可以将所有商品分为质数和非质数两类,并计算每种商品的占地面积。然后,将仓库的总面积作为限制条件,使用混合整数规划(MIP)来最大化仓库容量。以下是代码示例:
-- 计算每种商品的占地面积
SELECT
item_id,
CASE WHEN is_prime = 1 THEN prime_area ELSE nonprime_area END AS area
FROM
items
-- 使用MIP最大化仓库容量
WITH item_areas AS (
SELECT
item_id,
CASE WHEN is_prime = 1 THEN prime_area ELSE nonprime_area END AS area
FROM
items
),
problem AS (
SELECT
item_id,
area,
CAST(total_area / area AS INT) AS max_qty -- 计算每种商品最大可存放数量
FROM
item_areas,
(SELECT SUM(area) AS total_area FROM item_areas) -- 计算仓库总面积
),
vars AS (
SELECT item_id, INTEGER DIVISIONS FROM INTEGER DIVISIONS(0, max_qty) -- 创建一个整数变量,其值为0到最大数量
FROM problem
),
-- 最大化存储总量
SELECT MAX(SUM(qty)) AS max_storage
FROM (
SELECT
item_id,
qty * area AS used_area,
qty AS qty
FROM
problem,
vars
WHERE item_id = vars.item_id AND qty <= max_qty
) inventory
WHERE SUM(used_area) <= total_area;