import numpy as np
from scipy.optimize import linprog

def optimize_pipeline_flow(pipeline_network, supply, demand, capacities, costs):
    """
    Optimize flow through pipeline network

    Parameters:
    - pipeline_network: dict of {(source, destination): pipeline_id}
    - supply: dict of {source: available_volume}
    - demand: dict of {destination: required_volume}
    - capacities: dict of {pipeline_id: max_flow_rate}
    - costs: dict of {pipeline_id: cost_per_barrel}
    """
    from pulp import *

    # Create problem
    prob = LpProblem("Pipeline_Flow", LpMinimize)

    # Decision variables: flow through each pipeline
    flows = {}
    for (src, dest), pipe_id in pipeline_network.items():
        flows[pipe_id] = LpVariable(
            f"Flow_{src}_to_{dest}",
            lowBound=0,
            upBound=capacities[pipe_id]
        )

    # Objective: minimize transportation cost
    prob += lpSum([costs[pipe] * flows[pipe]
                   for pipe in flows])

    # Constraints: supply limits
    for source, max_supply in supply.items():
        outbound = [flows[pipe_id]
                   for (src, dest), pipe_id in pipeline_network.items()
                   if src == source]
        if outbound:
            prob += lpSum(outbound) <= max_supply

    # Constraints: demand satisfaction
    for destination, required in demand.items():
        inbound = [flows[pipe_id]
                  for (src, dest), pipe_id in pipeline_network.items()
                  if dest == destination]
        if inbound:
            prob += lpSum(inbound) >= required

    # Solve
    prob.solve(PULP_CBC_CMD(msg=0))

    return {
        'status': LpStatus[prob.status],
        'total_cost': value(prob.objective),
        'flows': {pipe: flows[pipe].varValue for pipe in flows}
    }

**Batching & Scheduling:**
- Sequential batching (different products)
- Contamination management
- Batch tracking and quality control

```python
def batch_schedule_pipeline(batches, pipeline_capacity, transit_times):
    """
    Schedule multiple product batches through pipeline

    Parameters:
    - batches: list of {product, volume, source, destination, priority}
    - pipeline_capacity: barrels/hour
    - transit_times: dict of {(source, destination): hours}
    """
    from collections import deque

    schedule = []
    current_time = 0

    # Sort by priority and volume
    sorted_batches = sorted(batches,
                           key=lambda x: (x['priority'], -x['volume']))

    for batch in sorted_batches:
        # Calculate transit time
        transit = transit_times.get(
            (batch['source'], batch['destination']), 24
        )

        # Calculate pump time
        pump_time = batch['volume'] / pipeline_capacity

        # Schedule
        schedule.append({
            'batch_id': batch['product'],
            'start_time': current_time,
            'pump_hours': pump_time,
            'arrival_time': current_time + pump_time + transit,
            'volume': batch['volume']
        })

        current_time += pump_time

    return schedule

undefined

def optimize_tanker_fleet(shipments, vessels, ports, costs):
    """
    Optimize tanker routing and scheduling

    Parameters:
    - shipments: list of {origin, destination, volume, earliest, latest}
    - vessels: list of {vessel_id, capacity, speed, position, available_time}
    - ports: dict of {port: {lat, lon}}
    - costs: dict with fuel_cost, charter_rate, port_fees
    """
    import numpy as np
    from pulp import *

    prob = LpProblem("Tanker_Routing", LpMinimize)

    # Variables: assign vessel v to shipment s
    x = {}
    for v, vessel in enumerate(vessels):
        for s, shipment in enumerate(shipments):
            if vessel['capacity'] >= shipment['volume']:
                x[v, s] = LpVariable(f"Assign_{v}_{s}", cat='Binary')

    # Objective: minimize total cost
    total_cost = []

    for (v, s), var in x.items():
        vessel = vessels[v]
        shipment = shipments[s]

        # Distance calculation (simplified)
        distance = calculate_sea_distance(
            ports[shipment['origin']],
            ports[shipment['destination']]
        )

        # Voyage cost
        voyage_time = distance / vessel['speed']  # hours
        fuel_cost = costs['fuel_cost'] * distance * vessel['capacity'] * 0.001
        charter_cost = costs['charter_rate'] * voyage_time
        port_cost = costs['port_fees'] * 2  # origin + destination

        total_cost.append((fuel_cost + charter_cost + port_cost) * var)

    prob += lpSum(total_cost)

    # Constraints: each shipment covered once
    for s in range(len(shipments)):
        prob += lpSum([x[v, s] for v, _ in x.keys() if _ == s]) == 1

    # Constraints: vessel availability
    for v in range(len(vessels)):
        assignments = [x[v, s] for _, s in x.keys() if _ == v]
        if assignments:
            prob += lpSum(assignments) <= 1  # One voyage at a time

    prob.solve(PULP_CBC_CMD(msg=0))

    return {
        'status': LpStatus[prob.status],
        'total_cost': value(prob.objective),
        'assignments': [(v, s) for (v, s) in x if x[v, s].varValue > 0.5]
    }

def calculate_sea_distance(port1, port2):
    """Calculate great circle distance between ports"""
    from math import radians, sin, cos, sqrt, atan2

    lat1, lon1 = radians(port1['lat']), radians(port1['lon'])
    lat2, lon2 = radians(port2['lat']), radians(port2['lon'])

    dlat = lat2 - lat1
    dlon = lon2 - lon1

    a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
    c = 2 * atan2(sqrt(a), sqrt(1-a))

    return 3959 * c  # miles

def optimize_truck_routes(deliveries, depot_location, truck_capacity, max_hours):
    """
    Vehicle routing for fuel delivery trucks

    Uses Clarke-Wright savings algorithm
    """
    import numpy as np

    # Calculate distances
    def distance(loc1, loc2):
        return np.sqrt((loc1[0] - loc2[0])**2 + (loc1[1] - loc2[1])**2)

    # Calculate savings for combining routes
    savings = []
    n = len(deliveries)

    for i in range(n):
        for j in range(i+1, n):
            save = (distance(depot_location, deliveries[i]['location']) +
                   distance(depot_location, deliveries[j]['location']) -
                   distance(deliveries[i]['location'], deliveries[j]['location']))
            savings.append((save, i, j))

    # Sort by savings (descending)
    savings.sort(reverse=True)

    # Build routes
    routes = [[i] for i in range(n)]
    route_loads = [deliveries[i]['volume'] for i in range(n)]

    for save, i, j in savings:
        # Find routes containing i and j
        route_i = next((r for r in routes if i in r), None)
        route_j = next((r for r in routes if j in r), None)

        if route_i != route_j and route_i and route_j:
            # Check if merge is feasible
            combined_load = route_loads[routes.index(route_i)] + \
                           route_loads[routes.index(route_j)]

            if combined_load <= truck_capacity:
                # Merge routes
                route_i.extend(route_j)
                route_loads[routes.index(route_i)] = combined_load
                routes.remove(route_j)

    return {
        'num_trucks': len(routes),
        'routes': routes,
        'utilization': [route_loads[routes.index(r)] / truck_capacity
                       for r in routes]
    }

import numpy as np
import pandas as pd

class EnergyInventoryOptimizer:
    """
    Optimize inventory levels for energy products
    considering price volatility and storage costs
    """

    def __init__(self, storage_capacity, storage_cost, initial_inventory=0):
        self.storage_capacity = storage_capacity
        self.storage_cost = storage_cost  # $/barrel/month
        self.inventory = initial_inventory

    def optimize_inventory_policy(self, demand_forecast, price_forecast,
                                  horizon=12):
        """
        Determine optimal inventory levels over planning horizon

        Uses dynamic programming approach
        """
        from pulp import *

        prob = LpProblem("Inventory_Optimization", LpMinimize)

        # Variables
        inventory = {}
        purchases = {}
        sales = {}

        for t in range(horizon):
            inventory[t] = LpVariable(f"Inventory_{t}",
                                     lowBound=0,
                                     upBound=self.storage_capacity)
            purchases[t] = LpVariable(f"Purchase_{t}", lowBound=0)
            sales[t] = LpVariable(f"Sales_{t}", lowBound=0)

        # Objective: maximize profit - storage costs
        total_revenue = lpSum([sales[t] * price_forecast[t]
                              for t in range(horizon)])
        total_purchase = lpSum([purchases[t] * price_forecast[t]
                               for t in range(horizon)])
        total_storage = lpSum([inventory[t] * self.storage_cost
                              for t in range(horizon)])

        prob += total_revenue - total_purchase - total_storage

        # Constraints: inventory balance
        for t in range(horizon):
            if t == 0:
                prev_inv = self.inventory
            else:
                prev_inv = inventory[t-1]

            prob += inventory[t] == prev_inv + purchases[t] - sales[t]

        # Constraints: meet demand
        for t in range(horizon):
            prob += sales[t] >= demand_forecast[t]

        # Solve
        prob.solve(PULP_CBC_CMD(msg=0))

        return {
            'status': LpStatus[prob.status],
            'profit': value(prob.objective),
            'inventory_levels': [inventory[t].varValue for t in range(horizon)],
            'purchase_plan': [purchases[t].varValue for t in range(horizon)],
            'sales_plan': [sales[t].varValue for t in range(horizon)]
        }

    def calculate_safety_stock(self, avg_demand, demand_std, lead_time,
                               service_level=0.95):
        """
        Calculate safety stock for energy products

        Uses standard normal distribution
        """
        from scipy.stats import norm

        z_score = norm.ppf(service_level)
        safety_stock = z_score * demand_std * np.sqrt(lead_time)

        reorder_point = (avg_demand * lead_time) + safety_stock

        return {
            'safety_stock': safety_stock,
            'reorder_point': reorder_point,
            'service_level': service_level
        }

---

import pandas as pd
from statsmodels.tsa.holtwinters import ExponentialSmoothing
from prophet import Prophet

def forecast_energy_demand(historical_data, external_factors, horizon=12):
    """
    Forecast energy demand using multiple methods

    Parameters:
    - historical_data: DataFrame with date and demand
    - external_factors: DataFrame with weather, economic data
    - horizon: forecast periods
    """

    # Method 1: Holt-Winters for seasonal data
    hw_model = ExponentialSmoothing(
        historical_data['demand'],
        seasonal_periods=12,
        trend='add',
        seasonal='multiplicative'
    )
    hw_fit = hw_model.fit()
    hw_forecast = hw_fit.forecast(steps=horizon)

    # Method 2: Prophet with external regressors
    prophet_df = historical_data.copy()
    prophet_df.columns = ['ds', 'y']

    model = Prophet(yearly_seasonality=True)

    # Add external factors
    for col in external_factors.columns:
        if col != 'date':
            prophet_df[col] = external_factors[col]
            model.add_regressor(col)

    model.fit(prophet_df)

    # Create future dataframe
    future = model.make_future_dataframe(periods=horizon, freq='M')
    # Would need to add future external factors here

    prophet_forecast = model.predict(future)

    # Ensemble: weighted average
    final_forecast = 0.5 * hw_forecast + 0.5 * prophet_forecast['yhat'][-horizon:]

    return {
        'hw_forecast': hw_forecast,
        'prophet_forecast': prophet_forecast['yhat'][-horizon:],
        'ensemble_forecast': final_forecast,
        'confidence_intervals': prophet_forecast[['yhat_lower', 'yhat_upper']][-horizon:]
    }

def calculate_hedge_ratio(spot_prices, futures_prices):
    """
    Calculate optimal hedge ratio using minimum variance

    Hedge ratio = Cov(ΔS, ΔF) / Var(ΔF)
    """
    import numpy as np

    # Calculate returns
    spot_returns = np.diff(spot_prices) / spot_prices[:-1]
    futures_returns = np.diff(futures_prices) / futures_prices[:-1]

    # Calculate hedge ratio
    covariance = np.cov(spot_returns, futures_returns)[0, 1]
    variance_futures = np.var(futures_returns)

    hedge_ratio = covariance / variance_futures

    return {
        'hedge_ratio': hedge_ratio,
        'correlation': np.corrcoef(spot_returns, futures_returns)[0, 1],
        'effectiveness': 1 - np.var(spot_returns - hedge_ratio * futures_returns) / np.var(spot_returns)
    }

def supply_chain_resilience_score(network_data):
    """
    Calculate supply chain resilience metrics
    """
    import networkx as nx

    # Create network graph
    G = nx.DiGraph()

    for edge in network_data['connections']:
        G.add_edge(edge['from'], edge['to'],
                  capacity=edge['capacity'],
                  reliability=edge['reliability'])

    metrics = {
        # Redundancy: multiple paths
        'redundancy': nx.node_connectivity(G.to_undirected()),

        # Centrality: identify critical nodes
        'critical_nodes': nx.betweenness_centrality(G),

        # Robustness: network efficiency after node removal
        'robustness': calculate_network_robustness(G)
    }

    return metrics

def calculate_network_robustness(G):
    """Simulate node failures and measure impact"""
    import random

    original_efficiency = nx.global_efficiency(G)

    robustness_scores = []
    nodes = list(G.nodes())

    for _ in range(100):  # Monte Carlo simulation
        # Randomly remove nodes
        num_failures = random.randint(1, len(nodes) // 4)
        failed_nodes = random.sample(nodes, num_failures)

        G_temp = G.copy()
        G_temp.remove_nodes_from(failed_nodes)

        if len(G_temp.nodes()) > 0:
            efficiency = nx.global_efficiency(G_temp)
            robustness_scores.append(efficiency / original_efficiency)

    return np.mean(robustness_scores)

def calculate_emissions(transportation_data, emission_factors):
    """
    Calculate CO2 emissions from energy logistics

    Parameters:
    - transportation_data: list of {mode, distance, volume}
    - emission_factors: dict of {mode: kg_CO2_per_barrel_mile}
    """

    total_emissions = 0

    for transport in transportation_data:
        mode = transport['mode']
        distance = transport['distance']
        volume = transport['volume']

        emissions = emission_factors.get(mode, 0) * distance * volume
        total_emissions += emissions

    return {
        'total_emissions_kg': total_emissions,
        'total_emissions_tons': total_emissions / 1000,
        'emissions_per_barrel': total_emissions / sum(t['volume'] for t in transportation_data)
    }

undefined