I'd like to ask about if there's an existing type of problems that fits to my question. (Searching it for a while but cannot get to the point)
Basic Problem Description:
Given a sequenced list (order fixed) of elements:
I need to group them into several bins (like the img below) so that the sum of each group fits in certain constraints -- i.e. lower, upper bound
The objective is to maximize the total return
V = SUM(v_i) of all groups -- each group will have value
v_i depends on the sum of all its sub-elements.
- Since the total number of groups is undefined, how to formulate this problem?
- Is there an existing type of OP or MIP problem like this to refer to?
An additional requirement for the basic version of the question is, the center of some bins/groups need to locate at a serious of fixed location -- say, one need to center at the 5th element, another need to center at the 30th element, etc.
- Is there a proper way to formulate it?
- Again, references will be appreciated.