[INPUT_SEPARATOR]
First, create a Cython helper module for distance calculations.
```python
edit
file: solver.py
lines: 0-0
---
import numpy as np
from typing import Any
import numba

# This version refines the float64 Numba solution by fusing the cost calculation
# into the main simulation loop. This creates a true single-pass algorithm,
# minimizing memory access by calculating the total cost on-the-fly, which
# improves cache performance.
@numba.njit(fastmath=True)
def _solve_and_cost_jit(initial_inventory: float, demand: np.ndarray, h: float, c: float, p: float):
    """
    A single, unified JIT-compiled function that simulates the policy and
    calculates the total cost in a single pass.
    """
    T = demand.shape[0]
    inventory = np.zeros(T, dtype=np.float64)
    orders = np.zeros(T, dtype=np.float64)
    stockouts = np.zeros(T, dtype=np.float64)
    total_cost = 0.0
    
    current_inventory = initial_inventory

    if h < 0:
        # Policy: Order everything upfront.
        total_demand = 0.0
        for i in range(T):
            total_demand += demand[i]
        
        required_order = total_demand - initial_inventory
        if required_order > 0:
            orders[0] = required_order
            total_cost += c * required_order # Cost of the single order
        
        # Simulation loop with fused cost calculation
        for t in range(T):
            inventory_after_order = current_inventory + orders[t]
            balance = inventory_after_order - demand[t]
            inv_t = max(0.0, balance)
            
            inventory[t] = inv_t
            # Stockouts will be 0 for this policy, so no need to calculate or add cost.
            current_inventory = inv_t
            
            total_cost += h * inv_t # Holding cost for the period

    elif c <= p:
        # Policy: Just-in-time (JIT), with fused cost calculation
        for t in range(T):
            demand_t = demand[t]
            order_t = max(0.0, demand_t - current_inventory)
            inv_t = current_inventory + order_t - demand_t
            
            orders[t] = order_t
            inventory[t] = inv_t
            current_inventory = inv_t
            
            # Update cost. Stockouts are 0.
            total_cost += h * inv_t + c * order_t
    
    else: # c > p and h >= 0
        # Policy: Never order, with fused cost calculation
        for t in range(T):
            demand_t = demand[t]
            stk_t = max(0.0, demand_t - current_inventory)
            inv_t = max(0.0, current_inventory - demand_t)
            
            stockouts[t] = stk_t
            inventory[t] = inv_t
            current_inventory = inv_t
            
            # Update cost. Orders are 0.
            total_cost += h * inv_t + p * stk_t

    return inventory, orders, stockouts, total_cost

class Solver:
    def solve(self, problem: dict) -> Any:
        """
        Solve the multi-period inventory management problem with a single-pass
        Numba JIT-compiled function that fuses simulation and cost calculation.
        """
        demand = np.array(problem["demand"], dtype=np.float64)
        h = float(problem["holding_cost"])
        c = float(problem["ordering_cost"])
        p = float(problem["stockout_penalty"])
        initial_inventory = float(problem["initial_inventory"])

        T = len(demand)
        if T == 0:
            return {"inventory": [], "orders": [], "stockouts": [], "total_cost": 0.0}

        if c < 0 or p < 0:
            return {"inventory": [], "orders": [], "stockouts": [], "total_cost": 0.0}

        # Call the single-pass JIT function.
        inventory, orders, stockouts, total_cost = _solve_and_cost_jit(
            initial_inventory, demand, h, c, p
        )

        return {
            "inventory": inventory.tolist(),
            "orders": orders.tolist(),
            "stockouts": stockouts.tolist(),
            "total_cost": float(total_cost),
        }
---
```
[INPUT_SEPARATOR]
First, create a Cython helper module for distance calculations.
```python
edit
file: solver.py
lines: 0-0
---
import numpy as np
from typing import Any
import numba

# This version refines the float64 Numba solution by fusing the cost calculation
# into the main simulation loop. This creates a true single-pass algorithm,
# minimizing memory access by calculating the total cost on-the-fly, which
# improves cache performance.
@numba.njit(fastmath=True, cache=True)
def _solve_and_cost_jit(initial_inventory: float, demand: np.ndarray, h: float, c: float, p: float):
    """
    A single, unified JIT-compiled function that simulates the policy and
    calculates the total cost in a single pass.
    """
    T = demand.shape[0]
    inventory = np.zeros(T, dtype=np.float64)
    orders = np.zeros(T, dtype=np.float64)
    stockouts = np.zeros(T, dtype=np.float64)
    total_cost = 0.0
    
    current_inventory = initial_inventory

    if h < 0:
        # Policy: Order everything upfront.
        total_demand = 0.0
        for i in range(T):
            total_demand += demand[i]
        
        required_order = total_demand - initial_inventory
        if required_order > 0:
            orders[0] = required_order
            total_cost += c * required_order # Cost of the single order
        
        # Simulation loop with fused cost calculation
        for t in range(T):
            inventory_after_order = current_inventory + orders[t]
            balance = inventory_after_order - demand[t]
            inv_t = max(0.0, balance)
            
            inventory[t] = inv_t
            # Stockouts will be 0 for this policy, so no need to calculate or add cost.
            current_inventory = inv_t
            
            total_cost += h * inv_t # Holding cost for the period

    elif c <= p:
        # Policy: Just-in-time (JIT), with fused cost calculation
        for t in range(T):
            demand_t = demand[t]
            order_t = max(0.0, demand_t - current_inventory)
            inv_t = current_inventory + order_t - demand_t
            
            orders[t] = order_t
            inventory[t] = inv_t
            current_inventory = inv_t
            
            # Update cost. Stockouts are 0.
            total_cost += h * inv_t + c * order_t
    
    else: # c > p and h >= 0
        # Policy: Never order, with fused cost calculation
        for t in range(T):
            demand_t = demand[t]
            stk_t = max(0.0, demand_t - current_inventory)
            inv_t = max(0.0, current_inventory - demand_t)
            
            stockouts[t] = stk_t
            inventory[t] = inv_t
            current_inventory = inv_t
            
            # Update cost. Orders are 0.
            total_cost += h * inv_t + p * stk_t

    return inventory, orders, stockouts, total_cost

class Solver:
    def solve(self, problem: dict) -> Any:
        """
        Solve the multi-period inventory management problem with a single-pass
        Numba JIT-compiled function that fuses simulation and cost calculation.
        """
        demand = np.array(problem["demand"], dtype=np.float64)
        h = float(problem["holding_cost"])
        c = float(problem["ordering_cost"])
        p = float(problem["stockout_penalty"])
        initial_inventory = float(problem["initial_inventory"])

        T = len(demand)
        if T == 0:
            return {"inventory": [], "orders": [], "stockouts": [], "total_cost": 0.0}

        if c < 0 or p < 0:
            return {"inventory": [], "orders": [], "stockouts": [], "total_cost": 0.0}

        # Call the single-pass JIT function.
        inventory, orders, stockouts, total_cost = _solve_and_cost_jit(
            initial_inventory, demand, h, c, p
        )

        return {
            "inventory": inventory.tolist(),
            "orders": orders.tolist(),
            "stockouts": stockouts.tolist(),
            "total_cost": float(total_cost),
        }
---
```