Fuels Transportation Network Design: Minimization of Risk Associated to Hazardous Materials Transportation

Fuels Transportation network design:

Extended Abstract

The transportation network design process of public and private companies for hazardous materials relies on optimal project selection of routes, nodes and other variables to accomplish efficiently the transportation. This network design is complicated because the difficult to optimize different goals and the large quantity of variables. The design must consider multiple criteria in order to identify the best route for the transportation. Distance between delivery locations, type and risk of hazardous materials, type of accident, area of incidence, people affected, type of vehicles used in the network and utility percentage are just few factors of the large number of variables that should be included in a network design modeling.

Colombian transportation authorities are interested in minimizing the risk involved in the transportation of hazardous material inside cities. Furthermore, private and public transporters are exploring new alternatives for minimizing costs of transportation. To design the transportation network of hazardous materials we propose a multi objective routing problem that includes costs of distances between delivery locations, risk involved in materials transported, and utility percentage of trucks used, to accomplish an efficient design of the network that can satisfy different goals of actors involved. In addition a risk valuation methodology is proposed to determine the risk involved in the transportation of hazardous materials.

To solve the multi objective routing problem an evolutionary genetic algorithm is proposed. The model minimizes simultaneously the risk and the distance of the transportation network and maximizes the percentage of utility of trucks used in the network.

In order to show the risk valuation methodology and possible results obtained from the genetic algorithm, a case study of Bogota fuel transportation network is presented in this paper.

Research

Different models have been proposed for the transportation of hazardous materials network design. Kara and Verter (2004) designed an integer optimization bi-level model. This model consists in classifying materials in different groups according to the risk associated. In its second level, the routing problem is developed by finding the required paths to minimize the transportation cost. In the first level, the objective function is the minimization of the total risk in the transportation network. However, the model presents some disadvantages that limit its use. The network design does not consider the interactions between different materials groups, because the optimization problem is independent for each material group. Additionally, the bi-level optimization model presents problems in the optimum stability and multiple solutions are produced over the network.

After this model, Erkut and Alp (2007) designed a one level transportation optimization problem avoiding the use of a bi-level formulation. In their model, the objective function was centered in risk minimization of the overall network. The model does not include the transportation cost, assuming that there is just one path between the origin and the destination point, path that is generated using a heuristic method. These are significant disadvantages for this model, because it can not be guaranteed that an optimum for the cost has been found.

Another model was proposed by Bianco and Caramia et al (2008). They proposed a bi-level flow model for hazmat transportation network design. The model objective function looks for risk minimization in both levels. In the design, authors divide the network in some regions looking to assign with equity the risk to each one according to government specifications for the global network. After that, in the other level of the optimization problem, they were focused in the minimization of risk in each region, trying to assign to each route a specific risk. However, the authors never considered the transportation cost of each route, just being interested in risk manipulation.

Risk valuation

Risk valuation involves the following steps:

1. Frequency and probability analysis.

Historical accidents reported in Aria?Barpie database were analyzed in order to establish deterministic probabilities of event occurrence after an accident. The events considered in fuels truck accidents were explosion, pool and pool fire. Using probabilistic trees and fault trees of accident sequences different scenarios were proposed. Those scenarios are the key to formulate the possible consequences of an accident.

2. Consequence modeling.

Incidence Area.

Once the probability of possible events has been determined, it is required to estimate the area affected if an accident has occurred. Those areas were estimated according to each event, material and different quantities transported, depending on each type of truck.

Population affected.

In addition, the methodology uses a square grid of 0.4 km over Bogota's map. The grid overlaps different layers to identify all kind of infrastructures (schools, hospitals, commercial buildings, etc) in order to estimate how many people are located in each square.

Using this information and the incidence area given an accident for each event, an estimation of the number of people affected in each square is determined. Then, the sum of the people affected in each square is calculated to establish the total population affected in the entire route.

3. Risk calculation.

Finally, risk is estimated using the next equation.

Where:

k: Possible event (Explosion, pool and pool fire)

R_ij:Risk for the segment i j.

P_k : Probability an event k.

N_ijk: Number of people in danger in the risk diameter of an event

Genetic Algorithm

Introduction

Heuristics are faster algorithms that can find good solutions in reasonable time (without optimal guarantee). This is an advantage from exact methods where time grows up exponentially with the size of the problem.

The genetic algorithm starts with a random initial solution. Then, nodes are extracted randomly from the route. Finally nodes are added to the route again in different positions producing a new solution.

The genetic algorithm uses different strategies to approach to a better result.

Crossover

Mutation rate

Results

First, the algorithm was used to optimize each goal individually in order to show the difficulty to achieve different objectives at the same time. Those results are presented in the next graph.

Minimizing risk criteria means the lowest risk in the network but not the best distance as it is possible. Similarly, if distance is the optimization goal, it is possible to establish the route with the shortest distance. However the shortest distance does not assure the lowest risk. For that reason, the design of this kind of networks is a difficult challenge due the different interests. What we propose is to extend the algorithm for different optimization objectives, to produce a complete network design that integrates each goal of interest.

What it is finally expected is to perform a graph that combines all objectives in order to identify different points in where solution can offer lower cost and higher utility of trucks with a tolerable risk.

Conclusion

Finally, this work will look to satisfy the interest of government and private transportation companies, contributing to increase safety in the city road network and to make equal distribution of the risk involved in hazardous material transportation. It is important to remark, that this analysis could apply for others transport systems in where the road network, population density and infrastructure can be known and analyzed particularly for each system. Furthermore, the heuristic approximation, the risk matrix, probability events and methodology can be used as a general approach for every transportation network analysis.