There are some handy tricks offering a lot of possibilities already, for example these use case. Make sure to tick the option Manage advanced routes for your warehouse from Settings > Configuration > Warehouse. 

1. Configure the warehouse as Pick Pack Ship from Warehouse > Configuration > Warehouses. Select your warehouse and in Outgoing Shippings, tick the option Make packages into a dedicated location, then bring them to the output location for shipping (Pick + Pack + Ship).
2. You need to activate Technical features for your user. Then go to Warehouse > Configuration > Procurement Rules, find the Stock -> Packing Zone procurement rule. Add a fixed procurement group by changing the value in Propagation of Procurement Group to Fixed.  Create a new procurement group with Delivery Method Partial.  This will bundle the moves from Stock > Packing Zone in one big picking.  
3. In order to test, you should create several sales orders and you will see that the moves from stock > packing zone will gather in one big picking for which you can handle everything that is available at once.  From Stock > Pick you will have one assignment per SO.

This can be elaborated further as you can create different zones in the warehouse which have products with different routes. 

I tried this solution in 8.0 but I can't make it work... It looks strange to me that it's so difficult to manage the use case where you receive more than one order from a customer and wish to organize deliveries by customer (sending for example one product from order 1 and one product from order 2, then create a backorder or similar) instead of by order. This use case is the standard for all my clients...

I am also looking for a solution in Odoo 11.

If I set the procurement group to "fixed", then there is one big picking, that's right, but the delivery orders won't be grouped by customer. So if I have 3 SO from one customer, that leads to 3 delivery orders.

Any solution?

Thank you