IJIT-D-13-00007
Risk of Traffic Incident Delay in Routing and Scheduling of Hazardous Materials
RESPONSE TO REVIEWER #2
We would like to express our sincere appreciation to the reviewer. We hope that the revisions made
are appropriate as response to the comments and questions posed by the reviewer.
Comments:
1. This paper presents a formulation for hazardous materials routing that uses an objective
function that is a weighted average of the population exposure and the "congestion-based"
cost. The constraints of the formulation are those associated with the typical vehicle
routing problem with time windows. The formulation is solved with an ant colony
optimization approach.
We acknowledge the observation of the reviewer.
2. The consideration of congestion when a hazmat accident occurs has been little explored in
the literature.
Detail analysis of congestion or the traffic incident delay considering only HazMat incident is not
available in literature. In the manuscript, we have included some literatures on modeling delays
of general traffic incidents. Further details in the literature review are added in the revised
manuscript. Following are the changes:
Page 2 Column 2 Line 46 to Line 59
Queueing (17, 20, 21) and shock wave (22) models have been proposed to determine delay
consequence of an incident in the road network. The models require detail information of the
traffic situation such as information on the occurrence of the incident, split of the traffic volumes
among various links of the network, detailed traffic arrival rate, road capacity reduction and the
incident duration. The models are suitable for after incident evaluations however are not
convenient to estimate the potential path consequences in HazMat-related Operations Research
(OR) studies. So far no routing study in literature has included the consequence of traffic
incident delay, which is the topic of this study.
3. Editing is still needed but the text is mostly understandable.
We acknowledge reviewer’s comment and have edited the manuscript with the help of a native
speaker.
4. A) The pseudo code on page 3 should include how the calculation of traffic incident delay is
performed, otherwise the pseudo code should be removed as it is not very informative.
Following reviewer’s comment, we have revised Figure 1 as follows:
Page 4 Column 1
Figure 1 Pseudocode for traffic incident delay attribute
B) Along these lines, I find the some of the related calculation discussion in section 3.1
difficult to follow. In the first paragraph in section 3.1 that converts the road network into
G(V,A), what is the cost metric of the shortest path? Is this some combination of the
exposure and congestion based risk or is it based on time? Are the hazmat trucks always
considered full of the chemical? Are the consequences adjusted for the volumes of hazmat
materials after a delivery has been made or if the original shipment does not require a full
truckload? In equations (5) and (6) summing the exposure and "congestion based" delays
along all arcs of a path may be the easiest calculation but it is not realistics as an incident
will not take place on all links of the path simultaneously.
Thus, the consequences are
inflated using the presented calculation method.
Some changes have been made in the manuscript to clarify the cost matrices used in determining
the shortest paths while converting the road network to the HVRPTW graph. In consistent with
the relevant literature on HazMat routing, we have considered a full truck load on each link
reflecting risk in the worst case scenario, and have summed up the risks of the links to determine
the risk of the arcs. We have added the explanation and the references in the current manuscript.
Following are the changes:
Page 3, Column 2, Line 22 to Line 26
In consistent with the relevant literatures in HazMat routing (9 to 12), the paper considers risk
consequences of the links for the worst case scenario. Therefore, for estimating the risk attributes,
each link in the network is assumed to have a full truck load.
Page 4, Column 2, Line 38 to Line 50
To transform the urban road network (N, L) into G(V, A), each arc (i, j)  A is a shortest path pij
from vertex i to j containing allied links of the road network. The arcs were obtained beforehand
using labeling algorithm. All arcs (i, j) except arcs (i, 0) that ends at depot vertex) were obtained
as shortest paths to minimize the total risk, sum of the population-based and the
congestion-based risks of the associated links in the road network. Trips returning back to the
depot were assumed empty and risk free. So, arcs (i, 0) were obtained as shortest paths to
minimize the total travel time of the associated links.
Page 5, Column 1, Line 11 to Line 15
The attributes are obtained as the sum of the corresponding terms of all the links that belongs to
the shortest path pij, consistent with the common practice in OR literatures in HazMat routing
(19).
C) Further, it is not quite clear how the congestion based consequence is determined.
Congestion should be based on re-routed volumes and propagation of queues. On which
network is the incident assumed to occur, the road network or G(V,A)? Which links are
then considered closed and how are the delays/new travel times calculated?
Following reviewer’s comment, we have revised the discussion on determining the congestion
based consequence. The incidents are assumed to occur on the links of the road network. The link
with the incident is assumed to be closed resulting delays (an increase of travel time) to traffic
flows in surrounding links (impacted links). For incident on a link in the network, all the
remaining 574 links are assumed to be impacted. Increases in the travel times given in Table 1 are
assumed values for illustration purpose. It is acknowledged that this paper considers only rough
estimate of the impact of the incident based congestion. A complete analysis of this phenomenon
(such as simulation of before and after scenario) is beyond the scope of this research. Following
changes have been made:
Page 3, Column 2, Line 11 to Line 12
The incident effects on all the links in the road network are handled at this stage in (N, L).
Page 3, Column 2, Line 49 to Line 59
When a HazMat incident occurs on a link l in the road network, the link with the incident is
considered closed. This closure causes re-routing of traffic flows of the surrounding links
(impacted links l ' L ). As a result, the traffic flows of the impacted links ( vl  ) suffer delays,
given by increase in the travel times of the links. Equation 1 is the expression to determine loss
per day due to congestion on an impacted link l ( l ) (Ministry of Land, Infrastructure,
Transport and Tourism, MLIT, Japan).
5. On page 9, lines 48-49 (col. 1), please be more specific about the difference between the
authors' previous work and this one. "solution construction" is vague.
The specific differences between our previous algorithm (10) with the current algorithm are
given in Page 6, Column 1, Line 9 to Line 21. Following reviewer’s comment, we have also
revised the explanation on Page 9 as follows:
Page 9, Column 1, Line 52 to 56
The ACS algorithm in the present study uses a single objective function, minimizing a weighted
sum of the two (population-based and congestion-based) risk costs in the HVRPTW; whereas,
our earlier work (10) is based on Pareto optimization.
6. The results of the sensitivity analysis could be interpreted more precisely. For example,
the discussion of table 4 says that solution quality for all three scenarios improved with
increasing beta until it is equal to 1. Really, this is only a transition from 0.5 to 1.0. Also,
what is meant by quality? The objective function value for two of the scenarios remains
the same. Only the first one decreases, although the computation time decreases for all
the two that did not have a lower objective function value. So is quality the ratio of
objective function value to computation time? This discussion also says that the first two
scenarios were insensitive with an increase in beta, but the objective function values
worsened and the computation time was variable.
Following reviewer’s comment, we have revised the discussion in the sensitivity analysis. We
have primarily compared the solutions for their objective values. Computation times are used
mainly to compare solutions with same objective values. To avoid the confusion, we have
reported the computation time for the full run rather than the computation time of attaining the
optimal value, as was the case in our previous manuscript. Following changes have been made:
Page 9, Column 2, Line 57 to Page 10, Column 1, Line 1
Tables 2 to 6 show impacts of parameters: number of iterations, Mˆ ,  , q0 , and ρ to the objective
values when varied between [10000, 25000], [2, 20], [0.5, 2], [0.1, 0.9] and [0.1, 0.9],
respectively.
Page 10, Column 1, Line 7 to Page 10, Column 2, Line 13
An increasing number of iterations provides more opportunities for solutions with lower
objective values to be computed. This holds true for all the three scenarios in Table 2 till the
number of iterations is increased to 20000. Further increase of the value from 20000 to 25000
continues to increase the computation time while the objective values remain insensitive.
ˆ  Cˆ /10 to Ĉ . Larger M̂ value can
The parameter M̂ in Table 3 is varied from M
improve the objective values, which is evident in solutions of all scenarios for M̂ = 2 to 10.
Further increase of M̂ from 10 to 20 is however insignificant for the current problem instance.
On the other hand, larger values can cause significant increase in the computation time as the
solutions of M̂ = 20 correspond to the most computationally expensive category.
The sensitivity test of β in Table 4 shows enhancement of objective values in all three
scenarios with increase of β from 0.5 to 1. The computation times are also reduced. But, the
objective values of the solutions are observed to be deteriorated with its further increase. This is
because ant favors larger savings in the objective with increased value of β as it is the parameter
that determines the relative effect of pheromone versus the risk cost saving. However, higher the
value of β, more is the chance that the algorithm will be trapped in a local optimum.
Large q0 favors exploitation of the information from previous best solution. Table 5 shows
the insensitiveness of the minimization process of the objectives and the computation times in
the three scenarios of the current instance with the q0 values. The results show best objective
values in all three scenarios for q0 values of 0.3 and 0.9.
Table 6 shows the impacts of various values of evaporation coefficient ρ on the objective
value.
7. Using the notation ij for both arcs and paths is confusing.
In representation of both the network (N, L) and the graph G(V, A), i and j represent origin and
destination vertex indices. Furthermore, the shortest path is denoted with a separate variable p
with ij as the subscript.