Obnoxious Facility Location

Yang,Fan

Supervisor:

contents

brief

Applications

Locating chemical plants Locating nuclear reactor plants Locating pollution plants Locating garbage dump sites Routing and location – routing of these a

pplications are considered in recent years.

models

Dispersion Problem (Daskin 1995)Undesirable Facility Location Problem

(Daskin 1995) Hazardous Materials Routing ProblemObnoxious Facilities Location-Routin

g ProblemMultiobjective Obnoxious Facilities L

ocation 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 k

ept away from population centers. All of facilities are similar and all of services ar

e 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 me

ans that, the problem’s inputs are not dependent to time.

Model Inputs

dij: it is distance between i and jM: it is large elected digit and it is often l

arger than the maximum distancebetween candidate pointsP: the number of facility to locateD: the minimum distance between faciliti

es

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

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 should divide 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

Model Outputs

Obnoxious Facilities Location-Routing Problem

Model Assumptions The model is single commodity, i.e. a single obnoxi

ous material is considered. The affected sites are represented as point in the p

lane. In this network there are some nodes that they do

n’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

Model Inputs

Model Outputs

Mathematical Model

Model Inputs

Model Outputs

Multiobjective Obnoxious Facilities Location Problem

Model Inputs

Model Outputs

前景理论的应用

谢谢！