Minimize:
  α × Σ Σ Σ (d[j,z[i]] × x[i,j,t])  # Travel distance
  + β × Σ Σ Σ (max(0, t - a[i]) × x[i,j,t])  # Waiting time
  + γ × Σ max_truck_overlap[j]  # Congestion penalty

where:
  α, β, γ = weights for different objectives

# 1. Each truck assigned to exactly one door at one time
for i in trucks:
    Σ Σ x[i,j,t] = 1  for all j, t

# 2. Door capacity (trucks per time slot)
for j in doors:
    for t in time_slots:
        Σ x[i,j,t] ≤ door_capacity[j]  for all i

# 3. No overlap (truck occupies door for processing time)
for j in doors:
    for t in time_slots:
        Σ x[i,j,t'] ≤ 1  for all i, where t' in [t, t+p[i]]

# 4. Truck can't be assigned before arrival
for i in trucks:
    for t < a[i]:
        Σ x[i,j,t] = 0  for all j

# 5. Staging area capacity
for j in doors:
    Σ (volume[i] × x[i,j,t]) ≤ staging_capacity[j]  for all i, t

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

def greedy_dock_assignment(trucks, doors, distances, processing_times):
    """
    Greedy heuristic for dock door assignment

    Assign each truck to the nearest available door

    Parameters:
    -----------
    trucks : list of dict
        [{truck_id, arrival_time, destination_zone, volume}, ...]
    doors : list of dict
        [{door_id, capacity, zone_affinity}, ...]
    distances : dict
        {(door_id, zone): distance}
    processing_times : dict
        {truck_id: duration_minutes}

    Returns:
    --------
    Assignment schedule
    """

    # Sort trucks by arrival time
    trucks_sorted = sorted(trucks, key=lambda x: x['arrival_time'])

    # Track door availability (door_id -> next_available_time)
    door_availability = {door['door_id']: datetime.min for door in doors}

    assignments = []

    for truck in trucks_sorted:
        truck_id = truck['truck_id']
        arrival = truck['arrival_time']
        dest_zone = truck['destination_zone']
        process_time = processing_times.get(truck_id, 60)  # default 60 min

        # Find best door
        best_door = None
        best_score = float('inf')

        for door in doors:
            door_id = door['door_id']
            available_time = door_availability[door_id]

            # Can't assign before door is available and truck arrives
            start_time = max(arrival, available_time)

            # Calculate score: distance + waiting time
            distance = distances.get((door_id, dest_zone), 1000)
            waiting_time = (start_time - arrival).total_seconds() / 60

            score = distance * 1.0 + waiting_time * 0.5

            if score < best_score:
                best_score = score
                best_door = door_id
                best_start = start_time

        # Assign truck to best door
        end_time = best_start + timedelta(minutes=process_time)
        door_availability[best_door] = end_time

        assignments.append({
            'truck_id': truck_id,
            'door_id': best_door,
            'scheduled_start': best_start,
            'scheduled_end': end_time,
            'arrival_time': arrival,
            'wait_time_min': (best_start - arrival).total_seconds() / 60,
            'destination_zone': dest_zone
        })

    return pd.DataFrame(assignments)


# Example usage
trucks = [
    {'truck_id': 'T001', 'arrival_time': datetime(2024, 1, 1, 8, 0),
     'destination_zone': 'A', 'volume': 1000},
    {'truck_id': 'T002', 'arrival_time': datetime(2024, 1, 1, 8, 15),
     'destination_zone': 'B', 'volume': 800},
    {'truck_id': 'T003', 'arrival_time': datetime(2024, 1, 1, 8, 30),
     'destination_zone': 'A', 'volume': 1200},
    {'truck_id': 'T004', 'arrival_time': datetime(2024, 1, 1, 9, 0),
     'destination_zone': 'C', 'volume': 900},
]

doors = [
    {'door_id': 'D1', 'capacity': 3, 'zone_affinity': 'A'},
    {'door_id': 'D2', 'capacity': 3, 'zone_affinity': 'B'},
    {'door_id': 'D3', 'capacity': 3, 'zone_affinity': 'C'},
]

distances = {
    ('D1', 'A'): 50, ('D1', 'B'): 150, ('D1', 'C'): 200,
    ('D2', 'A'): 150, ('D2', 'B'): 50, ('D2', 'C'): 180,
    ('D3', 'A'): 200, ('D3', 'B'): 180, ('D3', 'C'): 50,
}

processing_times = {
    'T001': 45, 'T002': 60, 'T003': 50, 'T004': 55
}

schedule = greedy_dock_assignment(trucks, doors, distances, processing_times)
print("Dock Assignment Schedule:")
print(schedule[['truck_id', 'door_id', 'scheduled_start', 'wait_time_min']])

from scipy.optimize import linear_sum_assignment
import numpy as np

def hungarian_dock_assignment(trucks, doors, cost_matrix):
    """
    Optimal one-to-one assignment using Hungarian algorithm

    Use when number of trucks = number of available door slots

    Parameters:
    -----------
    trucks : list
        Truck identifiers
    doors : list
        Door identifiers
    cost_matrix : 2D numpy array
        cost[i,j] = cost of assigning truck i to door j

    Returns:
    --------
    Optimal assignments
    """

    # Solve assignment problem
    row_ind, col_ind = linear_sum_assignment(cost_matrix)

    assignments = []
    total_cost = 0

    for i, j in zip(row_ind, col_ind):
        assignments.append({
            'truck_id': trucks[i],
            'door_id': doors[j],
            'cost': cost_matrix[i, j]
        })
        total_cost += cost_matrix[i, j]

    return {
        'assignments': assignments,
        'total_cost': total_cost
    }


# Example
trucks = ['T1', 'T2', 'T3', 'T4']
doors = ['D1', 'D2', 'D3', 'D4']

# Cost matrix: distance + penalty
cost_matrix = np.array([
    [50, 150, 200, 180],  # T1 costs to each door
    [150, 50, 180, 160],  # T2
    [50, 140, 210, 190],  # T3
    [200, 180, 50, 70],   # T4
])

result = hungarian_dock_assignment(trucks, doors, cost_matrix)
print("Optimal Assignment (Hungarian):")
for assignment in result['assignments']:
    print(f"  {assignment['truck_id']} → {assignment['door_id']} "
          f"(cost: {assignment['cost']})")
print(f"Total Cost: {result['total_cost']}")

from pulp import *
import pandas as pd

def optimize_dock_assignment(trucks, doors, time_slots, distances,
                             processing_times, arrivals):
    """
    Comprehensive dock assignment using MIP

    Parameters:
    -----------
    trucks : list
        Truck identifiers
    doors : list
        Door identifiers
    time_slots : list
        Time slot identifiers (e.g., [0, 1, 2, ...])
    distances : dict
        {(truck, door): distance_to_zone}
    processing_times : dict
        {truck: slots_required}
    arrivals : dict
        {truck: earliest_slot}

    Returns:
    --------
    Optimal assignment with timing
    """

    prob = LpProblem("Dock_Assignment", LpMinimize)

    # Decision variables
    # x[i,j,t] = 1 if truck i assigned to door j starting at time t
    x = LpVariable.dicts("assign",
                        [(i, j, t) for i in trucks
                                   for j in doors
                                   for t in time_slots],
                        cat='Binary')

    # Waiting time variables
    wait = LpVariable.dict("wait",
                          trucks,
                          lowBound=0,
                          cat='Continuous')

    # Objective: minimize weighted sum of distance and waiting
    alpha = 1.0  # distance weight
    beta = 0.5   # waiting time weight

    prob += (
        alpha * lpSum([
            distances.get((i, j), 1000) * x[i, j, t]
            for i in trucks for j in doors for t in time_slots
        ]) +
        beta * lpSum([wait[i] for i in trucks])
    ), "Total_Cost"

    # Constraints

    # 1. Each truck assigned to exactly one door-time combination
    for i in trucks:
        prob += lpSum([
            x[i, j, t] for j in doors for t in time_slots
        ]) == 1, f"Truck_{i}_Assignment"

    # 2. Door capacity: no overlapping assignments
    for j in doors:
        for t in time_slots:
            # Count trucks using this door at this time
            prob += lpSum([
                x[i, j, t_start]
                for i in trucks
                for t_start in range(max(0, t - processing_times.get(i, 1) + 1), t + 1)
                if t_start in time_slots
            ]) <= 1, f"Door_{j}_Time_{t}_Capacity"

    # 3. Truck can't be assigned before arrival
    for i in trucks:
        arrival_slot = arrivals.get(i, 0)
        for t in time_slots:
            if t < arrival_slot:
                for j in doors:
                    prob += x[i, j, t] == 0, f"Truck_{i}_Arrival_Time_{t}"

    # 4. Calculate waiting time
    for i in trucks:
        arrival_slot = arrivals.get(i, 0)
        prob += wait[i] >= lpSum([
            (t - arrival_slot) * x[i, j, t]
            for j in doors for t in time_slots
        ]), f"Wait_{i}"

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

    # Extract solution
    assignments = []
    for i in trucks:
        for j in doors:
            for t in time_slots:
                if x[i, j, t].varValue > 0.5:
                    assignments.append({
                        'truck_id': i,
                        'door_id': j,
                        'time_slot': t,
                        'wait_slots': wait[i].varValue if wait[i].varValue else 0
                    })

    return {
        'status': LpStatus[prob.status],
        'objective_value': value(prob.objective),
        'assignments': pd.DataFrame(assignments)
    }


# Example
trucks = ['T1', 'T2', 'T3', 'T4', 'T5']
doors = ['D1', 'D2', 'D3']
time_slots = list(range(0, 20))  # 20 time slots (e.g., 30-min each)

# Distance from each truck's destination zone to each door
distances = {
    ('T1', 'D1'): 50, ('T1', 'D2'): 150, ('T1', 'D3'): 200,
    ('T2', 'D1'): 150, ('T2', 'D2'): 50, ('T2', 'D3'): 180,
    ('T3', 'D1'): 50, ('T3', 'D2'): 140, ('T3', 'D3'): 210,
    ('T4', 'D1'): 200, ('T4', 'D2'): 180, ('T4', 'D3'): 50,
    ('T5', 'D1'): 100, ('T5', 'D2'): 100, ('T5', 'D3'): 100,
}

# Processing time in time slots (e.g., 2 slots = 1 hour)
processing_times = {'T1': 2, 'T2': 3, 'T3': 2, 'T4': 3, 'T5': 2}

# Arrival times (time slot)
arrivals = {'T1': 0, 'T2': 2, 'T3': 3, 'T4': 5, 'T5': 6}

result = optimize_dock_assignment(
    trucks, doors, time_slots, distances, processing_times, arrivals
)

print(f"Optimization Status: {result['status']}")
print(f"Objective Value: {result['objective_value']:.2f}")
print("\nAssignments:")
print(result['assignments'])

def optimize_crossdock_pairing(inbound_trucks, outbound_trucks,
                               crossdock_items, doors, distances):
    """
    Optimize door assignment for cross-docking operations

    Match inbound and outbound doors to minimize transfer distance

    Parameters:
    -----------
    inbound_trucks : list of dict
        [{truck_id, arrival_time, items: [sku_list]}, ...]
    outbound_trucks : list of dict
        [{truck_id, departure_time, items: [sku_list]}, ...]
    crossdock_items : dict
        {inbound_truck: {outbound_truck: [items_to_transfer]}}
    doors : dict
        {'inbound': [door_list], 'outbound': [door_list]}
    distances : dict
        {(inbound_door, outbound_door): transfer_distance}

    Returns:
    --------
    Paired door assignments
    """

    prob = LpProblem("CrossDock_Pairing", LpMinimize)

    inbound_ids = [t['truck_id'] for t in inbound_trucks]
    outbound_ids = [t['truck_id'] for t in outbound_trucks]
    inbound_doors = doors['inbound']
    outbound_doors = doors['outbound']

    # Decision variables
    # y_in[i,d] = 1 if inbound truck i assigned to door d
    y_in = LpVariable.dicts("inbound",
                           [(i, d) for i in inbound_ids for d in inbound_doors],
                           cat='Binary')

    # y_out[i,d] = 1 if outbound truck i assigned to door d
    y_out = LpVariable.dicts("outbound",
                            [(i, d) for i in outbound_ids for d in outbound_doors],
                            cat='Binary')

    # Flow variables: f[in_door, out_door] = volume transferred
    f = LpVariable.dicts("flow",
                        [(d1, d2) for d1 in inbound_doors for d2 in outbound_doors],
                        lowBound=0,
                        cat='Continuous')

    # Objective: minimize transfer distance
    prob += lpSum([
        distances.get((d1, d2), 100) * f[d1, d2]
        for d1 in inbound_doors for d2 in outbound_doors
    ]), "Transfer_Distance"

    # Constraints

    # Each truck assigned to one door
    for i in inbound_ids:
        prob += lpSum([y_in[i, d] for d in inbound_doors]) == 1

    for i in outbound_ids:
        prob += lpSum([y_out[i, d] for d in outbound_doors]) == 1

    # Link flow to door assignments
    # (Simplified: would need actual crossdock volumes)
    for d1 in inbound_doors:
        for d2 in outbound_doors:
            # Flow limited by door assignments
            prob += f[d1, d2] <= 1000, f"Flow_{d1}_{d2}"

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

    # Extract solution
    inbound_assignments = {}
    outbound_assignments = {}

    for i in inbound_ids:
        for d in inbound_doors:
            if y_in[i, d].varValue > 0.5:
                inbound_assignments[i] = d

    for i in outbound_ids:
        for d in outbound_doors:
            if y_out[i, d].varValue > 0.5:
                outbound_assignments[i] = d

    flows = {}
    for d1 in inbound_doors:
        for d2 in outbound_doors:
            if f[d1, d2].varValue > 0.01:
                flows[(d1, d2)] = f[d1, d2].varValue

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

from datetime import datetime, timedelta

class DockAppointmentScheduler:
    """
    Manage dock appointment scheduling with time windows
    """

    def __init__(self, doors, operating_hours, slot_duration=30):
        """
        Initialize scheduler

        Parameters:
        -----------
        doors : list
            Available door IDs
        operating_hours : dict
            {'start': time, 'end': time}
        slot_duration : int
            Minutes per appointment slot
        """
        self.doors = doors
        self.operating_hours = operating_hours
        self.slot_duration = slot_duration
        self.appointments = {}  # {(door, datetime): truck_id}
        self.truck_schedules = {}  # {truck_id: (door, start_time, end_time)}

    def generate_time_slots(self, date):
        """Generate available time slots for a date"""
        slots = []
        current = datetime.combine(date, self.operating_hours['start'])
        end = datetime.combine(date, self.operating_hours['end'])

        while current < end:
            slots.append(current)
            current += timedelta(minutes=self.slot_duration)

        return slots

    def find_available_slots(self, date, duration_minutes, preferred_doors=None):
        """
        Find available appointment slots

        Parameters:
        -----------
        date : datetime.date
            Target date
        duration_minutes : int
            Required duration
        preferred_doors : list, optional
            Preferred door IDs

        Returns:
        --------
        List of available (door, start_time) tuples
        """
        time_slots = self.generate_time_slots(date)
        slots_needed = int(np.ceil(duration_minutes / self.slot_duration))

        available = []
        doors_to_check = preferred_doors if preferred_doors else self.doors

        for door in doors_to_check:
            for i, start_time in enumerate(time_slots[:-slots_needed + 1]):
                # Check if all required slots are free
                all_free = True
                for offset in range(slots_needed):
                    slot_time = time_slots[i + offset]
                    if (door, slot_time) in self.appointments:
                        all_free = False
                        break

                if all_free:
                    end_time = time_slots[i + slots_needed - 1] + \
                              timedelta(minutes=self.slot_duration)
                    available.append({
                        'door': door,
                        'start_time': start_time,
                        'end_time': end_time,
                        'duration': duration_minutes
                    })

        return available

    def book_appointment(self, truck_id, door, start_time, duration_minutes):
        """
        Book an appointment

        Returns:
        --------
        Success (bool) and confirmation details
        """
        slots_needed = int(np.ceil(duration_minutes / self.slot_duration))

        # Check availability
        current_slot = start_time
        for _ in range(slots_needed):
            if (door, current_slot) in self.appointments:
                return {
                    'success': False,
                    'message': f'Slot {current_slot} on {door} already booked'
                }
            current_slot += timedelta(minutes=self.slot_duration)

        # Book slots
        current_slot = start_time
        for _ in range(slots_needed):
            self.appointments[(door, current_slot)] = truck_id
            current_slot += timedelta(minutes=self.slot_duration)

        end_time = start_time + timedelta(minutes=duration_minutes)
        self.truck_schedules[truck_id] = (door, start_time, end_time)

        return {
            'success': True,
            'truck_id': truck_id,
            'door': door,
            'start_time': start_time,
            'end_time': end_time,
            'confirmation': f'{truck_id} booked on {door} from {start_time} to {end_time}'
        }

    def cancel_appointment(self, truck_id):
        """Cancel an existing appointment"""
        if truck_id not in self.truck_schedules:
            return {'success': False, 'message': 'Appointment not found'}

        door, start_time, end_time = self.truck_schedules[truck_id]

        # Remove appointment slots
        current_slot = start_time
        while current_slot < end_time:
            if (door, current_slot) in self.appointments:
                del self.appointments[(door, current_slot)]
            current_slot += timedelta(minutes=self.slot_duration)

        del self.truck_schedules[truck_id]

        return {'success': True, 'message': f'Appointment {truck_id} cancelled'}

    def get_door_utilization(self, date):
        """Calculate door utilization for a date"""
        time_slots = self.generate_time_slots(date)
        total_slots = len(time_slots) * len(self.doors)

        booked_slots = sum(
            1 for (door, slot_time) in self.appointments
            if slot_time.date() == date
        )

        return {
            'date': date,
            'utilization': (booked_slots / total_slots * 100) if total_slots > 0 else 0,
            'booked_slots': booked_slots,
            'total_slots': total_slots
        }


# Example usage
from datetime import time

scheduler = DockAppointmentScheduler(
    doors=['D1', 'D2', 'D3', 'D4'],
    operating_hours={'start': time(6, 0), 'end': time(18, 0)},
    slot_duration=30
)

# Find available slots for 90-minute appointment
target_date = datetime(2024, 1, 15).date()
available = scheduler.find_available_slots(target_date, 90, preferred_doors=['D1', 'D2'])

print(f"Available slots on {target_date}:")
for slot in available[:5]:  # Show first 5
    print(f"  {slot['door']}: {slot['start_time'].strftime('%H:%M')} - "
          f"{slot['end_time'].strftime('%H:%M')}")

# Book appointments
booking1 = scheduler.book_appointment('TRUCK001', 'D1',
                                     datetime(2024, 1, 15, 8, 0), 90)
print(f"\n{booking1['confirmation']}")

booking2 = scheduler.book_appointment('TRUCK002', 'D1',
                                     datetime(2024, 1, 15, 10, 0), 60)
print(booking2['confirmation'])

# Check utilization
util = scheduler.get_door_utilization(target_date)
print(f"\nDoor Utilization: {util['utilization']:.1f}%")

# Optimization
from pulp import *  # Linear programming
from scipy.optimize import linear_sum_assignment  # Hungarian algorithm
from ortools.sat.python import cp_model  # Constraint programming

# Scheduling
import schedule  # Job scheduling
from datetime import datetime, timedelta
import pandas as pd

# Simulation
import simpy  # Discrete event simulation for dock operations

Truck T101:
  - Carrier: ABC Freight
  - Arrival: 05:45 (15 min early)
  - Assigned Door: D1
  - Scheduled: 06:00 - 07:30
  - Destination Zone: A
  - Distance to Zone: 45 ft
  - Status: Completed on time

Truck T102:
  - Carrier: XYZ Logistics
  - Arrival: 06:05 (5 min late)
  - Assigned Door: D2
  - Scheduled: 06:00 - 07:30
  - Destination Zone: B
  - Distance to Zone: 52 ft
  - Status: Completed with 10 min delay