The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Prefer Inner Join Over Left Join (modified query below): We identified that one or more left joined entities (e.g. `carrier_volumes`) are used in the 'where' clause, in a way that allows to replace it with an optimized inner join. Inner joins can be fully optimized by the database, while Left joins apply limitations on the database's optimizer.

Optimal indexes for this query:

CREATE INDEX carrier_units_idx_carrier_id_date ON "carrier_units" ("carrier_id","date");
CREATE INDEX carrier_volumes_idx_vehicle_id_date_id ON "carrier_volumes" ("vehicle_id","date","id");
CREATE INDEX carriers_idx_id ON "carriers" ("id");
CREATE INDEX units_idx_carrier_id_id ON "units" ("carrier_vehicle_id","id");
CREATE INDEX volumes_idx_value ON "volumes" ("value");

The optimized query:

SELECT
        u.id,
        cv.id 
    FROM
        units u 
    LEFT JOIN
        volumes v 
            ON v.value = u.value 
    LEFT JOIN
        carrier_units cu 
            ON cu.id = u.mccus_inspection_id 
    LEFT JOIN
        carriers c 
            ON c.id = cu.carrier_id 
    INNER JOIN
        carrier_volumes cv 
            ON cv.vehicle_id = v.id 
            AND cv.carrier_id = c.id 
    WHERE
        u.carrier_vehicle_id IS NULL 
        AND cv.id IS NOT NULL 
        AND u.id = 115215784 
        AND cv.date = cu.date