Classify an algorithm to maximize number of tips used by liquid handlers concurrently
If we focus solely on the dispensing operation, we can formulate this as a Set Cover Problem. Namely, we are given a set of tips that have already aspirated some source liquids and we are asked to minimze the number of dispense operations to fill up a given column of target vials. In this simplified set up, we aren't allowed to go back and aspirate new source liquids and we assume that the target volumes are less than the tip capacities.
To set this up as a Set Cover Problem, we treat each target vial as its own element in the universe. We associate with each configuration of the tips (e.g.: position and tip spacing) a set corresponding to the target vials that may be covered by this configuration, taking into account the aspirated fluids in each tip (i.e.: a target vial is &quot;covered&quot; by a tip configuration, if there is a tip that has aspirated the appropriate fluid and positioned over that vial).