Service caching in mobile edge computing (MEC) networks involves pre-storing computation programs on MEC servers to efficiently handle users’ computational tasks. By pre-loading these programs, service caching can significantly reduce both computation and transmission delays, addressing the diverse computational requirements of users. However, optimal caching placement is essential due to limited caching capacity, which directly impacts the efficiency of computation offloading. Proper cache placement ensures that relevant programs are readily available, thereby maximizing offloading performance and minimizing delays. This paper investigates a multi-tier MEC network consisting of caching-enabled edge servers, a cloud server, and multiple users. Users offload computational tasks to proximate edge servers, where locally cached programs facilitate immediate processing, thereby mitigating delays. When programs are absent from the cache, tasks are offloaded to the cloud, leading to additional latency. We formulate an optimization problem to minimize the overall communication and computation delay by jointly optimizing caching placement, transmission power, bandwidth allocation, and computation capacity. To tackle the complexity of this mixed-integer nonlinear programming (MINLP) problem, we propose two novel algorithms. The first is a Dinkelbach and big-M-based algorithm that reformulates the problem into a mixed-integer second-order cone programming (MI-SOCP) problem, approximating a near-optimal solution. Recognizing the computational demands of MI-SOCP, we also develop a low-complexity algorithm based on successive convex approximation (SCA) and alternating methods, which efficiently yields a high-quality sub-optimal solution. Simulation results confirm the effectiveness of the proposed algorithms in reducing network delays and emphasize the critical role of caching in improving network performance.