In brief
Combining several tasks can reduce distance and time with a cold engine. The benefit depends on the actual route.
Useful to know
FuelEconomy.gov lists two reasons for planning several tasks in a single trip: as little distance traveled as possible and as little cold-engined movement. [1] This is an organizational solution, not an addition to the car.
Example of conditional distances: three separate two-way routes of 8 km each mean a total of 24 km. If a realistic combined route is 18 km, the difference is 6 km. This is only arithmetic of the specified routes; it does not prove specific liters of saved fuel.
Before you merge the tasks, check their order and the times that the places are available. The shortest line on a map is not necessarily an executable route. It is also not necessary to travel by car for a task that can be solved in another suitable way.
Use your actual distances instead of carrying someone else's percentage. So you can see what exactly has changed - kilometers, number of cold departures or both.
Sources
For further detail and to check the information: