We study an inventory routing problem (IRP) for the restaurant chain. We proposed a model a multi-product multi-vehicle IRP (MMIRP) with multi-compatibility and site-dependency (MMIRP-MCSD). The problem was formulated as a mixed integer programming (MIP). This model is difficult to solve because it is a problem that integrates MMIRP, a multi-compartment vehicle routing problem (MCVRP), and a site dependent VRP (SDVRP), each of which is difficult even by itself. Therefore, in this study, we proposed three-stage Math Heuristics based on the cluster-first and route-second method. In the numerical experiment, verification was performed using actual data, and knowledge on the decision making of the optimum vehicle type was obtained.