AbstractIn this article, we consider a situation in which a group of facilities need to be constructed in order to serve a given set of customers. However, the facilities cannot guarantee an absolute coverage to any of the customers. Hence, we formulate this problem as one of maximizing the total service reliability of the system subject to a budgetary constraint. For this problem, we develop and test suitable branch‐and‐bound algorithms and study the effect of problem parameters on solution difficulty. Some generalizations of this problem are also mentioned as possible extensi