<p>Dynamic changes in water demand induce high flow/pressure fluctuations and increase electricity costs in the drinking water distribution system. The secondary water supply system (SWSS) is proposed to address the issues. The SWSS opens the inlet valves of the tanks and communities to stagger the storage of water among the tanks during off-peak periods with low electricity costs, and uses the tanks to supply water directly to residents during peak periods, reducing flow/pressure fluctuations and electricity costs. In this paper, we consider the tank regulation and storage problem (TRSP) in the SWSS and propose a novel mixed integer programming (MIP) formulation that determines the ON/OFF status of the inlet valves of the tanks and communities to minimize flow/pressure fluctuations and electricity costs during peak periods over a given planning horizon. Due to the large problem size, the TRSP cannot be solved within a reasonable time by state-of-the-art MIP solvers. To address this challenge, we develop an efficient Lagrangian decomposition approach that exploits the structure of the problem, dividing it into smaller subproblems that can be solved independently. Moreover, we enhance the Lagrangian decomposition approach with two improvement heuristics to find high-quality feasible solutions. Computational results on a testbed of 31 real-world TRSP instances demonstrate the efficacy of the proposed MIP formulation and the proposed Lagrangian decomposition approach.</p>