Earliest Arrival Flows with Multiple Sources

Baumann, Nadine; Skutella, Martin

doi:10.1287/moor.1090.0382

Cited by 69 publications

(54 citation statements)

References 30 publications

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“…It can be rewritten as (14) , , , : , : : 0 , , which can be rewritten again as is the objective function of P′, the proof is concluded. Figure 2 shows how the CT transformation is applied.…”

Section: Cost Transformationmentioning

confidence: 88%

“…Another evacuation optimization objective is to minimize the total travel time spent by all evacuees in the evacuation process; such a model is formulated as the minimum cost dynamic flow (MCDF) problem. Whereas solutions to the quickest flow problem minimize the time horizon, the earliest arrival flow problem aims to optimize the evacuation process (i.e., maximizing the number of evacuees reaching safety), not only at the ultimate moment of clearance time but also at every intermediate time point (14,15). Therefore, the earliest arrival flow problem is a multidimensional optimization problem on top of the quickest flow problem, exploited in several evacuation studies over the past decade (16,17).…”

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confidence: 99%

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Efficient Negative Cycle–Canceling Algorithm for Finding the Optimal Traffic Routing for Network Evacuation with Nonuniform Threats

Nassir

Zheng

Hickman

2014

Transportation Research Record: Journal of the Transportation R

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A new network flow solution method is designed to determine optimal traffic routing efficiently for the evacuation of networks with several threat zones and with nonuniform threat levels across zones. The objective is to minimize total exposure (as duration and severity) to the threat for all evacuees during the evacuation. The problem is formulated as a minimum cost dynamic flow problem coupled with traffic dynamic constraints. The traffic flow dynamic constraints are enforced by the well-known point queue and spatial queue models in a time-expanded network presentation. The key to the efficiency of the proposed method is that, for any feasible solution, the algorithm can find and can cancel multiple negative cycles (including the cycle with the largest negative cost) with a single shortest path calculation made possible by applying a proposed transformation to the original problem. A cost transformation function and a multisource shortest path algorithm are proposed to facilitate the efficient detection and cancelation of negative cycles. Zone by zone, negative cycles are canceled at the border links of the zones. The solution method is proved to be optimal. The algorithm is implemented, tested, and verified to be optimal for a midsized example problem.Over the past few decades, many human-caused and natural disasters (e.g., hurricanes, building fires, bomb threats, and chemical spills) have occurred. The increasing number and intensity of emergencies raise interest in the optimal preparation of an evacuation plan before an emergency arises. Evacuation problems have been studied extensively by many researchers in various modeling paradigms, with different selections of decision variables, objective functions, and constraint sets; moreover, the solution methods have generated a wide spectrum of approaches suitable for problem-specific purposes, contexts, capabilities, and performances.Evacuation management policies can be modeled, enhanced, and optimized with mathematical optimization techniques. Tactical decisions that provide the scope and context of the evacuation plan are made in various ways depending on the evacuation control tools available to the decision makers. Common decisions selected for optimization focus on generating evacuation advisory information, including departure times, evacuation routes, and destination choices for evacuees (1-5). Additional tactical decisions may entail optimizing traffic control and reconfiguring the network to take advantage of flexibilities in the network and create a more efficient evacuation plan (6-9).Without considering the fine details of traffic flow dynamics on roadways, an evacuation can be formulated as a general dynamic network flow problem, which optimizes the evacuation objective as a network flow problem on a dynamic network. Minimizing the network clearance time is one of the common objectives in the evacuation literature; its dynamic flow model counterpart is known as the quickest flow problem (10-13). Another evacuation optimization objective is to min...

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Section: Cost Transformationmentioning

confidence: 88%

mentioning

confidence: 99%

Efficient Negative Cycle–Canceling Algorithm for Finding the Optimal Traffic Routing for Network Evacuation with Nonuniform Threats

Nassir

Zheng

Hickman

2014

Transportation Research Record: Journal of the Transportation R

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“…Equation (1) represents total outflow from source node, equation (2) represents net flow at intermediate nodes, equation (3) represents total inflow towards sink and equation (4) represents capacity constraint. The objective is to maximize the flow as early as possible.…”

Section: Mathematical Formulation Of Earliest Arrival Flowmentioning

confidence: 99%

Earliest Arrival of Evacuees with Contraflow Approach

Gupta

Khadka

2017

J. Inst. Engineering

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Abstract:The earliest arrival flow problem sends a maximum number of evacuees as early as possible during the evacuation of people and/or property from dangerous zone to the safe zone. The contraflow approach significantly increases the capacity to send the evacuees at one hand and reduces the time the evacuation takes on the other hand. The problem has been extensively studied as an optimization problem with wide application. In this paper we briefly revisit the existing literature of the problem.

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“…The EAF problem has been solved pseudopolynomially by calculating the successive shortest paths for min-cost flow, (Wilkinson, 1971;Minieka, 1973). The EAF problem for multi-sources and a single-sink is solved with strongly polynomial time algorithm in the input plus output size, (Baumann and Skutella, 2009). …”

Section: Discrete Flows Over Timementioning

confidence: 99%

“…They show that finding a minimum cost temporally repeated flow is strongly -hard. The minimum cost flow over time is pseudo-polynomially solvable, (Baumann and Skutella, 2009). Fleischer and Skutella, (2003) consider the problem of minimizing the cost over time without intermediate storage in time-expanded networks.…”

Section: Minimum Cost Flow Problemsmentioning

confidence: 99%

Significance of Transportation Network Models in Emergency Planning of Cities

Dhamala

Pyakurel

2016

CPP

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Transportation network models within the framework of operations research have been established as one of the emerging field of research frontiers in today's very disastrous life and dense traffic system. The discrete as well as continuous flow over time models have been widely considered by social, engineering and applied scientists with wide varieties of real-life problems, like rush hour traffic and traffic management at the time of any disaster. Among the PPRR classification issues, the concentration will be given within the planning approach with transportation networks for urban cities.We present the models and solution strategies of the transportation networks that are dynamic in nature and directly apply in rush hour traffic or human-made or natural disasters in the urban cities. The difficulty levels of the varieties of algorithms, efficiencies of their solution software and the significance of the obtained solutions for the betterment of modern city plan are discussed with wide spectrum of model diversity. Among many others, we illustrate, also supporting with a case study, the impact of recent Nepal Earthquake 2015 and the meaningfulness of effective evacuation planning for saving the property and people in urban city like, Kathmandu, valley.The high performance of the technique of lane reversals in transportation or evacuation networks which has already been adopted a lot in practice, but has been analytically studied only recently are focused in this paper. Adopted this dynamic transportation strategy, the flow in the transportation can be doubled, the time can be saved significantly and many transportation arcs can be utilized for logistic supports or for emergency vehicles whenever necessary. Improved results are presented and the importance of integrated models dependent on time and vehicles is explored. The optimal solution thus obtained with contraflow, logistic supports and facility location at appropriate positions of transportation network proves the significance of these models in emergency planning.

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Earliest Arrival Flows with Multiple Sources

Cited by 69 publications

References 30 publications

Efficient Negative Cycle–Canceling Algorithm for Finding the Optimal Traffic Routing for Network Evacuation with Nonuniform Threats

Efficient Negative Cycle–Canceling Algorithm for Finding the Optimal Traffic Routing for Network Evacuation with Nonuniform Threats

Earliest Arrival of Evacuees with Contraflow Approach

Significance of Transportation Network Models in Emergency Planning of Cities

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