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Transportation Problem.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
from pyomo.core.base import ConcreteModel
from pyomo.environ import *
import math
import pandas as pd
# Creation of a Concrete Model
model = ConcreteModel()
## Define Sets ##
# Sets
# i Manufacturers
# j Customers
# k Products
model.i = Set(initialize=range(0, 13), doc='Manufacturers')
model.j = Set(initialize=range(0, 32), doc='Customers')
model.s = Set(initialize=range(0, 22), doc='Suppliers')
model.k = Set(initialize=['A', 'B'], doc='Sources')
model.sub_a = Set(initialize=range(0, 8), doc='Items for Product A')
model.sub_b = Set(initialize=range(0, 7), doc='Items for Product B')
## Define Parameters ##
# Parameters
# Ri Running costs for manufacturer
# Dij Distance from manufacturer to customer
# Tk Transport cost of product k
# CDjk Demand of product k for customer j
# Pk Selling price of k
# TCk Truck capacity for k
distances = pd.read_csv("distances.csv", header=None).T.to_dict()
D = {}
for j in range(0, 32):
for i in range(0, 13):
D[(i, j)] = distances[j][i]
model.D = Param(model.i, model.j, initialize=D, doc='Distances')
demands = pd.read_csv("demands.csv", header=None).T.to_dict()
CD = {}
for j in range(0, 32):
for k in ['A', 'B']:
if k == 'A':
CD[(j, k)] = demands[j][2]*1000
if k == 'B':
CD[(j, k)] = demands[j][5]*1000
model.CD = Param(model.j, model.k, initialize=CD, doc='Demands')
MC = {
0: 1404000,
1: 1452000,
2: 1476000,
3: 1482000,
4: 1500000,
5: 1488000,
6: 1434000,
7: 1356000,
8: 1464000,
9: 1470000,
10: 1458000,
11: 1392000,
12: 1392000
}
model.MC = Param(model.i, initialize=MC, doc='Running Costs')
CA = {}
capacities_a = pd.read_csv("capacity-a.csv", header=None).T.to_dict()
for s in range(0, 22):
for c in range(0, 8):
if capacities_a[s][c] != '-':
CA[(s, c)] = int(capacities_a[s][c])*1000
else:
CA[(s, c)] = 0
model.CA = Param(model.s, model.sub_a, initialize=CA, doc='Sub Item Capacities for A')
CB = {}
capacities_b = pd.read_csv("capacity-b.csv", header=None).T.to_dict()
for s in range(0, 22):
for c in range(0, 7):
if capacities_b[s][c] != '-':
CB[(s, c)] = int(capacities_b[s][c])*1000
else:
CB[(s, c)] = 0
model.CB = Param(model.s, model.sub_b, initialize=CB, doc='Sub Item Capacities for B')
PA = {}
pricing_a = pd.read_csv("pricing-a.csv", header=None).T.to_dict()
for s in range(0, 22):
for c in range(0, 8):
if pricing_a[s][c] != '-':
PA[(s, c)] = float(pricing_a[s][c])
else:
PA[(s, c)] = 0
model.PA = Param(model.s, model.sub_a, initialize=PA, doc='Sub Item Pricing for A')
PB = {}
pricing_b = pd.read_csv("pricing-b.csv", header=None).T.to_dict()
for s in range(0, 22):
for c in range(0, 7):
if pricing_b[s][c] != '-':
PB[(s, c)] = float(pricing_b[s][c])
else:
PB[(s, c)] = 0
model.PB = Param(model.s, model.sub_b, initialize=PB, doc='Sub Item Pricing for B')
model.T = Param(model.k, initialize={'A': 0.0015, 'B': 0.0020}, doc='Transport Costs')
model.TC = Param(model.k, initialize={'A': 50000, 'B': 30000}, doc='Truck Costs')
model.P = Param(model.k, initialize={'A': 5.2, 'B': 6.0}, doc='Product Price')
model.R = Param(model.k, initialize={'A': 35, 'B': 45}, doc="Hours of Work")
## Define variables ##
model.X = Var(model.i, model.j, model.k, within=NonNegativeIntegers, doc="Product k flow from i to j")
model.M = Var(model.i, within=Binary, doc="Manufacturing plant i exists")
model.NT = Var(model.i, model.j, within=NonNegativeIntegers, doc="Trucks Required")
model.MSA = Var(model.s, model.i, model.sub_a, within=NonNegativeIntegers, doc="Sub Item A flow from s to i")
model.MSB = Var(model.s, model.i, model.sub_b, within=NonNegativeIntegers, doc="Sub Item B flow from s to i")
## Define constraints ##
def Demand(model, j, k):
return sum(model.X[i, j, k] for i in model.i) <= model.CD[j, k]
model.Demand = Constraint(model.j, model.k, rule=Demand, doc='Supply Demand')
def Capacity(model, i):
return sum(model.X[i, j, k]*(model.R[k]/1000) for j in model.j for k in model.k) <= 25000*model.M[i]
model.Capacity = Constraint(model.i, rule=Capacity, doc='Manufacturer Capacity')
def Trucks(model, i, j):
return model.NT[i, j] >= ((5/3)*model.X[i, j, 'A'] + model.X[i, j, 'B'])/30000
model.Trucks = Constraint(model.i, model.j, rule=Trucks, doc='Trucks Required')
def SubDemandA(model, i, sub_a):
return sum(model.MSA[s, i, sub_a] for s in model.s) == sum(model.X[i, j, 'A'] for j in model.j)
model.SubDemandA = Constraint(model.i, model.sub_a, rule=SubDemandA, doc='Sub Items for A')
def SubDemandB(model, i, sub_b):
return sum(model.MSB[s, i, sub_b] for s in model.s) == sum(model.X[i, j, 'B'] for j in model.j)
model.SubDemandB = Constraint(model.i, model.sub_b, rule=SubDemandB, doc='Sub Items for B')
def SupplierCapacityA(model, s, sub_a):
return sum(model.MSA[s, i, sub_a] for i in model.i) <= model.CA[s, sub_a]
model.SupplierCapacityA = Constraint(model.s, model.sub_a, rule=SupplierCapacityA, doc='Supplier Capacities for A')
def SupplierCapacityB(model, s, sub_b):
return sum(model.MSB[s, i, sub_b] for i in model.i) <= model.CB[s, sub_b]
model.SupplierCapacityB = Constraint(model.s, model.sub_b, rule=SupplierCapacityB, doc='Supplier Capacities for B')
## Define Objective and solve ##
def objectiveRule(model):
return sum(sum(model.X[i, j, 'A']*(model.P['A'] - model.D[i, j]*model.T['A']) + model.X[i, j, 'B']*(model.P['B'] - model.D[i, j]*model.T['B']) - model.NT[i, j]*25000 for j in model.j) - model.M[i]*model.MC[i] for i in model.i) - sum(sum(sum(model.MSA[s, i, sub_a]*model.PA[s, sub_a] for sub_a in model.sub_a) for i in model.i) for s in model.s) - sum(sum(sum(model.MSB[s, i, sub_b]*model.PB[s, sub_b] for sub_b in model.sub_b) for i in model.i) for s in model.s)
model.objectiveRule = Objective(rule=objectiveRule, sense=maximize, doc='Define Objective Function')
def pyomo_postprocess(options=None, instance=None, results=None):
model.M.display()
model.X.display()
model.NT.display()
model.MSA.display()
model.MSB.display()
with open('Manufacturer.txt', 'w') as f:
for key, value in instance.M._data.items():
if value._value > 0:
f.write('%s,%s\n' % (key, value._value))
with open('Flow of Goods.txt', 'w') as f:
for key, value in instance.X._data.items():
if value._value > 0:
f.write('%s,%s,%s,%s\n' % (key[0], key[1], key[2], value._value))
with open('Number Of Trucks.txt', 'w') as f:
for key, value in instance.NT._data.items():
if value._value > 0:
f.write('%s,%s,%s\n' % (key[0], key[1], value._value))
with open('Supplier Flows - A.txt', 'w') as f:
for key, value in instance.MSA._data.items():
if value._value > 0:
f.write('%s,%s,%s,%s\n' % (key[0], key[1], key[2], value._value))
with open('Supplier Flows - B.txt', 'w') as f:
for key, value in instance.MSB._data.items():
if value._value > 0:
f.write('%s,%s,%s,%s\n' % (key[0], key[1], key[2], value._value))
if __name__ == '__main__':
# This emulates what the pyomo command-line tools does
from pyomo.opt import SolverFactory
import pyomo.environ
opt = SolverFactory("gurobi")
results = opt.solve(model)
# sends results to stdout
results.write()
print("\nWriting Solution\n" + '-' * 60)
pyomo_postprocess(None, model, results)
print("Complete")