scholarly journals A Robust VRPHTW Model with Travel Time Uncertainty

2014 ◽  
Vol 2 (4) ◽  
pp. 289-300 ◽  
Author(s):  
Fengmei Yang ◽  
Yakun Wang ◽  
Wenyan Yuan ◽  
Jian Li
Keyword(s):  
Travel Time ◽  
Time Window ◽  
Optimal Solution ◽  
Ant System ◽  
Routing Problem ◽  
Numerical Example ◽  
Time Uncertainty ◽  
Hard Time ◽  
Robust Model ◽  
Travel Time Uncertainty

AbstractVehicle routing problem with hard time window (VRPHTW) is extremely strict in travel time. However, the travel time is usually uncertain due to some stochastic factors such as weather and other road conditions. It is an important issue to take travel time uncertainty into consideration in VRPHTW. This paper develops a robust VRPHTW model to cope with time uncertainty. We use robustness method of Bertismas to consider the maximum change of uncertain travel time in the degree of robustness set by decision maker. The probability that the optimal solution violates constraints is derived. The violated probability shows that the robustness of VRPHTW model can reach a satisfactory level. Finally, one modified max-min ant system algorithm is proposed to solve this problem and one numerical example is conducted to illustrate the model and the algorithm. Both theory analysis and numerical example show the effectiveness of the proposed robust model.

scholarly journals The Electric Vehicle Routing Problem with Time Windows under Travel Time Uncertainty

2021 ◽  
Vol 2095 (1) ◽  
pp. 012032
Author(s):  
Dan Wang ◽  
Hong Zhou
Keyword(s):  
Travel Time ◽  
Vehicle Routing ◽  
Electric Vehicle ◽  
Electric Vehicles ◽  
Vehicle Routing Problem ◽  
Search Algorithm ◽  
Time Windows ◽  
Routing Problem ◽  
Time Uncertainty ◽  
Travel Time Uncertainty

Abstract Due to environmental friendliness, electric vehicles have become more and more popular nowadays in the transportation system. For many express companies, it is more and more important to meet the predetermined time window of customers. The uncertainty in travel times often causes uncertain energy consumption and uncertain recharging time, thus electric vehicles may miss the time windows of customers. Therefore, this paper addresses the electric vehicle routing problem with time windows under travel time uncertainty, which aims to determine the optimal delivery strategy under travel time uncertainty. To solve this problem, a robust optimization model is built based on the route-dependent uncertainty sets. However, considering the complexity of the problem, the robust model can only solve few instances including the small number of customers. Thus, a hybrid metaheuristic consisting of the adaptive large neighborhood search algorithm and the local search algorithm is proposed. The results show that the algorithm can obtain the optimal solution for the small-sized instances and the large-sized instances.

scholarly journals A Time-Dependent Fuzzy Programming Approach for the Green Multimodal Routing Problem with Rail Service Capacity Uncertainty and Road Traffic Congestion

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Yan Sun ◽  
Martin Hrušovský ◽  
Chen Zhang ◽  
Maoxiang Lang
Keyword(s):  
Sensitivity Analysis ◽  
Exact Solution ◽  
Travel Time ◽  
Time Dependent ◽  
Mixed Integer ◽  
Programming Approach ◽  
Routing Problem ◽  
Time Uncertainty ◽  
Capacity Uncertainty ◽  
Travel Time Uncertainty

This study explores an operational-level container routing problem in the road-rail multimodal service network. In response to the demand for an environmentally friendly transportation, we extend the problem into a green version by using both emission charging method and bi-objective optimization to optimize the CO2 emissions in the routing. Two uncertain factors, including capacity uncertainty of rail services and travel time uncertainty of road services, are formulated in order to improve the reliability of the routes. By using the triangular fuzzy numbers and time-dependent travel time to separately model the capacity uncertainty and travel time uncertainty, we establish a fuzzy chance-constrained mixed integer nonlinear programming model. A linearization-based exact solution strategy is designed, so that the problem can be effectively solved by any exact solution algorithm on any mathematical programming software. An empirical case is presented to demonstrate the feasibility of the proposed methods. In the case discussion, sensitivity analysis and bi-objective optimization analysis are used to find that the bi-objective optimization method is more effective than the emission charging method in lowering the CO2 emissions for the given case. Then, we combine sensitivity analysis and fuzzy simulation to identify the best confidence value in the fuzzy chance constraint. All the discussion will help decision makers to better organize the green multimodal transportation.

scholarly journals Updates to the Regional Seismic Travel Time (RSTT) Model: 2. Path-dependent Travel-time Uncertainty

2021 ◽  
Vol 178 (2) ◽  
pp. 313-339
Author(s):  
Michael L. Begnaud ◽  
Dale N. Anderson ◽  
Stephen C. Myers ◽  
Brian Young ◽  
James R. Hipp ◽  
...  
Keyword(s):  
Travel Time ◽  
Random Effects ◽  
Mean Squared Error ◽  
Random Effects Model ◽  
Location Error ◽  
Crust And Upper Mantle ◽  
Time Uncertainty ◽  
Uncertainty Estimates ◽  
Event Location ◽  
Travel Time Uncertainty

AbstractThe regional seismic travel time (RSTT) model and software were developed to improve travel-time prediction accuracy by accounting for three-dimensional crust and upper mantle structure. Travel-time uncertainty estimates are used in the process of associating seismic phases to events and to accurately calculate location uncertainty bounds (i.e. event location error ellipses). We improve on the current distance-dependent uncertainty parameterization for RSTT using a random effects model to estimate slowness (inverse velocity) uncertainty as a mean squared error for each model parameter. The random effects model separates the error between observed slowness and model predicted slowness into bias and random components. The path-specific travel-time uncertainty is calculated by integrating these mean squared errors along a seismic-phase ray path. We demonstrate that event location error ellipses computed for a 90% coverage ellipse metric (used by the Comprehensive Nuclear-Test-Ban Treaty Organization International Data Centre (IDC)), and using the path-specific travel-time uncertainty approach, are more representative (median 82.5% ellipse percentage) of true location error than error ellipses computed using distance-dependent travel-time uncertainties (median 70.1%). We also demonstrate measurable improvement in location uncertainties using the RSTT method compared to the current station correction approach used at the IDC (median 74.3% coverage ellipse).

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