Offloading computation based on mobile edge computing paradigms can augment the computational capabilities of resource-scarce mobile devices. However, the capacity limitations of edge servers constrain the performance improvement achieved through computation offloading. In this paper, we consider a three-tier computation offloading schema with multiple users, edge servers and cloud servers. Computation can be offloaded from mobile devices to edge servers or can be further offloaded to remote cloud servers if necessary. Since a number of mobile devices connected to edge servers will share a common wireless communication network, which may contain both uplink and downlink channels, the assignment of bandwidth assignment the channels also constrains the performance improvement of computation offloading. In this paper, the problems of how to determine the offloading strategy and of how to assign the bandwidth are jointly studied and formulated as a programming problem to minimize the average application response time. We analyze the joint problem and further transform it into a piecewise convex programming problem. We propose an efficient algorithm that can find the optimal solution. Extensive experiments demonstrate that our algorithm significantly outperforms previous algorithms. The experimental results also show that the performance of our algorithm is highly robust.