Abstract
The disaster response routes play a crucial role in transporting injured people and goods during the 72 golden hours after disaster. These routes connect the major disaster relief centers. Prior identification of the disaster response routes for a city enables the response teams to reach the disaster locations quickly and conduct relief and rescue operations without being obstructed by the outbound flow of evacuees from the city. These routes should not generally be used by the public unlike the evacuation routes. In this paper, a multi-objective stochastic disaster response routes design problem is presented. In this study, with the goal of reducing vulnerability, the disaster response routes network can be protected against disaster scenarios to maintain its connectivity using more independent routes. An exact approach including a bounded objective function method for considering the multi-objective functions, including the network factors (OD connectivity, vulnerability, and management) and an exact method (branch-and-cut) for solving the proposed model are suggested. The results for Sioux-Falls and Tehran networks show the effectiveness of the model.
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Abbreviations
- A :
-
Set of all links of transportation network, a
- Ā :
-
Set of road links that are candidates of the network protection strategies, ā ⊂ A
- \(\rlap{-} A\) :
-
Set of suggested links, \(\rlap{-} a \subset A\)
- B :
-
Budget for the DRRsN protection
- b :
-
Budget plan, the fraction of the full network protection budget (B)
- C ̄a :
-
Protection cost, cost for protecting link ā
- c ̄a :
-
Retrofit percentage for candidate link ā
- \(C_{\rlap{-} a}\) :
-
Design cost, cost for adding suggested link \(\rlap{-} a\)
- \(cs_{\rlap{-} a}\) :
-
1 if suggested link \(\rlap{-} a\) is used, and 0 otherwise
- \(d_{od}^s\) :
-
Number of unconnected disaster response trips (o, d) under scenario s
- E a :
-
Maximum permitted number of paths traversing link a
- f ā :
-
Optimum protection level of link ā
- K :
-
Set of coverage points, kg ∈ K denotes the type of k)
- L :
-
Maximum allowable length for the DRRsN
- l a :
-
Length of link a
- M :
-
A large enough positive number
- N :
-
Set of all nodes, n
- N g :
-
Number of cover points with type g
- \(N_{od}^s\) :
-
Number of access routes that should provide multiple connections between each OD pair under scenario s
- OD :
-
Set of origin-destination, (o, d)
- P s :
-
Probability of scenario s
- \(p_{\bar{a}}^s\) :
-
Survival probability of link ā under scenario s
- \(\bar{p}_{\bar{a}}^s\) :
-
Survival probability of link ā under scenario s after allocating the protection cost
- \(q_{\bar{a}}^s\) :
-
Survival probability of link ā under scenario s after complete protection
- R :
-
Set of all routes, r
- S :
-
Set of all disaster scenarios, s
- T r :
-
Travel time of route r
- t a :
-
Travel time of link a
- \(w_a^s\) :
-
Number of paths traversing link a (path-link) under scenario s
- \(x_r^s\) :
-
1 if route r under scenario s is used, and 0 otherwise
- y a :
-
1 if link a is used, and 0 otherwise
- \(z_k^g\) :
-
1 if cover point k with type g is used, and 0 otherwise
- \(\delta_r^a\) :
-
Parameters for link-path incidence relationships. If link a is on route r, \(\delta_r^a=1\); otherwise \(\delta_r^a=0\).
- \(\delta_r^{od}\) :
-
Parameters for OD point-path incidence relationships. If route r connects point o to d, \(\delta_r^{od}=1\); otherwise, \(\delta_r^{od}=0\)
- \(\delta_a^k\) :
-
Parameters for cover point-link incidence relationships. If link a covers point, k \(\delta_a^k=1\); otherwise, \(\delta_a^k=0\)
- ∝ g :
-
Required coverage of points with type g
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Shariat Mohaymany, A., Nikoo, N. Designing Large-Scale Disaster Response Routes Network in Mitigating Earthquake Risk Using a Multi-Objective Stochastic Approach. KSCE J Civ Eng 24, 3050–3063 (2020). https://doi.org/10.1007/s12205-020-1844-x
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DOI: https://doi.org/10.1007/s12205-020-1844-x