Optimization of Routes for Hazardous Materials Transportation

A Case Study of Fuel Deliveries in Lisbon

Duarte Correia

, Marta Castilho Gomes

, Alexandre B. Gonçalves

and Sílvia Shrubsall

Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, Lisboa, Portugal

CERIS, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, Lisboa, Portugal

Keywords: Hazardous Materials Transportation, Bi-level Linear Programming, Road Safety in Urban Areas,

Geographical Information Systems (GIS).

Abstract: This study aims at contributing to increase road safety by expanding knowledge on how to identify safe

urban routes for Hazardous Materials that are commercially doable. A bi-level linear model was

implemented in GAMS modelling software considering fuel distribution data and the road network for the

city of Lisbon. Its first level consists in road risk minimization whereas the second level aims at maintaining

the economic viability of the itineraries. This work expands the research of Rodrigues et al. (2015) by

increasing: (1) the comprehensiveness of the road data, and (2) the complexity of the analysis by including,

besides resident population, hospital and school users potentially affected by an accident, and by comparing

different itineraries and the computational time needed to solve the model. The work analyses much more

comprehensive data than those found in previous studies in the literature and was successful in identifying

optimal solutions, most of which in short computational time. This suggests that this methodology can be

used by the industry to identify routes for fuel distribution in urban environments. In the future, the routes

generated by the model will be compared with routes currently used in fuel distribution.

1 INTRODUCTION

Societies nowadays are extremely dependent on

Hazardous Materials (HazMats), which fulfil a wide

range of purposes, including energy supply to cities,

vehicles and industries (Erkut et al., 2007).

This study deals with the transportation of fuels,

which are also classified as HazMats (Verter and

Kara, 2008). Even though the number of accidents

involving HazMats is relatively small –

approximately four times less than the probability of

being struck by lightning (Transportation and

Infrastructure Committee, 2011), when accidents

involving HazMats occur, the severity of damages

(both personal, environmental and material) can be

high (Erkut et al., 2007).

The objective of this research is to contribute to

increase road safety through the identification of

routes for the transportation of HazMats that

minimize the risk of accident without compromising

the economic feasibility of the industry. It builds

upon and continues the research of Rodrigues (2015)

with further challenges of the road network given

that here the entire city of Lisbon (Portugal) was

analysed as the case study.

2 OPTIMIZATION MODEL

In order to identify safe routes for the transportation

of HazMats, the bi-level linear programming model

presented by Kara and Verter (2004) was

implemented. This model features two problems,

which are hierarchically solved. The problems are

related and correspond to different entities, in which

the choice that one makes is directly influenced by

the choice of the other (Bianco et al., 2009). In this

particular case, it is acceptable to consider that the

regulator, whose objective is to minimize total risk

(defined as total population exposure) is in the outer

level. Then the transportation companies correspond

to the inner level and their objective is to minimize

total cost. It is thus clear that the outer level chooses

a network where risk is controlled and the inner

level then chooses the minimum cost path from

those available (Kara and Verter, 2004).

Correia, D., Gomes, M., Gonçalves, A. and Shrubsall, S.

Optimization of Routes for Hazardous Materials Transportation - A Case Study of Fuel Deliveries in Lisbon.

DOI: 10.5220/0005711703570361

In Proceedings of 5th the International Conference on Operations Research and Enterprise Systems (ICORES 2016), pages 357-361

ISBN: 978-989-758-171-7

357

In Kara and Verter (2004) model, the authors

consider that the consequences of an accident

involving HazMats occur until a given distance from

the place where the accident happened. This means

that when a truck is driving through a given arc, only

the people within that distance to the arc are exposed

to risk. In this model, total risk is the measure used

by the regulator and total time spent travelling is

used by companies for selecting the routes.

However, this can easily be adapted and other risk

and economic measures can be used (Rodrigues,

2014).

The outer problem decision regards which arcs

should be made available for the transportation of

HazMats and has risk as the objective function.

Since the inner problem consists in choosing which

routes will actually be used for transportation, the

binary decision variables from the outer problem

constitute parameters for the inner problem. This is

essentially the minimum cost flow problem, which

minimizes the objective function time (or distance)

travelled.

To solve the bi-level model a transformation was

applied using the Karush-Kuhn-Tucker (KKT)

conditions. The resulting model is of the mixed

integer linear programming (MILP) type, having as

the objective function the one of the outer problem

(total risk).

A detailed description of both the bi-level linear

programming model as well as the MILP model can

be found in Rodrigues (2014) and Rodrigues et al.,

(2015).

3 CASE STUDY DESCRIPTION

This work follows the methodology that was

presented by Rodrigues (2014) but with a different

road network for the Lisbon case study, which

translates into a larger problem size.

The methodology for data collection and

processing as well as the problem simplifications

were similar to the one described in Rodrigues et al.

(2015), and so only the main differences are

highlighted in this section.

Data characterising the fuel distribution includes

petrol stations and direct clients in Lisbon

municipality, supplied by the company. The amount

of daily distribution during 2013 was provided and

then aggregated to obtain annual amounts.

Rodrigues (2014) used a network for a specific

district of Lisbon (Olivais parish). This dataset was a

very detailed network, with 654 nodes and 6 origin-

destination (O-D) pairs. For the present work, the

road network for the entire Lisbon city (mapped in a

desktop geographical information system (GIS),

namely ArcGIS 10, was analyzed but considering

only the higher hierarchy routes. Even though only a

part of the roads are featured, this network consists

of 2685 arcs and 2285 nodes, which represents a

significant increase compared to the networks that

have been used previously in the reviewed literature.

There is a total of 26 O-D pairs, which also

represents a considerable increase in complexity of

the problem to be solved.

Figure 1: Road network and census tracts in Lisbon.

Figure 1 represents the road network plus the

geographical information referencing basis (census

tracts), from which the resident population was

determined (Census 2011 data).

The locations of the destinations were given by

the petrol company as a list of latitude and longitude

GPS coordinates and were georeferenced in the

ArcGIS software. Then there was the need to find

out which arcs were the closest to each of these

locations, which was done using the nearest function

available in the software. Figure 2 shows in blue the

destinations operating in 2013 (26 in total) and in

black those that operated in 2012 but were shut

down during 2013 (6 in total).

Figure 2: Destinations in the road network.

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Besides the resident population, people in

schools and hospitals nearby network arcs were also

considered (based on facility capacity data provided

by Lisbon Municipality). This encompassed 124

public and private schools and 25 public hospitals,

depicted in Figures 3 and 4.

Figure 3: Location of schools in the road network.

Figure 4: Location of hospitals in the road network.

The incorporation of high-density population

centres such as schools or hospitals in models

aiming to calculate safe routes for HazMats were not

found in the literature review. Authors such as Kara

and Verter (2004) had previously discussed the

importance of its consideration.

4 COMPUTATIONAL TOOLS

The MILP model was implemented in GAMS

modelling system and solved with CPLEX version

12.4.0.0 on a 2.8GHz Intel Core i7 4GB RAM.

The data was extracted from ArcGIS version 10

to an MS Excel spreadsheet, which was then read by

GAMS. Functionalities xls2gms and gdx that make

the connection between Excel and GAMS regarding

model input and output, respectively, were used.

After solving the model, an Excel output file is

written with a binary table where the arcs used in the

route to each destination are expressed.

As a measure of the problem data size, there are

over 1200 columns and 6600 rows in the largest

table in the Excel input data file.

5 CASE STUDY RESULTS AND

DISCUSSION

Results for the case study were obtained based on

four different sets of population figures assigned to

the network arcs. The MILP model was solved for

each of these sets henceforth named “population

combination”. For each network arc, two population

figures were computed using the GIS software: the

population living nearby each arc (the “arc

population”) and the fluctuating population due to

the schools and public hospitals considered.

Table 1 displays the four different ways these

populations figures were combined in a weighted

sum to obtain the final value for each arc, which was

the one used when solving the MILP model (i.e., the

actual model parameter). For solutions A through C

a 300 m buffer was applied, while for D the distance

of 800 m was used. Thus, comparison of objective

function values should consider that the population

that was accounted for varies among solutions.

Table 1: Weighted population combinations tested.

Solution Population combinations

A 1 x arc population + 0 x hosp_school

B 0 x arc population + 1 x hosp_school

0.5 x arc population +

0.5 hosp_school

D 0.5 x arc population + 0.5 x hosp_school (800m)

Table 2 shows the numeric characteristics of the

model (which depend solely on the road network)

and Table 3 shows the results when solving the

model to optimality: number of iterations, CPU time

and objective function value.

Table 2: Numeric characteristics of the model.

No. of variables No. of binary variables No. of constraints

271,842 72,603 1,824,265

Table 3: Summary of results.

Solution No. of iterations CPU time (s)

Objective

function value

A 76,155 304.6 341,974

B 1,242,987 5,010.1 706,069

C 586,489 706.0 286,199

D 28,681 29.8 316,173

Optimization of Routes for Hazardous Materials Transportation - A Case Study of Fuel Deliveries in Lisbon

359

It is worthwhile noticing that the even though the

dimension of the model was the same, CPU times

ranged from 30 sec observed for solution D to

approximately 5 min and 12 minutes in solutions A

and C, respectively, and up to 1 hour and 20 minutes

in solution B (where only school and hospital

population is considered). In solution B, population

is concentrated only in a set of points and the impact

of not having a more homogeneously distributed

population relatively to the network arcs was

decisive upon the time required to compute the

optimal solution.

Table 4 summarizes, for each solution, the

average values of population exposure, travel time

and number of arcs per route (chosen to each

destination). The average number of trucks per

destination is 112.12 per year. This number is

constant for each destination as it only depends on

the quantity of fuel delivered (information provided

by the company). Hence, it is a model parameter,

unlike the population exposure, travel time and

number of arcs per route that were computed based

on the value of the decision variables after solving

the model.

It is clear that solution B, the one that accounts

for hospitals and schools population only, stands out

for presenting higher values for time and number of

arcs per route. On the other hand, solution D, with a

weight of 0.5 for each type of population and a

buffer of 800 meters, is the solution where the

population associated with each arc, when solving

the MILP model, is more uniform, therefore it is also

the one with lowest values for time and number of

arcs. Solutions A and C present similar values and

intermediate between those of solutions B and D.

Table 4: Summary of results (average values per

destination).

Solution

Population exposure

(average)

Time (min.)

(average)

No. of arcs

used

(average)

A 13,152 14.76 79.88

B 27,156 26.96 129.23

C 11,007 15.18 74.23

D 12,160 12.29 55.58

Table 5 compares the different solutions for a

particular destination (destination 23, for which the

number of trucks used is 271). This is located in the

the middle of the city, far away from the route origin

(A1 highway entrance in Lisbon). While there are

only minor changes along the route for solutions A,

C and D, there is a major change for solution B.

Population exposure is the lowest for solutions C

and D, the ones that have a split contribution from

each population source. Solution A, the one where

all the population from the census tracts is taken into

account, is the one with the least amount of people

exposed. The one where the most people are

exposed is solution B, which is also the longest route

(average travel time and number of arcs used).

Table 5: Comparison of model outputs for destination 23.

Solution Population exposure Time (min.)

No. of arcs

used

A 25,018 19.43 97

B 32,663 50.51 225

C 20,429 18.58 89

D 21,377 15.67 70

Figure 5 illustrates the route for destination 23

and solution A.

Figure 5: Route for solution A and destination 23.

6 CONCLUSIONS

There is a consensual belief on the importance of

minimizing risks associated to HazMats

transportation, particularly in urban areas, where

increasingly more people live. The growing

complexity and density of urban environments is

pressing the development of reliable and practical

tools to support the industry identifying safe and

economically viable HazMats routes. However, the

research found in the literature is still limited

particularly in the complexity of the analyzed road

networks. Aiming at contributing to increase urban

road safety and urban economic growth by

specifically supporting safe and feasible fuel

distribution, this work studied the whole city of

Lisbon, capital of Portugal, using up-to-date

distribution data provided by one petrol company

operating in the city.

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A Geographical Information System (GIS)

platform was used in which the road network and

population were represented for Lisbon. Information

extracted from the GIS was subsequently introduced

into the mathematical modelling software GAMS.

The adopted MILP model successfully identified

optimal routes, i.e. those with least population

exposure to risk while still keeping economic

viability. Results indicate that with an optimized

method of representing population exposure along

the road network arcs it is possible to compare

population exposure for different routes and identify

options on best routes for HazMats distribution.

The presented model can be further improved by

refining the road network representation, the

information on both resident and commuter adjusted

daytime population distribution and include traffic

data. Once these recommended improvements are

built-in and adequate model calibration has been

performed there is a real potential for industry

adoption of the described methodology for HazMats

route planning.

Regarding the impact of this work, the company

is very interested in gaining more control upon the

fuel distribution routes, which are currently a

decision of the subcontracted transportation

companies. With the proposed model application,

risk and cost are made explicit and both can be

considered when deciding the routes.

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