bakery-ia/shared/utils/optimization.py

"""
Optimization Utilities

Provides optimization algorithms for procurement planning including
MOQ rounding, economic order quantity, and multi-objective optimization.
"""

import math
from decimal import Decimal
from typing import List, Tuple, Dict, Optional
from dataclasses import dataclass


@dataclass
class OrderOptimizationResult:
    """Result of order quantity optimization"""
    optimal_quantity: Decimal
    order_cost: Decimal
    holding_cost: Decimal
    total_cost: Decimal
    orders_per_year: float
    reasoning: str


def calculate_economic_order_quantity(
    annual_demand: float,
    ordering_cost: float,
    holding_cost_per_unit: float
) -> float:
    """
    Calculate Economic Order Quantity (EOQ).

    EOQ = sqrt((2 × D × S) / H)
    where:
    - D = Annual demand
    - S = Ordering cost per order
    - H = Holding cost per unit per year

    Args:
        annual_demand: Annual demand in units
        ordering_cost: Cost per order placement
        holding_cost_per_unit: Annual holding cost per unit

    Returns:
        Optimal order quantity
    """
    if annual_demand <= 0 or ordering_cost <= 0 or holding_cost_per_unit <= 0:
        return 0.0

    eoq = math.sqrt((2 * annual_demand * ordering_cost) / holding_cost_per_unit)
    return eoq


def optimize_order_quantity(
    required_quantity: Decimal,
    annual_demand: float,
    ordering_cost: float = 50.0,
    holding_cost_rate: float = 0.25,
    unit_price: float = 1.0,
    min_order_qty: Optional[Decimal] = None,
    max_order_qty: Optional[Decimal] = None
) -> OrderOptimizationResult:
    """
    Optimize order quantity considering EOQ and constraints.

    Args:
        required_quantity: Quantity needed for current period
        annual_demand: Estimated annual demand
        ordering_cost: Fixed cost per order
        holding_cost_rate: Annual holding cost as % of unit price
        unit_price: Cost per unit
        min_order_qty: Minimum order quantity (MOQ)
        max_order_qty: Maximum order quantity (storage limit)

    Returns:
        OrderOptimizationResult with optimal quantity and costs
    """
    holding_cost_per_unit = unit_price * holding_cost_rate

    # Calculate EOQ
    eoq = calculate_economic_order_quantity(
        annual_demand,
        ordering_cost,
        holding_cost_per_unit
    )

    # Start with EOQ or required quantity, whichever is larger
    optimal_qty = max(float(required_quantity), eoq)

    reasoning = f"Base EOQ: {eoq:.2f}, Required: {required_quantity}"

    # Apply minimum order quantity
    if min_order_qty and Decimal(optimal_qty) < min_order_qty:
        optimal_qty = float(min_order_qty)
        reasoning += f", Applied MOQ: {min_order_qty}"

    # Apply maximum order quantity
    if max_order_qty and Decimal(optimal_qty) > max_order_qty:
        optimal_qty = float(max_order_qty)
        reasoning += f", Capped at max: {max_order_qty}"

    # Calculate costs
    orders_per_year = annual_demand / optimal_qty if optimal_qty > 0 else 0
    annual_ordering_cost = orders_per_year * ordering_cost
    annual_holding_cost = (optimal_qty / 2) * holding_cost_per_unit
    total_annual_cost = annual_ordering_cost + annual_holding_cost

    return OrderOptimizationResult(
        optimal_quantity=Decimal(str(optimal_qty)),
        order_cost=Decimal(str(annual_ordering_cost)),
        holding_cost=Decimal(str(annual_holding_cost)),
        total_cost=Decimal(str(total_annual_cost)),
        orders_per_year=orders_per_year,
        reasoning=reasoning
    )


def round_to_moq(
    quantity: Decimal,
    moq: Decimal,
    round_up: bool = True
) -> Decimal:
    """
    Round quantity to meet minimum order quantity.

    Args:
        quantity: Desired quantity
        moq: Minimum order quantity
        round_up: If True, always round up to next MOQ multiple

    Returns:
        Rounded quantity
    """
    if quantity <= 0 or moq <= 0:
        return quantity

    if quantity < moq:
        return moq

    # Calculate how many MOQs needed
    multiples = quantity / moq

    if round_up:
        return Decimal(math.ceil(float(multiples))) * moq
    else:
        return Decimal(round(float(multiples))) * moq


def round_to_package_size(
    quantity: Decimal,
    package_size: Decimal,
    allow_partial: bool = False
) -> Decimal:
    """
    Round quantity to package size.

    Args:
        quantity: Desired quantity
        package_size: Size of one package
        allow_partial: If False, always round up to full packages

    Returns:
        Rounded quantity
    """
    if quantity <= 0 or package_size <= 0:
        return quantity

    packages_needed = quantity / package_size

    if allow_partial:
        return quantity
    else:
        return Decimal(math.ceil(float(packages_needed))) * package_size


def apply_price_tier_optimization(
    base_quantity: Decimal,
    unit_price: Decimal,
    price_tiers: List[Dict]
) -> Tuple[Decimal, Decimal, str]:
    """
    Optimize quantity to take advantage of price tiers.

    Args:
        base_quantity: Base quantity needed
        unit_price: Current unit price
        price_tiers: List of dicts with 'min_quantity' and 'unit_price'

    Returns:
        Tuple of (optimized_quantity, unit_price, reasoning)
    """
    if not price_tiers:
        return base_quantity, unit_price, "No price tiers available"

    # Sort tiers by min_quantity
    sorted_tiers = sorted(price_tiers, key=lambda x: x['min_quantity'])

    # Calculate cost at base quantity
    base_cost = base_quantity * unit_price

    # Find current tier
    current_tier_price = unit_price
    for tier in sorted_tiers:
        if base_quantity >= Decimal(str(tier['min_quantity'])):
            current_tier_price = Decimal(str(tier['unit_price']))

    # Check if moving to next tier would save money
    best_quantity = base_quantity
    best_price = current_tier_price
    best_savings = Decimal('0')
    reasoning = f"Current tier price: ${current_tier_price}"

    for tier in sorted_tiers:
        tier_min_qty = Decimal(str(tier['min_quantity']))
        tier_price = Decimal(str(tier['unit_price']))

        if tier_min_qty > base_quantity:
            # Calculate cost at this tier
            tier_cost = tier_min_qty * tier_price

            # Calculate savings
            savings = base_cost - tier_cost

            if savings > best_savings:
                # Additional quantity needed
                additional_qty = tier_min_qty - base_quantity

                # Check if savings justify additional inventory
                # Simple heuristic: savings should be > 10% of additional cost
                additional_cost = additional_qty * tier_price
                if savings > additional_cost * Decimal('0.1'):
                    best_quantity = tier_min_qty
                    best_price = tier_price
                    best_savings = savings
                    reasoning = f"Upgraded to tier {tier_min_qty}+ for ${savings:.2f} savings"

    return best_quantity, best_price, reasoning


def aggregate_requirements_for_moq(
    requirements: List[Dict],
    moq: Decimal
) -> List[Dict]:
    """
    Aggregate multiple requirements to meet MOQ efficiently.

    Args:
        requirements: List of requirement dicts with 'quantity' and 'date'
        moq: Minimum order quantity

    Returns:
        List of aggregated orders
    """
    if not requirements:
        return []

    # Sort requirements by date
    sorted_reqs = sorted(requirements, key=lambda x: x['date'])

    orders = []
    current_batch = []
    current_total = Decimal('0')

    for req in sorted_reqs:
        req_qty = Decimal(str(req['quantity']))

        # Check if adding this requirement would exceed reasonable aggregation
        # (e.g., don't aggregate more than 30 days worth)
        if current_batch:
            days_span = (req['date'] - current_batch[0]['date']).days
            if days_span > 30:
                # Finalize current batch
                if current_total > 0:
                    orders.append({
                        'quantity': round_to_moq(current_total, moq),
                        'date': current_batch[0]['date'],
                        'requirements': current_batch.copy()
                    })
                current_batch = []
                current_total = Decimal('0')

        current_batch.append(req)
        current_total += req_qty

        # If we've met MOQ, finalize this batch
        if current_total >= moq:
            orders.append({
                'quantity': round_to_moq(current_total, moq),
                'date': current_batch[0]['date'],
                'requirements': current_batch.copy()
            })
            current_batch = []
            current_total = Decimal('0')

    # Handle remaining requirements
    if current_batch:
        orders.append({
            'quantity': round_to_moq(current_total, moq),
            'date': current_batch[0]['date'],
            'requirements': current_batch
        })

    return orders


def calculate_order_splitting(
    total_quantity: Decimal,
    suppliers: List[Dict],
    max_supplier_capacity: Optional[Decimal] = None
) -> List[Dict]:
    """
    Split large order across multiple suppliers.

    Args:
        total_quantity: Total quantity needed
        suppliers: List of supplier dicts with 'id', 'capacity', 'reliability'
        max_supplier_capacity: Maximum any single supplier should provide

    Returns:
        List of allocations with 'supplier_id' and 'quantity'
    """
    if not suppliers:
        return []

    # Sort suppliers by reliability (descending)
    sorted_suppliers = sorted(
        suppliers,
        key=lambda x: x.get('reliability', 0.5),
        reverse=True
    )

    allocations = []
    remaining = total_quantity

    for supplier in sorted_suppliers:
        if remaining <= 0:
            break

        supplier_capacity = Decimal(str(supplier.get('capacity', float('inf'))))

        # Apply max capacity constraint
        if max_supplier_capacity:
            supplier_capacity = min(supplier_capacity, max_supplier_capacity)

        # Allocate to this supplier
        allocated = min(remaining, supplier_capacity)

        allocations.append({
            'supplier_id': supplier['id'],
            'quantity': allocated,
            'reliability': supplier.get('reliability', 0.5)
        })

        remaining -= allocated

    # If still remaining, distribute across suppliers
    if remaining > 0:
        # Distribute remaining proportionally to reliability
        total_reliability = sum(s.get('reliability', 0.5) for s in sorted_suppliers)

        for i, supplier in enumerate(sorted_suppliers):
            if total_reliability > 0:
                proportion = supplier.get('reliability', 0.5) / total_reliability
                additional = remaining * Decimal(str(proportion))

                allocations[i]['quantity'] += additional

    return allocations


def calculate_buffer_stock(
    lead_time_days: int,
    daily_demand: float,
    demand_variability: float,
    service_level: float = 0.95
) -> Decimal:
    """
    Calculate buffer stock based on demand variability.

    Buffer Stock = Z × σ × √(lead_time)
    where:
    - Z = service level z-score
    - σ = demand standard deviation
    - lead_time = lead time in days

    Args:
        lead_time_days: Supplier lead time in days
        daily_demand: Average daily demand
        demand_variability: Coefficient of variation (CV = σ/μ)
        service_level: Target service level (0-1)

    Returns:
        Buffer stock quantity
    """
    if lead_time_days <= 0 or daily_demand <= 0:
        return Decimal('0')

    # Z-scores for common service levels
    z_scores = {
        0.90: 1.28,
        0.95: 1.65,
        0.975: 1.96,
        0.99: 2.33,
        0.995: 2.58
    }

    # Get z-score for service level
    z_score = z_scores.get(service_level, 1.65)  # Default to 95%

    # Calculate standard deviation
    stddev = daily_demand * demand_variability

    # Buffer stock formula
    buffer = z_score * stddev * math.sqrt(lead_time_days)

    return Decimal(str(buffer))


def calculate_reorder_point(
    daily_demand: float,
    lead_time_days: int,
    safety_stock: Decimal
) -> Decimal:
    """
    Calculate reorder point.

    Reorder Point = (Daily Demand × Lead Time) + Safety Stock

    Args:
        daily_demand: Average daily demand
        lead_time_days: Supplier lead time in days
        safety_stock: Safety stock quantity

    Returns:
        Reorder point
    """
    lead_time_demand = Decimal(str(daily_demand * lead_time_days))
    return lead_time_demand + safety_stock