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workforce1.py
#!/usr/bin/python # Copyright 2016, Gurobi Optimization, Inc. # 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. from gurobipy import * # Number of workers required for each shift shifts, shiftRequirements = 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 shift workers, pay = multidict({ "Amy": 10, "Bob": 12, "Cathy": 10, "Dan": 8, "Ed": 8, "Fred": 9, "Gu": 11 }) # Worker availability availability = 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') ]) # Model m = 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 = {} for w,s in availability: x[w,s] = m.addVar(ub=1, obj=pay[w], name=w+"."+s) # The objective is to minimize the total pay costs m.modelSense = GRB.MINIMIZE # Update model to integrate new variables m.update() # Constraint: assign exactly shiftRequirements[s] workers to each shift s reqCts = {} for s in shifts: reqCts[s] = m.addConstr( quicksum(x[w,s] for w,s in availability.select('*', s)) == shiftRequirements[s], s) # Optimize m.optimize() status = m.status if status == GRB.Status.UNBOUNDED: print('The model cannot be solved because it is unbounded') exit(0) if status == GRB.Status.OPTIMAL: print('The optimal objective is %g' % m.objVal) exit(0) if status != GRB.Status.INF_OR_UNBD and status != GRB.Status.INFEASIBLE: print('Optimization was stopped with status %d' % status) exit(0) # do IIS print('The model is infeasible; computing IIS') m.computeIIS() print('\nThe following constraint(s) cannot be satisfied:') for c in m.getConstrs(): if c.IISConstr: print('%s' % c.constrName)