postgres-列总和的约束（无触发器）

我想将父实体的子实体的某个属性的总和限制为该父实体的某个属性。我想使用PostgreSQL而不使用触发器来执行此操作。下面是一个例子；

假设我们有一个带有volume属性的箱子。我们要用较小的盒子填充它，它们具有自己的体积属性。板条箱中所有盒子的体积总和不能大于板条箱的体积。

我想到的想法是这样的：

CREATE TABLE crates (
  crate_id int NOT NULL,
  crate_volume int NOT NULL,
  crate_volume_used int NOT NULL DEFAULT 0,

  CONSTRAINT crates_pkey PRIMARY KEY (crate_id),

  CONSTRAINT ukey_for_fkey_ref_from_boxes 
    UNIQUE (crate_id, crate_volume, crate_volume_used),

  CONSTRAINT crate_volume_used_cannot_be_greater_than_crate_volume 
    CHECK (crate_volume_used <= crate_volume),

  CONSTRAINT crate_volume_must_be_positive CHECK (crate_volume >= 0)
);



CREATE TABLE boxes (
  box_id int NOT NULL,
  box_volume int NOT NULL,

  crate_id int NOT NULL,
  crate_volume int NOT NULL,
  crate_volume_used int NOT NULL,

  id_of_previous_box int,
  previous_sum_of_volumes_of_boxes int,
  current_sum_of_volumes_of_boxes int NOT NULL,

  id_of_next_box int,

  CONSTRAINT boxes_pkey PRIMARY KEY (box_id),

  CONSTRAINT box_volume_must_be_positive CHECK (box_volume >= 0),

  CONSTRAINT crate_fkey FOREIGN KEY (crate_id, crate_volume, crate_volume_used) 
    REFERENCES crates (crate_id, crate_volume, crate_volume_used) MATCH SIMPLE
    ON UPDATE CASCADE ON DELETE NO ACTION DEFERRABLE INITIALLY DEFERRED,

  CONSTRAINT previous_box_self_ref_fkey FOREIGN KEY (id_of_previous_box, previous_sum_of_volumes_of_boxes) 
    REFERENCES boxes (box_id, current_sum_of_volumes_of_boxes) MATCH SIMPLE
    ON UPDATE CASCADE ON DELETE NO ACTION DEFERRABLE INITIALLY DEFERRED,
  CONSTRAINT ukey_for_previous_box_self_ref_fkey UNIQUE (box_id, current_sum_of_volumes_of_boxes),
  CONSTRAINT previous_box_self_ref_fkey_validity UNIQUE (crate_id, id_of_previous_box),

  CONSTRAINT next_box_self_ref_fkey FOREIGN KEY (id_of_next_box) 
    REFERENCES boxes (box_id) MATCH SIMPLE
    ON UPDATE CASCADE ON DELETE NO ACTION DEFERRABLE INITIALLY DEFERRED,
  CONSTRAINT next_box_self_ref_fkey_validity UNIQUE (crate_id, id_of_next_box),

  CONSTRAINT self_ref_key_integrity CHECK (
    (id_of_previous_box IS NULL AND previous_sum_of_volumes_of_boxes IS NULL) OR
    (id_of_previous_box IS NOT NULL AND previous_sum_of_volumes_of_boxes IS NOT NULL)
  ),

  CONSTRAINT sum_of_volumes_of_boxes_check1 CHECK (current_sum_of_volumes_of_boxes <= crate_volume),
  CONSTRAINT sum_of_volumes_of_boxes_check2 CHECK (
    (previous_sum_of_volumes_of_boxes IS NULL AND current_sum_of_volumes_of_boxes=box_volume) OR
    (previous_sum_of_volumes_of_boxes IS NOT NULL AND current_sum_of_volumes_of_boxes=box_volume+previous_sum_of_volumes_of_boxes)
  ),

  CONSTRAINT crate_volume_used_check CHECK (
    (id_of_next_box IS NULL AND crate_volume_used=current_sum_of_volumes_of_boxes) OR
    (id_of_next_box IS NOT NULL)
  )
);

CREATE UNIQUE INDEX single_first_box ON boxes (crate_id) WHERE id_of_previous_box IS NULL;
CREATE UNIQUE INDEX single_last_box ON boxes (crate_id) WHERE id_of_next_box IS NULL;

我的问题是这是否是一种方法，以及是否有更好的方法（减少混乱，更优化等）。还是我应该坚持使用触发器？

提前致谢。