Inventory Allocation

Your challenge is to implement an inventory allocation function that determines how to fulfill an order from one or more warehouses.

Problem Description:

You are given an order in the form of a dictionary where each key is a product name (a string) and the value is the quantity required (an integer). You are also given a list of warehouses. Each warehouse is represented as a dictionary with a name (string) and an inventory (a dictionary where each key is a product name and the value is the available quantity).

Implement a function with the following signature (the exact signature may vary based on your programming language):

allocate_order(order, warehouses) -> shipping_plan

The function should return a shipping plan represented as a list of dictionaries. Each dictionary in the list should have the following format:

{
  "name": <warehouse_name>,
  "items": { <product1>: <quantity_shipped>, <product2>: <quantity_shipped>, ... }
}

Rules & Requirements:

1. Complete Fulfillment: The order must be completely fulfilled. If it is impossible to fulfill it (because the total available quantity for any product is less than the required amount), the function should return an empty list (or equivalent in your language).

2. Warehouse Selection: You may use as many warehouses as needed, but try to minimize the number of warehouses used in the shipping plan if possible.

3. Partial Shipments: For each product, you may ship partial amounts from one warehouse and the rest from another.

4. Order of Warehouses: You can assume that warehouses are listed in an order. If multiple allocations are possible, you can follow the given warehouse order to decide from which warehouse to pull the inventory.

5. Output Format: The shipping plan should be a list of shipments. Each shipment is a dictionary with the warehouse's name and an items dictionary of product allocations from that warehouse. Do not include a warehouse in the shipping plan if no items are allocated from that warehouse.

Example:

Input:

order = { "apple": 5, "banana": 5, "orange": 5 }
warehouses = [
    { "name": "OWD", "inventory": { "apple": 5, "orange": 10 } },
    { "name": "DM", "inventory": { "banana": 5, "orange": 10 } }
]

Possible Output:

[
    { "name": "OWD", "items": { "apple": 5, "orange": 5 } },
    { "name": "DM", "items": { "banana": 5 } }
]

If the order cannot be fully allocated, return an empty list.

Write the complete function to solve this problem. You are free to decide on any additional helper structures or functions you might need.