As a current trend in Artificial Intelligence (AI), large foundation models are increasingly employed as the core of AI services. However, even after training, serving such models at scale remains a challenging task due to their heavy resource footprints, particularly in terms of GPU memory. While recent works revealed unique characteristics of systems serving foundation models that distinguish them from traditional distributed computing systems, there is still a lack of fundamental understanding of the underlying system management problems. This work aims at addressing this gap by extracting a novel problem of "server chain composition" via block placement and cache allocation for serving chainstructured jobs with large memory footprints, which models a fundamental problem in serving large foundation models through pipeline parallelism. After showing the NP-hardness of the optimal solution, the focus is turned to developing scalable algorithms with guaranteed performance under state-of-the-art load balancing. Application of the proposed solution to a distributed large language model (LLM) serving system shows significant reduction of response times compared to state-of-the-art solutions.