optimization was stopped with status{status}")sys.exit(0)# do IISprint("The model is infeasible; computing IIS")m.computeIIS()ifm.IISMinimal:print("IIS is minimal\n")else:print("IIS is not minimal\n")print("\nThe following constraint(s) cannot be satisfied:")forcinm.getConstrs():ifc.IISConstr:print(c.ConstrName)