The study defines a "retrieval sequencing problem" for compact storage systems where bins sit in vertical stacks and must be lifted to create a temporary tunnel so a robot can grab a target bin. The authors prove that the energy cost of a retrieval cycle depends only on the number of bins lifted. They then show that if the system has only two stacks, the optimal retrieval order can be found quickly using a polynomial‑time algorithm. For three stacks, they develop a recursive decomposition and dynamic‑programming method that solves a certain class of retrieval orders in polynomial time. The work also describes how the energy‑optimal order always has a laminar shape within each stack and discusses the potential extra savings when several bins are retrieved in a single cycle. The paper places these results in the context of previous research on robotic compact storage systems, such as AutoStore.