"""
Stochastic Benders - Sequential GAMS Loop (SPBENDERS1)
This example demonstrates a stochastic Benders implementation for the
simple transport example.
This is the first example of a sequence of stochastic Benders
implementations using various methods to solve the master and
subproblem.
This first example implements the stochastic Benders algorithm using
sequential solves of the master and subproblems in a GAMS loop.
Keywords: linear programming, stochastic Benders algorithm, transportation
problem
"""
from __future__ import annotations
import os
import pandas as pd
import gamspy.math as gams_math
from gamspy import Container
from gamspy import Equation
from gamspy import Model
from gamspy import Parameter
from gamspy import Sense
from gamspy import Set
from gamspy import Sum
from gamspy import Variable
def main():
m = Container(
system_directory=os.getenv("SYSTEM_DIRECTORY", None),
delayed_execution=int(os.getenv("DELAYED_EXECUTION", False)),
)
# Prepare data
cost = pd.DataFrame(
[
["f1", "d1", 2.49],
["f1", "d2", 5.21],
["f1", "d3", 3.76],
["f1", "d4", 4.85],
["f1", "d5", 2.07],
["f2", "d1", 1.46],
["f2", "d2", 2.54],
["f2", "d3", 1.83],
["f2", "d4", 1.86],
["f2", "d5", 4.76],
["f3", "d1", 3.26],
["f3", "d2", 3.08],
["f3", "d3", 2.60],
["f3", "d4", 3.76],
["f3", "d5", 4.45],
]
)
scenarios = pd.DataFrame(
[
["lo", "d1", 150],
["lo", "d2", 100],
["lo", "d3", 250],
["lo", "d4", 300],
["lo", "d5", 600],
["lo", "prob", 0.25],
["mid", "d1", 160],
["mid", "d2", 120],
["mid", "d3", 270],
["mid", "d4", 325],
["mid", "d5", 700],
["mid", "prob", 0.50],
["hi", "d1", 170],
["hi", "d2", 135],
["hi", "d3", 300],
["hi", "d4", 350],
["hi", "d5", 800],
["hi", "prob", 0.25],
]
)
cut_coefficients = pd.DataFrame(
[
[idx, f"d{center}", 0]
for idx in range(1, 26)
for center in range(1, 6)
]
)
# Set
i = Set(m, name="i", records=["f1", "f2", "f3"])
j = Set(m, name="j", records=["d1", "d2", "d3", "d4", "d5"])
s = Set(m, name="s", records=["lo", "mid", "hi"])
# Data
capacity = Parameter(
m,
name="capacity",
domain=[i],
records=pd.DataFrame([["f1", 500], ["f2", 450], ["f3", 650]]),
)
demand = Parameter(
m,
name="demand",
domain=[j],
records=pd.DataFrame(
[["d1", 160], ["d2", 120], ["d3", 270], ["d4", 325], ["d5", 700]]
),
)
prodcost = Parameter(m, name="prodcost", records=14)
price = Parameter(m, name="price", records=24)
wastecost = Parameter(m, name="wastecost", records=4)
transcost = Parameter(m, name="transcost", domain=[i, j], records=cost)
ScenarioData = Parameter(
m, name="scenariodata", domain=[s, "*"], records=scenarios
)
# Set
iter = Set(m, name="iter", records=[f"{idx}" for idx in range(1, 26)])
itActive = Set(m, name="itActive", domain=[iter])
# Parameter
cutconst = Parameter(
m,
name="cutconst",
domain=[iter],
records=pd.DataFrame([[f"{idx}", 0] for idx in range(1, 26)]),
)
cutcoeff = Parameter(
m, name="cutcoeff", domain=[iter, j], records=cut_coefficients
)
# Variable
ship = Variable(m, name="ship", domain=[i, j], type="Positive")
product = Variable(m, name="product", domain=[i])
received = Variable(m, name="received", domain=[j])
zmaster = Variable(m, name="zmaster")
theta = Variable(m, name="theta")
# Equation
masterobj = Equation(m, name="masterobj")
production = Equation(m, name="production", domain=[i])
receive = Equation(m, name="receive", domain=[j])
optcut = Equation(m, name="optcut", domain=[iter])
masterobj[...] = zmaster == theta - Sum(
(i, j), transcost[i, j] * ship[i, j]
) - Sum(i, prodcost * product[i])
receive[j] = received[j] == Sum(i, ship[i, j])
production[i] = product[i] == Sum(j, ship[i, j])
optcut[itActive] = theta <= cutconst[itActive] + Sum(
j, cutcoeff[itActive, j] * received[j]
)
product.up[i] = capacity[i]
masterproblem = Model(
m,
name="masterproblem",
equations=m.getEquations(),
problem="LP",
sense=Sense.MAX,
objective=zmaster,
)
# Variable
sales = Variable(m, name="sales", domain=[j], type="Positive")
waste = Variable(m, name="waste", domain=[j], type="Positive")
zsub = Variable(m, name="zsub")
# Equation
subobj = Equation(m, name="subobj")
selling = Equation(m, name="selling", domain=[j])
market = Equation(m, name="market", domain=[j])
subobj[...] = zsub == Sum(j, price * sales[j]) - Sum(
j, wastecost * waste[j]
)
selling[j] = sales[j] + waste[j] == received.l[j]
market[j] = sales[j] <= demand[j]
subproblem = Model(
m,
name="subproblem",
equations=[subobj, selling, market],
problem="LP",
sense=Sense.MAX,
objective=zsub,
)
# Scalar
rgap = Parameter(m, name="rgap", records=0)
lowerBound = Parameter(m, name="lowerBound", records=float("-inf"))
upperBound = Parameter(m, name="upperBound", records=float("inf"))
objMaster = Parameter(m, name="objMaster", records=0)
objSub = Parameter(m, name="objSub", records=0)
rtol = 0.001
received.l[j] = 0
for iteration, _ in iter.records.itertuples(index=False):
objSub[...] = 0
for scenario, _ in s.records.itertuples(index=False):
demand[j] = ScenarioData[scenario, j]
subproblem.solve()
objSub[...] = objSub + ScenarioData[scenario, "prob"] * zsub.l
cutconst[iteration] = cutconst[iteration] + ScenarioData[
scenario, "prob"
] * Sum(j, market.m[j] * demand[j])
cutcoeff[iteration, j] = (
cutcoeff[iteration, j]
+ ScenarioData[scenario, "prob"] * selling.m[j]
)
itActive[iteration] = True
if (
lowerBound.records.values[0][0]
< objMaster.records.values[0][0] + objSub.records.values[0][0]
):
lowerBound[...] = objMaster + objSub
rgap[...] = (upperBound - lowerBound) / (1 + gams_math.abs(upperBound))
if rgap.records.values[0][0] < rtol:
break
masterproblem.solve()
upperBound.setRecords(zmaster.records["level"])
objMaster.setRecords(zmaster.records["level"] - theta.records["level"])
if __name__ == "__main__":
main()
