Try our new documentation site (beta).
Filter Content By
Version
Text Search
${sidebar_list_label} - Back
Filter by Language
workforce1.py
#!/usr/bin/env python3.7 # Copyright 2021, 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 gurobipy as gp from gurobipy import GRB import sys # Number of workers required for each shift shifts, 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 shift workers, pay = gp.multidict({ "Amy": 10, "Bob": 12, "Cathy": 10, "Dan": 8, "Ed": 8, "Fred": 9, "Gu": 11, }) # Worker availability availability = 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') ]) # Model m = 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 costs m.setObjective(gp.quicksum(pay[w]*x[w, s] for w, s in availability), GRB.MINIMIZE) # Constraints: assign exactly shiftRequirements[s] workers to each shift s reqCts = m.addConstrs((x.sum('*', s) == shiftRequirements[s] for s in shifts), "_") # 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 model m.write('workforce1.lp') # Optimize m.optimize() status = m.status if status == GRB.UNBOUNDED: print('The model cannot be solved because it is unbounded') sys.exit(0) if status == GRB.OPTIMAL: print('The optimal objective is %g' % m.objVal) sys.exit(0) if status != GRB.INF_OR_UNBD and status != GRB.INFEASIBLE: print('Optimization was stopped with status %d' % status) sys.exit(0) # do IIS print('The model is infeasible; computing IIS') m.computeIIS() if m.IISMinimal: print('IIS is minimal\n') else: print('IIS is not minimal\n') print('\nThe following constraint(s) cannot be satisfied:') for c in m.getConstrs(): if c.IISConstr: print('%s' % c.constrName)