IJIT-D-13-00007
Risk of Traffic Incident Delay inRouting and Scheduling of Hazardous Materials
Response to Reviewer#2
We would like to express our sincere appreciation to the reviewer. Wehope that the revisions made are appropriate as response to the comments and questions posed by the reviewer.
Comments:
- 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.
- 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 modelingdelays 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.
- 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.
- 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
Figure1Pseudocode 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 reflectingrisk 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.
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To transform the urban road network (N, L) intoG(V, A), each arc (i, j) Ais a shortest path pijfrom 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 withthe 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 beenmade:
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). As a result, the traffic flows of the impacted links () 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 animpacted link () (Ministry of Land, Infrastructure, Transport and Tourism, MLIT, Japan).
- 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 usesa single objective function,minimizinga 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.
- 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 theirobjective 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 beenmade:
Page 9, Column 2, Line 57 to Page 10, Column 1, Line 1
Tables 2 to 6 show impacts of parameters: number of iterations,and ρto 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.
The parameter in Table 3 is varied from to . Larger value can improve the objective values, which is evident in solutions of all scenarios for = 2 to 10. Further increase of 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 = 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.
- 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), iand j represent origin and destination vertex indices. Furthermore, the shortest path is denoted with a separate variablep with ij as the subscript.