Distribute a number of tasks into multiple days (scheduling)
Suppose that you have 200 tasks to be scheduled in 100 days. The capacity of each day is 4. Task 1 has capacity 1, task 200 has capacity 3, and tasks 2 to 199 have capacity 2. 

In any solution, task 1 and task 200 have to be assigned to the same day. That means that there is a big violation of the ordering of the tasks. So even if you could solve your problem effectively, the best solution (which is indeed hard to compute) might still be very bad. 

Even worse, even if we totally disregard the ordering constraint, there could still be no solution. Consider two days of capacity 7 and four tasks of length 2, 3, 3, 6, respectively. The total length is 14 = 2 $\times$ 7, yet there is no way to separate the tasks into two days of capacity 7. 
This problem (in which the precedences are not taken into account) is called the Partition problem, so that is one keyword you might want to search for. Unfortunately,  checking if a solution to the Partition problem exists is a strongly NP-complete problem whenever you have 3 days or more.