Locating dangerous goods with constant and variable impact radius

Making decisions about dangerous goods positioning is crucial when it is necessary to minimize environmental risks. In this paper, a specific problem of locating various kinds of dangerous goods (with different characteristics) has been considered. Such goods should be located in a known discrete set of potential storage sites, under condition of the minimum safety distance (MSD) between selected locations. The existence of the MSD is a consequence of the possibility that dangerous goods transfer their undesirable effects to the objects in the neighborhood. The objective here is to maximize the quantity of different kinds of dangerous goods stored meanwhile respecting MSDs. For some dangerous goods, the MSD may be determined as a constant value, which depends only on the dangerous goods' characteristics. On the other hand, the MSD may vary depending on quantity and characteristics of particular dangerous goods. Mixed integer linear programming models are proposed for these two types of MSDs. The spirit of the anti-covering location problem (ACLP) is present in the proposed formulations and thus these models can be viewed as a modification and extension of the ACLP. Finally, a randomly generated numerical example has been used to verify and illustrate the proposed models.