Today, organizations outsource their logistics activities to third-party logistics (3PL) providers to focus more on their key capabilities. A 3PL company is an external provider that controls, manages, and provides logistics services for the manufacture. The success of a 3PL company tremendously depends on the design of its logistics network. This paper studies the problem of designing a reliable hub-and-spoke network using consolidation hubs considering disruption risks and product perishability. To lessen network failure risks, disruption is dealt with using backup facilities, fortification of facilities, and multiple sourcing simultaneously. This problem is formulated as a bi-objective MINLP model that decides on the location, number, and fortification of main and backup hubs and distribution centers, the location of backup facilities, the inventory of perishable products and the back-ordering of products to minimize the cost and time of the supply chain network simultaneously. One of the highlights of this model is that disruption of hubs and distribution centers, which have the role of storing and distributing products, affects product perishability because the storing and distributing conditions and requirements are not met under facilities disruption. The model is linearized, and the uncertainty of facility disruption probabilities is dealt with by using credibility-based possibilistic programming so that an optimal solution can be provided. A major pharmaceutical distribution 3PL company in Iran is considered as a practical application of the model to validate and solve it. Numerical results reveal the relation between product perishability and disruption of the storing facilities and the 3PL policy in distribution, storage, back-ordering, and fortification.