A Robust Optimization Approach for the Express Delivery Routing Problem with Demand and 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.

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

Complexity ◽

10.1155/2018/8645793 ◽

2018 ◽

Vol 2018 ◽

pp. 1-22 ◽

Cited By ~ 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.

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A Robust VRPHTW Model with Travel Time Uncertainty

Journal of Systems Science and Information ◽

10.1515/jssi-2014-0289 ◽

2014 ◽

Vol 2 (4) ◽

pp. 289-300 ◽

Cited By ~ 1

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.

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