Try our new documentation site (beta).
multiscenario.py
#!/usr/bin/env python3.11
# Copyright 2024, Gurobi Optimization, LLC
# Facility location: a company currently ships its product from 5 plants to
# 4 warehouses. It is considering closing some plants to reduce costs. What
# plant(s) should the company close, in order to minimize transportation
# and fixed costs?
#
# Since the plant fixed costs and the warehouse demands are uncertain, a
# scenario approach is chosen.
#
# Note that this example is similar to the facility.py example. Here we
# added scenarios in order to illustrate the multi-scenario feature.
#
# Note that this example uses lists instead of dictionaries. Since
# it does not work with sparse data, lists are a reasonable option.
#
# Based on an example from Frontline Systems:
# http://www.solver.com/disfacility.htm
# Used with permission.
import gurobipy as gp
from gurobipy import GRB
# Warehouse demand in thousands of units
demand = [15, 18, 14, 20]
# Plant capacity in thousands of units
capacity = [20, 22, 17, 19, 18]
# Fixed costs for each plant
fixedCosts = [12000, 15000, 17000, 13000, 16000]
maxFixed = max(fixedCosts)
minFixed = min(fixedCosts)
# Transportation costs per thousand units
transCosts = [
[4000, 2000, 3000, 2500, 4500],
[2500, 2600, 3400, 3000, 4000],
[1200, 1800, 2600, 4100, 3000],
[2200, 2600, 3100, 3700, 3200],
]
# Range of plants and warehouses
plants = range(len(capacity))
warehouses = range(len(demand))
# Model
m = gp.Model("multiscenario")
# Plant open decision variables: open[p] == 1 if plant p is open.
open = m.addVars(plants, vtype=GRB.BINARY, obj=fixedCosts, name="open")
# Transportation decision variables: transport[w,p] captures the
# optimal quantity to transport to warehouse w from plant p
transport = m.addVars(warehouses, plants, obj=transCosts, name="trans")
# You could use Python looping constructs and m.addVar() to create
# these decision variables instead. The following would be equivalent
# to the preceding two statements...
#
# open = []
# for p in plants:
# open.append(m.addVar(vtype=GRB.BINARY,
# obj=fixedCosts[p],
# name="open[%d]" % p))
#
# transport = []
# for w in warehouses:
# transport.append([])
# for p in plants:
# transport[w].append(m.addVar(obj=transCosts[w][p],
# name="trans[%d,%d]" % (w, p)))
# The objective is to minimize the total fixed and variable costs
m.ModelSense = GRB.MINIMIZE
# Production constraints
# Note that the right-hand limit sets the production to zero if the plant
# is closed
m.addConstrs(
(transport.sum("*", p) <= capacity[p] * open[p] for p in plants), "Capacity"
)
# Using Python looping constructs, the preceding would be...
#
# for p in plants:
# m.addConstr(sum(transport[w][p] for w in warehouses)
# <= capacity[p] * open[p], "Capacity[%d]" % p)
# Demand constraints
demandConstr = m.addConstrs(
(transport.sum(w) == demand[w] for w in warehouses), "Demand"
)
# ... and the preceding would be ...
# for w in warehouses:
# m.addConstr(sum(transport[w][p] for p in plants) == demand[w],
# "Demand[%d]" % w)
# We constructed the base model, now we add 7 scenarios
#
# Scenario 0: Represents the base model, hence, no manipulations.
# Scenario 1: Manipulate the warehouses demands slightly (constraint right
# hand sides).
# Scenario 2: Double the warehouses demands (constraint right hand sides).
# Scenario 3: Manipulate the plant fixed costs (objective coefficients).
# Scenario 4: Manipulate the warehouses demands and fixed costs.
# Scenario 5: Force the plant with the largest fixed cost to stay open
# (variable bounds).
# Scenario 6: Force the plant with the smallest fixed cost to be closed
# (variable bounds).
m.NumScenarios = 7
# Scenario 0: Base model, hence, nothing to do except giving the scenario a
# name
m.Params.ScenarioNumber = 0
m.ScenNName = "Base model"
# Scenario 1: Increase the warehouse demands by 10%
m.Params.ScenarioNumber = 1
m.ScenNName = "Increased warehouse demands"
for w in warehouses:
demandConstr[w].ScenNRhs = demand[w] * 1.1
# Scenario 2: Double the warehouse demands
m.Params.ScenarioNumber = 2
m.ScenNName = "Double the warehouse demands"
for w in warehouses:
demandConstr[w].ScenNRhs = demand[w] * 2.0
# Scenario 3: Decrease the plant fixed costs by 5%
m.Params.ScenarioNumber = 3
m.ScenNName = "Decreased plant fixed costs"
for p in plants:
open[p].ScenNObj = fixedCosts[p] * 0.95
# Scenario 4: Combine scenario 1 and scenario 3
m.Params.ScenarioNumber = 4
m.ScenNName = "Increased warehouse demands and decreased plant fixed costs"
for w in warehouses:
demandConstr[w].ScenNRhs = demand[w] * 1.1
for p in plants:
open[p].ScenNObj = fixedCosts[p] * 0.95
# Scenario 5: Force the plant with the largest fixed cost to stay open
m.Params.ScenarioNumber = 5
m.ScenNName = "Force plant with largest fixed cost to stay open"
open[fixedCosts.index(maxFixed)].ScenNLB = 1.0
# Scenario 6: Force the plant with the smallest fixed cost to be closed
m.Params.ScenarioNumber = 6
m.ScenNName = "Force plant with smallest fixed cost to be closed"
open[fixedCosts.index(minFixed)].ScenNUB = 0.0
# Save model
m.write("multiscenario.lp")
# Guess at the starting point: close the plant with the highest fixed costs;
# open all others
# First open all plants
for p in plants:
open[p].Start = 1.0
# Now close the plant with the highest fixed cost
p = fixedCosts.index(maxFixed)
open[p].Start = 0.0
print(f"Initial guess: Closing plant {p}\n")
# Use barrier to solve root relaxation
m.Params.Method = 2
# Solve multi-scenario model
m.optimize()
# Print solution for each scenario
for s in range(m.NumScenarios):
# Set the scenario number to query the information for this scenario
m.Params.ScenarioNumber = s
print(f"\n\n------ Scenario {s} ({m.ScenNName})")
# Check if we found a feasible solution for this scenario
if m.ModelSense * m.ScenNObjVal >= GRB.INFINITY:
if m.ModelSense * m.ScenNObjBound >= GRB.INFINITY:
# Scenario was proven to be infeasible
print("\nINFEASIBLE")
else:
# We did not find any feasible solution - should not happen in
# this case, because we did not set any limit (like a time
# limit) on the optimization process
print("\nNO SOLUTION")
else:
print(f"\nTOTAL COSTS: {m.ScenNObjVal:g}")
print("SOLUTION:")
for p in plants:
if open[p].ScenNX > 0.5:
print(f"Plant {p} open")
for w in warehouses:
if transport[w, p].ScenNX > 0:
print(
f" Transport {transport[w, p].ScenNX:g} units to warehouse {w}"
)
else:
print(f"Plant {p} closed!")
# Print a summary table: for each scenario we add a single summary line
print("\n\nSummary: Closed plants depending on scenario\n")
print(f"{'':8} | {'Plant':>17} {'|':>13}")
tableStr = [f"{'Scenario':8} |"]
tableStr += [f"{p:>5}" for p in plants]
tableStr += [f"| {'Costs':>6} Name"]
print(" ".join(tableStr))
for s in range(m.NumScenarios):
# Set the scenario number to query the information for this scenario
m.Params.ScenarioNumber = s
tableStr = f"{s:<8} |"
# Check if we found a feasible solution for this scenario
if m.ModelSense * m.ScenNObjVal >= GRB.INFINITY:
if m.ModelSense * m.ScenNObjBound >= GRB.INFINITY:
# Scenario was proven to be infeasible
print(tableStr, f"{'infeasible':<30}| {'-':>6} {m.ScenNName:<}")
else:
# We did not find any feasible solution - should not happen in
# this case, because we did not set any limit (like a time
# limit) on the optimization process
print(tableStr, f"{'no solution found':<30}| {'-':>6} {m.ScenNName:<}")
else:
for p in plants:
if open[p].ScenNX > 0.5:
tableStr += f" {' ':>5}"
else:
tableStr += f" {'x':>5}"
print(tableStr, f"| {m.ScenNObjVal:6g} {m.ScenNName:<}")
