Operations Research Using Python is the application of statistics, mathematical models, and algorithms to support decision-making is encompassed in Operations Research (OR), especially for the enhancement of frameworks, resource allocation, or procedures. For operations research, Python is considered as an ideal tool because of having a wide range of frameworks and libraries. We have all the needed tools to get your work done right. As a means to employ Python for different factors of operations research, we provide an instruction in a detailed way:
from pulp import LpMaximize, LpProblem, LpVariable
# Define the problem
model = LpProblem(name=”simple-maximization”, sense=LpMaximize)
# Define decision variables
x = LpVariable(name=”x”, lowBound=0)
y = LpVariable(name=”y”, lowBound=0)
# Define the objective function
model += 2 * x + 3 * y, “Objective”
# Define the constraints
model += 2 * x + y <= 20, “constraint_1”
model += 4 * x + 3 * y <= 36, “constraint_2”
model += x >= 0, “constraint_3”
model += y >= 0, “constraint_4″
# Solve the problem
model.solve()
print(f”Optimal value: {model.objective.value()}”)
print(f”x: {x.value()}, y: {y.value()}”)
from pulp import LpMaximize, LpProblem, LpVariable
# Define the problem
model = LpProblem(name=”integer-programming”, sense=LpMaximize)
# Define decision variables (integer)
x = LpVariable(name=”x”, lowBound=0, cat=’Integer’)
y = LpVariable(name=”y”, lowBound=0, cat=’Integer’)
# Define the objective function
model += 2 * x + 3 * y, “Objective”
# Define the constraints
model += 2 * x + y <= 20, “constraint_1”
model += 4 * x + 3 * y <= 36, “constraint_2″
# Solve the problem
model.solve()
print(f”Optimal value: {model.objective.value()}”)
print(f”x: {x.value()}, y: {y.value()}”)
import networkx as nx
# Create a directed graph
G = nx.DiGraph()
# Add edges along with capacities
G.add_edge(‘A’, ‘B’, capacity=15.0)
G.add_edge(‘A’, ‘C’, capacity=10.0)
G.add_edge(‘B’, ‘D’, capacity=10.0)
G.add_edge(‘C’, ‘D’, capacity=10.0)
# Compute the maximum flow between A and D
flow_value, flow_dict = nx.maximum_flow(G, ‘A’, ‘D’)
print(f”Maximum flow: {flow_value}”)
print(f”Flow per edge: {flow_dict}”)
from ortools.linear_solver import pywraplp
# Create the solver
solver = pywraplp.Solver.CreateSolver(‘SCIP’)
# Variables: x1, x2
x1 = solver.IntVar(0, 10, ‘x1’)
x2 = solver.IntVar(0, 10, ‘x2′)
# Constraints
solver.Add(2 * x1 + x2 <= 14)
solver.Add(4 * x1 – 5 * x2 >= 5)
solver.Add(-x1 + x2 <= 3)
# Objective function: maximize x1 + 2 * x2
solver.Maximize(x1 + 2 * x2)
# Solve
status = solver.Solve()
if status == pywraplp.Solver.OPTIMAL:
print(f’Solution: x1 = {x1.solution_value()}, x2 = {x2.solution_value()}’)
else:
print(‘No optimal solution found.’)
import simpy
import random
def customer(env, name, server, service_time):
yield env.timeout(random.expovariate(1.0/service_time))
print(f”{name} finished service at {env.now}”)
def setup(env, num_servers, service_time):
server = simpy.Resource(env, num_servers)
for i in range(5):
env.process(customer(env, f”Customer {i+1}”, server, service_time))
env = simpy.Environment()
env.process(setup(env, 1, 10))
env.run()
import numpy as np
from scipy.optimize import linprog
# Demand forecast
demand = np.array([100, 150, 200])
# Cost parameters
holding_cost = 1
shortage_cost = 5
# Inventory optimization using linear programming
c = [holding_cost, shortage_cost]
A = [[1, -1], [-1, 1]]
b = demand
x_bounds = (0, None)
res = linprog(c, A_ub=A, b_ub=b, bounds=[x_bounds, x_bounds])
print(res)
from decisiontree import DecisionTreeClassifier
# Create a decision tree classifier and train it
X = [[0, 0], [1, 1]]
y = [0, 1]
clf = DecisionTreeClassifier()
clf = clf.fit(X, y)
# Predict
print(clf.predict([[2., 2.]]))
import nashpy as nash
# Define the payoff matrices for both players
A = [[3, 1], [0, 2]]
B = [[3, 0], [1, 2]]
# Create the game
game = nash.Game(A, B)
# Find Nash equilibrium
equilibria = game.support_enumeration()
for eq in equilibria:
print(eq)
import simpy
def customer(env, name, counter, service_time):
yield env.timeout(service_time)
print(f”{name} finished at {env.now}”)
def setup(env, num_servers, service_time):
counter = simpy.Resource(env, num_servers)
for i in range(5):
env.process(customer(env, f”Customer {i+1}”, counter, service_time))
env = simpy.Environment()
env.process(setup(env, 1, 10))
env.run()
One of the important factors of operations research is supply chain optimization. In order to resolve intricate supply chain issues, various tools are offered by Python. For supply chain optimization, we provide an instance which utilizes Google OR-Tools:
from ortools.linear_solver import pywraplp
# Create the solver
solver = pywraplp.Solver.CreateSolver(‘SCIP’)
# Define decision variables
x1 = solver.IntVar(0, solver.infinity(), ‘x1’)
x2 = solver.IntVar(0, solver.infinity(), ‘x2′)
# Define the constraints
solver.Add(2 * x1 + x2 <= 100)
solver.Add(x1 + 3 * x2 <= 90)
# Define the objective function: maximize profit
solver.Maximize(3 * x1 + 2 * x2)
# Solve the problem
status = solver.Solve()
if status == pywraplp.Solver.OPTIMAL:
print(f’Optimal solution found:’)
print(f’x1 = {x1.solution_value()}’)
print(f’x2 = {x2.solution_value()}’)
print(f’Maximum profit = {solver.Objective().Value()}’)
else:
print(‘No optimal solution found.’)
The amounts of two products to manufacture are depicted as x1 and x2 in this instance. By demonstrating boundaries in resources such as materials or workforce, it includes the conditions. Profit enhancement is considered as the objective function.
In supply chain and operations research issues, Python’s PuLP and Google OR-Tools libraries are employed in an extensive manner. For different optimization issues, they provide robust solvers and adaptability.
Operations Research (OR) is an efficient domain which assists in the process of making decisions. By encompassing different fields and techniques, we suggest a collection of 150 OR-based topics, which are highly appropriate to investigate through Python:
To assist you to utilize Python for diverse Operations research factors, we offered an in-depth instruction, including Python tools and instances. Relevant to different fields and techniques, several operations research topics are recommended by us, which could be investigated with the aid of Python.
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