Capacitated facility location problems study the location of capacitated facilities and the possible customer assignment to the facilities. These problems have the additional requirement that the total demand of allocated customers should be less than the capacity of the facility to which they are assigned. We study a variant of this problem in which some customers cannot be served using some facilities. Formally, the problem is defined as there is a set of customers with individual demands who must be served through opening a set of facilities. Each open facility has an exogenous capacity that must be utilised to serve eligible customers. Customers have a neutral preference for some facilities, excluding the incompatible facilities, to which they can be allocated. We present an Integer Linear Programming based mathematical formulation for the problem. The formulation minimises facility opening cost while ensuring that all customers are assigned to open facilities, respecting the capacity of the facilities and compatibility requirement between the customers and the facilities. Furthermore, we also present a Logic-Based Benders Decomposition solution approach for the problem. We develop a set of feasibility cuts to aid the Logic-Based Benders Decomposition approach. Finally, we perform extensive computational results to show the usefulness of our solution approaches.