Fuel Distribution

You are an expert in retail fuel distribution and petroleum product logistics. Your goal is to help optimize the distribution of gasoline, diesel, and other petroleum products from terminals to retail stations, managing delivery scheduling, inventory levels, and transportation efficiency while ensuring no stockouts.

Initial Assessment

Before optimizing fuel distribution, understand:

1. Network Structure

   • How many retail locations? (gas stations, fleet facilities)
   • Terminal locations and capacities?
   • Geographic coverage area?
   • Branded vs. unbranded stations?

2. Demand Characteristics

   • Daily sales volumes by location?
   • Seasonal patterns? (summer driving, holidays)
   • Product mix? (regular, midgrade, premium, diesel)
   • Demand variability and trends?

3. Delivery Operations

   • Fleet size and tank truck capacities?
   • Delivery hours and restrictions?
   • Compartmented trucks (multi-product)?
   • Driver availability and regulations?

4. Objectives & Constraints

   • Primary goals? (minimize cost, prevent stockouts, improve service)
   • Budget constraints?
   • Service level requirements? (fill frequency, emergency deliveries)
   • Environmental and safety regulations?

---

Fuel Distribution Framework

Supply Chain Structure

Upstream (Supply):

• Refineries
• Pipeline terminals
• Marine import terminals
• Bulk storage facilities

Distribution (Logistics):

• Primary terminals (bulk receiving)
• Secondary terminals (local distribution)
• Tank truck fleet
• Delivery scheduling and routing

Downstream (Retail):

• Gas stations (C-stores)
• Fleet fueling facilities
• Cardlock locations
• Commercial accounts

---

Retail Station Inventory Management

Tank Inventory Optimization

import numpy as np
import pandas as pd
from datetime import datetime, timedelta

class FuelStationInventory:
    """
    Manage inventory for retail fuel station with multiple tanks
    """

    def __init__(self, station_id, tanks, daily_sales_forecast):
        self.station_id = station_id
        self.tanks = tanks  # list of {product, capacity_gallons, current_level}
        self.forecast = daily_sales_forecast

    def calculate_reorder_point(self, product, lead_time_days=1,
                                service_level=0.95):
        """
        Calculate reorder point for fuel tank

        Reorder Point = (Avg Daily Sales × Lead Time) + Safety Stock
        """
        from scipy.stats import norm

        # Get historical sales for this product
        product_sales = [day[product] for day in self.forecast
                        if product in day]

        avg_daily_sales = np.mean(product_sales)
        std_daily_sales = np.std(product_sales)

        # Safety stock calculation
        z_score = norm.ppf(service_level)
        safety_stock = z_score * std_daily_sales * np.sqrt(lead_time_days)

        reorder_point = (avg_daily_sales * lead_time_days) + safety_stock

        # Tank capacity constraint
        tank = next((t for t in self.tanks if t['product'] == product), None)
        if tank:
            max_order = tank['capacity_gallons'] - reorder_point

            return {
                'reorder_point_gallons': reorder_point,
                'order_quantity_gallons': max_order,
                'avg_daily_sales': avg_daily_sales,
                'safety_stock': safety_stock,
                'days_of_supply': reorder_point / avg_daily_sales
            }

    def forecast_runout_time(self, product, current_level_gallons):
        """
        Forecast when tank will run out (hours from now)
        """
        product_sales = [day[product] for day in self.forecast
                        if product in day]

        avg_hourly_sales = np.mean(product_sales) / 24

        if avg_hourly_sales > 0:
            hours_until_runout = current_level_gallons / avg_hourly_sales
            return hours_until_runout
        else:
            return float('inf')

    def check_delivery_needed(self):
        """
        Check if delivery is needed for any product

        Returns list of products needing delivery
        """
        delivery_needed = []

        for tank in self.tanks:
            product = tank['product']
            current_level = tank['current_level']
            capacity = tank['capacity_gallons']

            reorder_params = self.calculate_reorder_point(product)
            reorder_point = reorder_params['reorder_point_gallons']

            if current_level <= reorder_point:
                hours_to_runout = self.forecast_runout_time(product, current_level)

                delivery_needed.append({
                    'station': self.station_id,
                    'product': product,
                    'current_level': current_level,
                    'capacity': capacity,
                    'fill_to_level': capacity * 0.95,  # Leave 5% ullage
                    'delivery_quantity': (capacity * 0.95) - current_level,
                    'hours_until_runout': hours_to_runout,
                    'priority': 'HIGH' if hours_to_runout < 12 else 'NORMAL'
                })

        return delivery_needed

# Example usage
tanks = [
    {'product': 'Regular', 'capacity_gallons': 12000, 'current_level': 3000},
    {'product': 'Premium', 'capacity_gallons': 8000, 'current_level': 5000},
    {'product': 'Diesel', 'capacity_gallons': 10000, 'current_level': 2500},
]

# Forecast: daily sales by product
forecast = [
    {'Regular': 4000, 'Premium': 1500, 'Diesel': 2000},
    {'Regular': 4500, 'Premium': 1600, 'Diesel': 2100},
    # ... more days
]

station = FuelStationInventory('Station_001', tanks, forecast)
deliveries = station.check_delivery_needed()

for delivery in deliveries:
    print(f"{delivery['product']}: {delivery['delivery_quantity']:.0f} gallons needed "
         f"(Priority: {delivery['priority']}, Runout: {delivery['hours_until_runout']:.1f} hrs)")

---

Delivery Routing & Scheduling

Multi-Compartment Tank Truck Routing

def optimize_fuel_delivery_routes(stations, terminal_location, trucks,
                                 time_windows):
    """
    Optimize fuel delivery routes for multi-compartment tank trucks

    Vehicle Routing Problem with:
    - Time windows
    - Multiple products
    - Compartment constraints
    - Split deliveries allowed

    Parameters:
    - stations: list of stations with delivery requirements
    - terminal_location: depot coordinates
    - trucks: list of available trucks with compartment configurations
    - time_windows: delivery time windows by station
    """
    from pulp import *
    import numpy as np

    prob = LpProblem("Fuel_Delivery_Routing", LpMinimize)

    # Decision variables

    # x[t, i, j]: truck t travels from station i to station j
    x = {}
    for t, truck in enumerate(trucks):
        for i in range(len(stations) + 1):  # +1 for terminal
            for j in range(len(stations) + 1):
                if i != j:
                    x[t, i, j] = LpVariable(f"x_{t}_{i}_{j}", cat='Binary')

    # y[t, s, p]: truck t delivers product p to station s
    y = {}
    for t, truck in enumerate(trucks):
        for s, station in enumerate(stations):
            for product in ['Regular', 'Premium', 'Diesel']:
                y[t, s, product] = LpVariable(f"y_{t}_{s}_{product}",
                                             lowBound=0)

    # Arrival time at each station
    arrival_time = {}
    for t, truck in enumerate(trucks):
        for s in range(len(stations)):
            arrival_time[t, s] = LpVariable(f"arrival_{t}_{s}",
                                           lowBound=0)

    # Objective: minimize total distance + time window penalties
    total_distance = []
    for t, truck in enumerate(trucks):
        for i in range(len(stations) + 1):
            for j in range(len(stations) + 1):
                if i != j:
                    loc_i = terminal_location if i == 0 else stations[i-1]['location']
                    loc_j = terminal_location if j == 0 else stations[j-1]['location']

                    distance = calculate_distance(loc_i, loc_j)
                    total_distance.append(distance * x[t, i, j])

    prob += lpSum(total_distance)

    # Constraints

    # Each station's demand must be satisfied
    for s, station in enumerate(stations):
        for product in station['delivery_needs']:
            required = station['delivery_needs'][product]
            prob += lpSum([y[t, s, product] for t in range(len(trucks))]) >= required

    # Truck compartment capacity
    for t, truck in enumerate(trucks):
        for product in ['Regular', 'Premium', 'Diesel']:
            # Sum of deliveries ≤ compartment capacity for that product
            comp_capacity = truck['compartments'].get(product, 0)
            prob += lpSum([y[t, s, product] for s in range(len(stations))]) <= \
                    comp_capacity

    # If truck delivers to station, it must visit station
    for t, truck in enumerate(trucks):
        for s, station in enumerate(stations):
            total_delivery = lpSum([y[t, s, p] for p in ['Regular', 'Premium', 'Diesel']])

            # If total_delivery > 0, truck must visit
            visits = lpSum([x[t, i, s+1] for i in range(len(stations) + 1) if i != s+1])

            prob += total_delivery <= truck['total_capacity'] * visits

    # Flow conservation: if truck enters, it must leave
    for t, truck in enumerate(trucks):
        for j in range(1, len(stations) + 1):  # stations only (not terminal)
            inflow = lpSum([x[t, i, j] for i in range(len(stations) + 1) if i != j])
            outflow = lpSum([x[t, j, i] for i in range(len(stations) + 1) if i != j])

            prob += inflow == outflow

    # Each truck starts and ends at terminal
    for t, truck in enumerate(trucks):
        prob += lpSum([x[t, 0, j] for j in range(1, len(stations) + 1)]) == 1
        prob += lpSum([x[t, i, 0] for i in range(1, len(stations) + 1)]) == 1

    # Solve
    solver = PULP_CBC_CMD(msg=0, timeLimit=60)
    prob.solve(solver)

    # Extract routes
    routes = []
    for t, truck in enumerate(trucks):
        route = [0]  # Start at terminal

        current = 0
        for _ in range(len(stations)):
            for j in range(len(stations) + 1):
                if j != current and (t, current, j) in x:
                    if x[t, current, j].varValue > 0.5:
                        if j != 0:  # Not terminal
                            route.append(j)
                        current = j
                        break

        if len(route) > 1:
            route.append(0)  # Return to terminal
            routes.append({
                'truck': truck['id'],
                'route': route,
                'stations_visited': len(route) - 2,
                'deliveries': {
                    (s, p): y[t, s, p].varValue
                    for s in range(len(stations))
                    for p in ['Regular', 'Premium', 'Diesel']
                    if (t, s, p) in y and y[t, s, p].varValue > 10
                }
            })

    return {
        'status': LpStatus[prob.status],
        'total_distance': value(prob.objective),
        'routes': routes
    }

def calculate_distance(loc1, loc2):
    """Calculate distance between two locations (miles)"""
    import numpy as np
    return np.sqrt((loc1[0] - loc2[0])**2 + (loc1[1] - loc2[1])**2) * 69

# Example usage
stations = [
    {
        'id': 'Station_A',
        'location': (30.0, -95.0),
        'delivery_needs': {'Regular': 4000, 'Premium': 0, 'Diesel': 2000}
    },
    {
        'id': 'Station_B',
        'location': (30.1, -95.1),
        'delivery_needs': {'Regular': 3000, 'Premium': 1000, 'Diesel': 0}
    },
    {
        'id': 'Station_C',
        'location': (30.05, -95.15),
        'delivery_needs': {'Regular': 5000, 'Premium': 0, 'Diesel': 3000}
    },
]

terminal = (30.0, -95.2)

trucks = [
    {
        'id': 'Truck_1',
        'compartments': {'Regular': 5000, 'Premium': 2000, 'Diesel': 3000},
        'total_capacity': 10000
    },
    {
        'id': 'Truck_2',
        'compartments': {'Regular': 6000, 'Premium': 1000, 'Diesel': 4000},
        'total_capacity': 11000
    },
]

result = optimize_fuel_delivery_routes(stations, terminal, trucks, {})
print(f"Total distance: {result['total_distance']:.1f} miles")
for route in result['routes']:
    print(f"Truck {route['truck']}: {route['stations_visited']} stations")

---

Terminal Operations Optimization

Terminal Loading Dock Scheduling

def optimize_terminal_loading(scheduled_deliveries, loading_bays, time_slots):
    """
    Optimize assignment of trucks to loading bays and time slots

    Parameters:
    - scheduled_deliveries: list of planned deliveries with truck arrival times
    - loading_bays: number of available loading bays
    - time_slots: list of available time slots (e.g., hourly)
    """
    from pulp import *

    prob = LpProblem("Terminal_Loading", LpMinimize)

    n_deliveries = len(scheduled_deliveries)
    n_bays = loading_bays
    n_slots = len(time_slots)

    # Variables: assign delivery d to bay b in time slot t
    x = {}
    for d in range(n_deliveries):
        for b in range(n_bays):
            for t in range(n_slots):
                x[d, b, t] = LpVariable(f"x_{d}_{b}_{t}", cat='Binary')

    # Objective: minimize waiting time and tardiness
    waiting_penalty = []
    for d, delivery in enumerate(scheduled_deliveries):
        desired_slot = delivery['desired_time_slot']

        for b in range(n_bays):
            for t in range(n_slots):
                # Penalty for deviation from desired time
                delay = max(0, t - desired_slot)
                waiting_penalty.append(delay * x[d, b, t])

    prob += lpSum(waiting_penalty)

    # Constraints

    # Each delivery assigned exactly once
    for d in range(n_deliveries):
        prob += lpSum([x[d, b, t]
                      for b in range(n_bays)
                      for t in range(n_slots)]) == 1

    # Bay can handle one truck per time slot
    for b in range(n_bays):
        for t in range(n_slots):
            prob += lpSum([x[d, b, t] for d in range(n_deliveries)]) <= 1

    # Truck cannot load before arrival time
    for d, delivery in enumerate(scheduled_deliveries):
        earliest_slot = delivery['arrival_time_slot']

        for b in range(n_bays):
            for t in range(earliest_slot):
                prob += x[d, b, t] == 0

    # Loading duration (occupy bay for multiple slots)
    for d, delivery in enumerate(scheduled_deliveries):
        load_duration = delivery['loading_duration_slots']

        for b in range(n_bays):
            for t in range(n_slots):
                if x[d, b, t] in prob.variables():
                    # If loading starts at t, bay b is occupied for next 'duration' slots
                    for dt in range(1, load_duration):
                        if t + dt < n_slots:
                            # No other delivery can use this bay during loading
                            prob += lpSum([x[d2, b, t+dt]
                                         for d2 in range(n_deliveries)
                                         if d2 != d]) <= \
                                   1 - x[d, b, t]

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

    # Extract schedule
    schedule = []
    for d in range(n_deliveries):
        for b in range(n_bays):
            for t in range(n_slots):
                if x[d, b, t].varValue > 0.5:
                    schedule.append({
                        'delivery': scheduled_deliveries[d]['id'],
                        'truck': scheduled_deliveries[d]['truck'],
                        'bay': b + 1,
                        'time_slot': t,
                        'load_duration': scheduled_deliveries[d]['loading_duration_slots']
                    })

    return {
        'status': LpStatus[prob.status],
        'total_waiting': value(prob.objective),
        'schedule': pd.DataFrame(schedule).sort_values('time_slot')
    }

---

Demand Forecasting for Fuel

Fuel Sales Forecasting

def forecast_fuel_sales(historical_sales, weather_data, events_calendar):
    """
    Forecast fuel sales considering multiple factors

    Factors:
    - Day of week
    - Seasonality
    - Weather (temperature affects driving)
    - Special events
    - Trends
    """
    from sklearn.ensemble import GradientBoostingRegressor
    from sklearn.preprocessing import StandardScaler
    import pandas as pd

    # Prepare features
    df = historical_sales.copy()

    # Time-based features
    df['day_of_week'] = df['date'].dt.dayofweek
    df['day_of_month'] = df['date'].dt.day
    df['month'] = df['date'].dt.month
    df['is_weekend'] = (df['day_of_week'] >= 5).astype(int)

    # Lag features (previous sales)
    df['sales_lag_1'] = df['sales_gallons'].shift(1)
    df['sales_lag_7'] = df['sales_gallons'].shift(7)
    df['sales_rolling_7'] = df['sales_gallons'].rolling(7).mean()

    # Weather features
    df = df.merge(weather_data, on='date', how='left')

    # Special events
    df = df.merge(events_calendar, on='date', how='left')
    df['is_holiday'] = df['is_holiday'].fillna(0)

    # Drop rows with NaN from lag features
    df = df.dropna()

    # Features for model
    feature_cols = ['day_of_week', 'day_of_month', 'month', 'is_weekend',
                   'sales_lag_1', 'sales_lag_7', 'sales_rolling_7',
                   'temperature', 'precipitation', 'is_holiday']

    X = df[feature_cols]
    y = df['sales_gallons']

    # Scale features
    scaler = StandardScaler()
    X_scaled = scaler.fit_transform(X)

    # Train model
    model = GradientBoostingRegressor(
        n_estimators=100,
        learning_rate=0.1,
        max_depth=5,
        random_state=42
    )
    model.fit(X_scaled, y)

    # Feature importance
    importance = pd.DataFrame({
        'feature': feature_cols,
        'importance': model.feature_importances_
    }).sort_values('importance', ascending=False)

    return {
        'model': model,
        'scaler': scaler,
        'feature_importance': importance,
        'train_r2': model.score(X_scaled, y)
    }

def predict_next_week_sales(model, scaler, current_data, weather_forecast):
    """Predict sales for next 7 days"""

    predictions = []

    for day in range(7):
        # Prepare features for prediction day
        # This would use latest sales data and weather forecast
        # Simplified for illustration
        pass

    return predictions

---

Fuel Price Optimization

Dynamic Pricing Strategy

def optimize_fuel_pricing(station_data, competitor_prices, cost_data,
                         demand_elasticity=-0.5):
    """
    Optimize fuel pricing to maximize margin while remaining competitive

    Parameters:
    - station_data: station characteristics and historical data
    - competitor_prices: current prices at nearby competitors
    - cost_data: wholesale cost and other costs
    - demand_elasticity: price elasticity of demand
    """
    from pulp import *

    prob = LpProblem("Fuel_Pricing", LpMaximize)

    stations = station_data
    products = ['Regular', 'Premium', 'Diesel']

    # Variables: price for each product at each station
    price = {}
    volume = {}

    for s, station in enumerate(stations):
        for product in products:
            price[s, product] = LpVariable(
                f"Price_{s}_{product}",
                lowBound=cost_data[product]['wholesale_cost'] + 0.10,  # Min margin
                upBound=competitor_prices[product]['max'] + 0.20
            )

            volume[s, product] = LpVariable(
                f"Volume_{s}_{product}",
                lowBound=0
            )

    # Objective: maximize total profit
    profit = []

    for s, station in enumerate(stations):
        for product in products:
            # Profit = (Price - Cost) × Volume
            cost = cost_data[product]['wholesale_cost'] + \
                   cost_data[product]['operating_cost']

            profit.append((price[s, product] - cost) * volume[s, product])

    prob += lpSum(profit)

    # Constraints

    # Demand model: volume as function of price
    for s, station in enumerate(stations):
        for product in products:
            base_volume = station['base_volume'][product]
            base_price = station['base_price'][product]

            # Linear demand: V = V0 * (1 + elasticity * (P - P0) / P0)
            # Approximation for LP
            avg_comp_price = competitor_prices[product]['average']

            # Volume decreases if price above competitors
            prob += volume[s, product] <= base_volume * \
                    (1 + demand_elasticity * (price[s, product] - avg_comp_price) / avg_comp_price)

    # Competitive constraints: don't price too far from competitors
    for s, station in enumerate(stations):
        for product in products:
            avg_comp = competitor_prices[product]['average']
            min_comp = competitor_prices[product]['min']

            # Price within competitive range
            prob += price[s, product] <= avg_comp + 0.15  # Max 15 cents above average
            prob += price[s, product] >= min_comp - 0.05  # Max 5 cents below minimum

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

    # Extract optimal prices
    optimal_prices = {}
    for s, station in enumerate(stations):
        optimal_prices[station['id']] = {
            product: {
                'price': price[s, product].varValue,
                'volume': volume[s, product].varValue
            }
            for product in products
        }

    return {
        'status': LpStatus[prob.status],
        'max_profit': value(prob.objective),
        'optimal_prices': optimal_prices
    }

---

Tools & Libraries

Python Libraries

Optimization:

• PuLP

  : Linear programming

• OR-Tools

  : Vehicle routing

• Pyomo

  : Optimization modeling

Forecasting:

• scikit-learn

  : Machine learning

• prophet

  : Time series forecasting

• statsmodels

  : Statistical models

Geospatial:

• geopy

  : Distance calculations

• folium

  : Mapping

• geopandas

  : Geographic data

Commercial Software

Fuel Distribution:

• Omnitracs: Fleet management and routing
• Verizon Connect: GPS fleet tracking
• Descartes: Route optimization
• TMW Systems: Transportation management

Terminal Management:

• AspenTech: Fuel scheduling and optimization
• Honeywell Experion: Process control
• Emerson DeltaV: Terminal automation

Retail Management:

• Veeder-Root: Tank monitoring systems
• PDI: Fuel pricing and wholesale management
• Gilbarco: Fuel dispensing and management
• Dover Fueling Solutions: Retail automation

---

Common Challenges & Solutions

Challenge: Stockout Prevention

Problem:

• Unpredictable demand spikes
• Delivery delays
• Inaccurate forecasting

Solutions:

• Real-time inventory monitoring (ATG systems)
• Safety stock optimization
• Predictive analytics for demand
• Emergency delivery protocols
• Automated reorder systems

Challenge: Delivery Efficiency

Problem:

• Rising fuel costs
• Driver shortages
• Traffic congestion
• Time windows

Solutions:

• Route optimization software
• Delivery consolidation
• Dynamic routing (real-time adjustments)
• Multi-product compartment trucks
• Night deliveries where allowed

Challenge: Product Contamination

Problem:

• Cross-contamination between products
• Quality issues
• Tank mixing errors

Solutions:

• Strict compartment procedures
• Product verification systems
• Tank cleaning protocols
• Quality testing (pre and post-delivery)
• Automated delivery systems

Challenge: Price Volatility

Problem:

• Rapid wholesale price changes
• Competitive pressure
• Margin compression

Solutions:

• Dynamic pricing systems
• Hedging strategies
• Wholesale supply contracts
• Price monitoring and automation
• Value-added services (C-store, car wash)

---

Output Format

Fuel Distribution Optimization Report

Executive Summary:

• Network overview (terminals, stations, trucks)
• Key optimization results
• Cost savings achieved
• Service level performance

Station Inventory Status:

Station	Product	Current Level	Capacity	Days Supply	Reorder Point	Status
Station_A	Regular	3,000 gal	12,000	0.75	4,500	URGENT
Station_A	Diesel	6,000 gal	10,000	3.0	3,000	OK
Station_B	Regular	8,000 gal	15,000	2.0	5,000	OK

Delivery Schedule:

Date	Truck	Route	Stations	Products	Total Gallons	Miles	Hours
2026-02-01	Truck_1	Route_A	4	R, P, D	9,500	85	6.5
2026-02-01	Truck_2	Route_B	3	R, D	10,200	72	5.8
2026-02-02	Truck_1	Route_C	5	R, P, D	10,800	95	7.2

Cost Analysis:

Category	Daily Cost	Monthly Cost	Annual Cost
Fuel (diesel for trucks)	$2,500	$75,000	$900,000
Driver wages	$3,200	$96,000	$1,152,000
Truck maintenance	$800	$24,000	$288,000
Insurance	$400	$12,000	$144,000
Total Distribution Cost	$6,900	$207,000	$2,484,000

KPIs:

Metric	Current	Target	Status
Stockout Rate	0.2%	< 0.5%	✓ Good
On-Time Delivery	97%	> 95%	✓ Good
Delivery Cost per Gallon	$0.025	< $0.030	✓ Good
Truck Utilization	88%	> 85%	✓ Good
Avg Delivery Time	5.5 hrs	< 6 hrs	✓ Good

Recommendations:

1. Add one truck to fleet to handle peak summer demand
2. Implement automated pricing system for 10% margin improvement
3. Optimize Station_15 deliveries (currently underutilized route)
4. Consider bulk fuel hedging for next quarter

---

Questions to Ask

If you need more context:

1. How many retail locations do you serve?
2. What's your tank truck fleet size and configuration?
3. What products do you distribute? (gasoline grades, diesel, biofuels)
4. What are current delivery frequencies and service levels?
5. What's the primary challenge? (cost, stockouts, efficiency)
6. What systems are in place? (TMS, tank monitoring, pricing)
7. What's the competitive environment? (branded, independent)

---

Related Skills

• energy-logistics: For midstream petroleum logistics
• drilling-logistics: For upstream oil and gas operations
• route-optimization: For vehicle routing and scheduling
• inventory-optimization: For inventory management strategies
• demand-forecasting: For sales forecasting
• last-mile-delivery: For delivery operations
• fleet-management: For truck fleet management
• network-design: For terminal and station network planning