Determining unused values in a M:N database system - mysql

Question

This problem consists of a database system relating components to their suppliers with corresponding costs, which are used to build widget assemblies.
Here is the database and tables:
CREATE DATABASE IF NOT EXISTS DB;
USE DB;
CREATE TABLE components (
c_id INT AUTO_INCREMENT NOT NULL,
name_c VARCHAR(255),
PRIMARY KEY (c_id)
);
CREATE TABLE suppliers (
s_id INT AUTO_INCREMENT NOT NULL,
name_s VARCHAR(255),
PRIMARY KEY (s_id)
);
CREATE TABLE widgets (
w_id INT AUTO_INCREMENT NOT NULL,
name_w VARCHAR(255),
PRIMARY KEY (w_id)
);
CREATE TABLE assemblies (
w_id INT,
c_id INT,
FOREIGN KEY (w_id)
REFERENCES widgets (w_id),
FOREIGN KEY (c_id)
REFERENCES components (c_id)
);
CREATE TABLE prices (
p_id INT AUTO_INCREMENT NOT NULL,
s_id INT,
c_id INT,
cost INT,
PRIMARY KEY (p_id),
FOREIGN KEY (s_id)
REFERENCES suppliers (s_id),
FOREIGN KEY (c_id)
REFERENCES components (c_id)
);
insert into components(name_c)
values('C1');
insert into components(name_c)
values('C2');
insert into components(name_c)
values('C3');
insert into components(name_c)
values('C4');
insert into components(name_c)
values('C5');
insert into components(name_c)
values('C6');
insert into suppliers(name_s)
values('S1');
insert into suppliers(name_s)
values('S2');
insert into suppliers(name_s)
values('S3');
insert into suppliers(name_s)
values('S4');
insert into suppliers(name_s)
values('S5');
insert into widgets(name_w)
values('A1');
insert into widgets(name_w)
values('A2');
insert into widgets(name_w)
values('A3');
insert into widgets(name_w)
values('A4');
insert into assemblies(w_id, c_id)
values(1,1);
insert into assemblies(w_id, c_id)
values(2,2);
insert into assemblies(w_id, c_id)
values(2,3);
insert into assemblies(w_id, c_id)
values(3,4);
insert into assemblies(w_id, c_id)
values(3,5);
insert into assemblies(w_id, c_id)
values(4,6);
insert into assemblies(w_id, c_id)
values(4,3);
insert into prices(s_id, c_id, cost)
values(1,1,121);
insert into prices(s_id, c_id, cost)
values(1,2,135);
insert into prices(s_id, c_id, cost)
values(2,2,94);
insert into prices(s_id, c_id, cost)
values(2,3,155);
insert into prices(s_id, c_id, cost)
values(3,3,178);
insert into prices(s_id, c_id, cost)
values(3,4,199);
insert into prices(s_id, c_id, cost)
values(4,4,122);
insert into prices(s_id, c_id, cost)
values(4,5,155);
insert into prices(s_id, c_id, cost)
values(5,5,133);
insert into prices(s_id, c_id, cost)
values(5,6,184);
The resulting tables are as follows:
components
c_id | name_c
1 C1
2 C2
3 C3
4 C4
5 C5
6 C6
(Note: tables components, suppliers, and widgets all defined analogously such that widgets with 1-A1, 2-A2, etc. and suppliers with 1-S1, 2-S2, etc.)
prices - list of supplier-component cost combinations
p_id s_id c_id cost
1 1 1 121
2 1 2 135
3 2 2 94
4 2 3 155
5 3 3 178
6 3 4 199
7 4 4 122
8 4 5 155
9 5 5 133
10 5 6 184
assemblies - list of components used to build the widget assemblies
w_id | c_id
1 1
2 2
2 3
3 4
3 5
4 6
4 3
For the first part, with help I was able to determine the correct query to find the minimum-cost outputs with respect to assemblies as follows (objective was to determine the minimum-cost components to build each widget assembly):
select w.name_w, sum(price_min.min_cost) as min_cost
from widgets as w
left join assemblies as a on a.w_id = w.w_id
left join (select c_id, min(cost) as min_cost from prices group by c_id) as price_min on price_min.c_id = a.c_id
group by w.name_w
order by w.w_id
Output:
name_w min_cost
A1 121
A2 249
A3 255
A4 339
However, I'm stuck trying to figure out how to determine which suppliers (name_s) are not used in this cost optimization (i.e., did not provide a competitive component price to be used in the corresponding widget-assembly build incorporating those suppliers' components). Working out on paper, I expect the following result:
name_s
S3
But I can't seem to get this result using SQL (specifically MySQL)...
Thanks in advance!

Answer 1

Modified from the query for finding the minimum cost:
select distinct s.name_s
from suppliers s
left join
prices p
on s.s_id = p.s_id
where p.s_id not in (
select distinct s_id from prices p1 -- suppliers of low cost components
inner join
(select a.c_id, price_min.min_cost
from widgets as w
left join assemblies as a on a.w_id = w.w_id
left join (select c_id, min(cost) as min_cost from prices group by c_id) as price_min
on price_min.c_id = a.c_id ) t -- component price details before sum()
on p1.cost = t.min_cost and
p1.c_id = t.c_id )