The quick delivery of emergency road services (ERS) to rescue disabled vehicles is a significant task for maintaining the meticulously planned logistics and transportation network in modern society. The location optimization of service base shops of ERS is an effective strategy for minimizing the waiting time of ERS users. For the optimization in real ERS situation, we must consider the effects of various uncertain factors such as trouble situations, shop characteristics, and backup service. Additionally, straightforward incorporation of such variables to location optimization problems causes computational complexity due to the calculation of higher-order nonlinear discrete optimization. The study presents a novel and simple analytical framework to incorporate the various factors in real ERS situations to reduce the waiting time of ERS users. In an experiment using the actual records of Bridgestone Corporation's emergency road service in Japan, we demonstrate that the proposed method successfully yields an equivalent result to the solution by the strict expected value optimization without high computational costs and reduces the waiting time by up to 27.0% relative to the conventional method.