Applications Locating chemical plants Locating nuclear reactor plants Locating pollution plants Locating garbage dump sites Routing and location – routing of these applications are considered in recent years.
models Dispersion Problem (Daskin 1995) Undesirable Facility Location Problem (Daskin 1995) Hazardous Materials Routing Problem Obnoxious Facilities Location- Routing Problem Multiobjective Obnoxious Facilities Location Problem
Dispersion Problem In this problem, suppose that there are some candidate centers for installation facilities. The purpose is to find P points for locating in order that maximize the minimum distance between located facilities.
Model Assumptions The problem is investigated on the discrete network and nodes are representative of candidate points. This network is general or it’s possible to have loops. The facilities often are general. In other word, investor (government) focuses on keeping away facilities from population centers. In these cases, environmental costs and some other ones are more important than installation costs.
Model Assumptions The numbers of facilities are predetermined. All of facilities are obnoxious and should be kept away from population centers. All of facilities are similar and all of services are equal too. The installation cost is not considered. The facilities replacement is not considered. All of parameters are deterministic. The problem is formulated in static form. It means that, the problem’s inputs are not dependent to time.
Model Inputs dij: it is distance between i and j M: it is large elected digit and it is often larger than the maximum distance between candidate points P: the number of facility to locate D: the minimum distance between facilities
Model Outputs Xj : 1 if facility is installed in node j ; 0 otherwise
Objective Function and its Constraints
Undesirable Facility Location Problem In Maxisum models, the subject is locating facilities such as incinerators that, decision maker attend to far it from demand centers
Model Inputs P: the number of facilities should be located
Model Outputs (Decision Variables)
Objective Function and its Constraints
Hazardous Materials Routing Problem Hazardous materials that are briefly called HazMats, consist of explosives, flammable,substances, oxidizing substances, poisonous substances, radioactive materials, infected materials, corrosives and hazardous wastes.
Risk Evaluation for HazardousWaste Transportation Risk management activities could result in an accurate assessment of the risks and therefore it would be possible to create strategies for reduction of risk level to its lowest level.
Risk Evaluation for HazardousWaste Transportation Erkut and Verter (1998) suggested much evaluation risk models. The simplest model in this category yields the product of the accident consequences, the probability of a hazardous waste accident, activity volume.
Risk Evaluation for HazardousWaste Transportation
Generally, the accident consequences are measured by population exposure and the accident probability depends on material type and rout nature. In practice, the rout is divided to equal segments (k/m or mile) then; the consequences probability is calculated for all segments by population exposure in accident place.
Different types of risk evaluation models
Risk Equality Certainly in spite of all discussed conditions, we can not find a rout or place without any risk or any effect on the environment. Consequently, the decision maker shoulddivide the risk among segments and reach to minimum variance.
Risk Equality This subject is named “risk equality” in hazardous waste literature and can formulate in different ways. The general type of it was followed here:
Risk Equality In (14.18), N represents population of a center, y determines the number of accident casualties and constant a is less than zero. It is simply provable that, minimum equality will be obtained, when the number of accident casualties is half of population. With moving away from each side, the equality increases and in ultimate it reaches to zero value and it is best state.
Designing Optimum Routes for Material Transportation
Obnoxious Facilities Location- Routing Problem Model Assumptions The model is single commodity, i.e. a single obnoxious material is considered. The affected sites are represented as point in the plane. In this network there are some nodes that they don’t use hazardous material and they don’t produce hazardous material too, but they influenced by hazardous material transportation consequences. For each site, location and routing exposure thresholds are give
Multiobjective Obnoxious Facilities Location Problem Model Inputs