In this era of ubiquitous networks that become increasingly vulnerable to disruptions, network reliability has emerged as a critical issue in their design and operation. Businesses and individuals become ever more dependent on networks and demand reliable delivery of critical services every time. This paper finds Pareto optimal locations for a single facility on an existing tree network that maximizes service availability to customers by considering both the average and the lowest level of service delivery with respect to all customers. Examples are the location of decision entities on information infrastructures, servers or databases on computer networks, control systems on telecommunication networks, critical information on social networks, supply centers on supply chain networks, and location of emergency response facilities to intentional or natural disasters. Model properties are identified in decision and objective space and used to develop an efficient algorithm for finding the efficient and the non-dominated sets. Numerical examples are provided to illustrate the algorithm and to show special conditions for the efficient and non-dominated sets to be continuous.