As you mentioned, your current response is quite fast already, but you could try to run all computations in one query with pgr_dijkstraCostMatrix if you need a full matrix, or recently the shortest path functions also allow so called "combinations" as input,for example https://docs.pgrouting.org/latest/en/pgr_dijkstraCost.html#combinations. This ...
Just ST_Union the results:
SELECT ST_AsEncodedPolyline(ST_Union(geom), 5) AS enc
SELECT gid AS id, source, target, ST_Length(geom) AS cost
) AS di
JOIN network AS pt
ON di.edge = pt.gid
While precision := 5 is the default, it is ...
You could have a look at the set of functions offered by pgRouting in the field of VRP http://docs.pgrouting.org/latest/en/VRP-category.html?highlight=vrp. Some additional information can be found here http://osgeo-org.1560.x6.nabble.com/pgrouting-users-Introduction-to-VRP-with-time-windows-Work-done-in-Gsoc-2014-td5197304.html and here https://github.com/...