Maximal Overlap of Rectangles

Find the maximal overlap of rectangles so, that every selected rectangle covers the full width of the overlap area.

A selected rectangle can be larger than the overlap area, but not smaller.

Problem Parameters:

• a set of rectangles aligned on the x-axis
• rectanges can have different heigt
• rectangles show arbitrary overlap

Model

Parameters

$$ i \in [1..N],\ \text{ index: N rectangles }\\ s_i \in R^+,\ \text{ start of rectangle \(i\) }\\ e_i \in R^+,\ \text{ end of rectangle \(i\) }\\ h_i \in R^+,\ \text{ height of rectangle \(i\) }\\ M \in R^+,\ \text{ Big-M constant, upper limit for x }\\ $$