#!/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. We use multi-objective optimization to solve the model.# The highest-priority objective minimizes the sum of the slacks# (i.e., the total number of uncovered shifts). The secondary objective# minimizes the difference between the maximum and minimum number of# shifts worked among all workers.  The second optimization is allowed# to degrade the first objective by up to the smaller value of 10% and 2 */importgurobipyasgpfromgurobipyimportGRBimportsys# Sample data# Sets of days and workersShifts=["Mon1","Tue2","Wed3","Thu4","Fri5","Sat6","Sun7","Mon8","Tue9","Wed10","Thu11","Fri12","Sat13","Sun14",]Workers=["Amy","Bob","Cathy","Dan","Ed","Fred","Gu","Tobi"]# Number of workers required for each shiftS=[3,2,4,4,5,6,5,2,2,3,4,6,7,5]shiftRequirements={s:S[i]fori,sinenumerate(Shifts)}# Worker availability: 0 if the worker is unavailable for a shiftA=[[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],[0,1,1,1,0,1,1,0,1,1,1,0,1,1],[1,1,1,0,1,1,1,1,1,1,1,1,1,1],]availability={(w,s):A[j][i]fori,sinenumerate(Shifts)forj,winenumerate(Workers)}try:# Create model with a context manager. Upon exit from this block,# model.dispose is called automatically, and memory consumed by the model# is released.## The model is created in the default environment, which will be created# automatically upon model construction.  For safe release of resources# tied to the default environment, disposeDefaultEnv is called below.withgp.Model("workforce5")asmodel:# Initialize assignment decision variables:# x[w][s] == 1 if worker w is assigned to shift s.# This is no longer a pure assignment model, so we must# use binary variables.x=model.addVars(availability.keys(),ub=availability,vtype=GRB.BINARY,name="x")# Slack variables for each shift constraint so that the shifts can# be satisfiedslacks=model.addVars(Shifts,name="Slack")# Variable to represent the total slacktotSlack=model.addVar(name="totSlack")# Variables to count the total shifts worked by each workertotShifts=model.addVars(Workers,name="TotShifts")# Constraint: assign exactly shiftRequirements[s] workers# to each shift s, plus the slackmodel.addConstrs((x.sum("*",s)+slacks[s]==shiftRequirements[s]forsinShifts),name="shiftRequirement",)# Constraint: set totSlack equal to the total slackmodel.addConstr(totSlack==slacks.sum(),name="totSlack")# Constraint: compute the total number of shifts for each workermodel.addConstrs((totShifts[w]==x.sum(w,"*")forwinWorkers),name="totShifts")# Constraint: set minShift/maxShift variable to less/greater than the# number of shifts among all workersminShift=model.addVar(name="minShift")maxShift=model.addVar(name="maxShift")model.addGenConstrMin(minShift,totShifts.values(),name="minShift")model.addGenConstrMax(maxShift,totShifts.values(),name="maxShift")# Set global sense for ALL objectivesmodel.ModelSense=GRB.MINIMIZE# Set up primary objectivemodel.setObjectiveN(totSlack,index=0,priority=2,abstol=2.0,reltol=0.1,name="TotalSlack")# Set up secondary objectivemodel.setObjectiveN(maxShift-minShift,index=1,priority=1,name="Fairness")# Save problemmodel.write("workforce5.lp")# Optimizemodel.optimize()status=model.Statusifstatusin(GRB.INF_OR_UNBD,GRB.INFEASIBLE,GRB.UNBOUNDED):print("Model cannot be solved because it is infeasible or unbounded")sys.exit(0)ifstatus!=GRB.OPTIMAL:print(f"Optimization was stopped with status{status}")sys.exit(0)# Print total slack and the number of shifts worked for each workerprint("")print(f"Total slack required:{totSlack.X}")forwinWorkers:print(f"{w} worked{totShifts[w].X} shifts")print("")exceptgp.GurobiErrorase:print(f"Error code{e.errno}:{e}")exceptAttributeErrorase:print(f"Encountered an attribute error:{e}")finally:# Safely release memory and/or server side resources consumed by# the default environment.gp.disposeDefaultEnv()