Shell-and-tube latent heat thermal energy storage units employ phase change materials to store and release heat at a nearly constant temperature, deliver high effectiveness of heat transfer, as well as high charging/discharging power. Even though many studies have investigated the material formulation, heat transfer through simulation, and experimental studies, there is limited research dedicated to the storage unit design methodology. This study proposes a comprehensive methodology that includes the material assessment with multi-attribute decision-making and multi-objective decision-making tools, epsilon-NTU method, and cost minimization using Genetic Algorithm. The methodology is validated by a series of experimental results, and implemented in the optimization of a storage unit for solar absorption chiller application. A unit cost of as low as USD 8396 per unit is reported with a power of 1.42 kW. The methodology proves to be an efficient, reliable, and systematic tool to fulfill the preliminary design of shell-and-tube LHTES before the computational fluid dynamics or detailed experimental studies are engaged.