Algorithm for units allotment to the customers based on preferences
This is not an answer.

This post is used to show that the problem in the question is not the same as the stable marriage problem. There are three differences. 


The number of customers might not be the same as the number of units. However, there is an asymmetrical version of stable marriage problem as described here. So this is not a critical difference.
Each customer may not have ranked all units. However, it can be understood each customer ranks all units not explicitly ranked lower than all units ranked. So this is not a critical difference.
None of the unit ranks the customers at all. In stable marriage problem, each man ranks all women while each woman ranks all men. This is an important difference that makes every algorithm for stable marriage problem not applicable directly for the current situation.  


We could assign a random (strict) ranking (and possibly different) of customers to each unit. Now we can apply any algorithm for stable marriage problem to our customers and units.
We could assume that all units rank all customers indifferently. We can then find super-stable or strongly-stable "marriage" between customers and units. 


Although we could assign rankings of the customers to the units so as to apply the algorithms for stable marriage problem, it adds an extra dimension of condition as well as probably extra steps in the solution algorithms. It might/should be better that the problem and its solution is kept as it is, agnostic to any rankings of the customers by the units.


(This post could be changed to an answer should the question be updated with the addition of a priority table by units.)