Multi-product multi-vehicle inventory routing problem with vehicle compatibility and site dependency: A case study in the restaurant chain industry

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.

Site and tree factors determining the distribution of Phellinus tremulae in Populus tremuloides in Utah, USA

Populus tremuloides Michx. is an iconic tree of the mountains of the western United States. In Utah, it very commonly suffers from white trunk rot caused by Phellinus tremulae (Bondartsev) Bondartsev & P.N.Borisov. The incidence of this disease is affected by tree and site characteristics, but the magnitude of these effects appears to be site-dependent. To minimize harvest wood loss in Utah, we determined the locally important factors that explain the wide variation in the incidence of sporocarps of Phellinus tremulae. To avoid confounding of factors, we utilized a multiple regression approach. We found that while the incidence of Phellinus tremulae sporocarps on quaking aspen was always low at high elevations, it was variable at low elevations. Our logistic regression model indicated that variation in the incidence of sporocarps at low elevations was attributable, in part, to variation in aspect, slope, environmental stress, and tree age and size. Based on these results, we recommend that harvesting at elevations below 2500 m be confined to younger trees or to sites on relatively steep, north-facing slopes. Because of site-dependency, the same general method could be used to establish harvesting criteria in other regions.