Before i begun, i would like to clear a fact that Productivity is FULLY & TOTALLY dependent upon the person who is delivering.
Irrespective of number of working hours, we must provide a healthy environment to the people who are working and we can then notice that even after working for 10 hours, productivity is still at the Highest Level.
I have personally FELT & SEEN it myself in both cases when i was working for a company just as an employee and also when I was and am the CEO of the company and handling people.
I think Logistics is a 24x7 process even when the delivery time is from 10-10 and you said it well that you have to do a million things at the same time for a long time.
Try to automate as much as possible, involve technology as much as possible BUT we must not forget the best machine is a HUMAN BEING. Maintaining Human with Machines will improve the productivity of both drastically.
There is no proven formula of Increased productivity but when the employee feel comfortable in his/her work and at the same time when company is getting good results then we can definitely measure productivity and by scaling the no. of hours a person is working.