Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and Cut

This paper studies the location-routing problem of emergency facilities with time window under demand uncertainty. We propose a robust mathematical model in which uncertain requirements are represented by two forms: the support set defined by cardinal constraint set. When the demand value of rescue point changes in a given definition set, the model can ensure the feasibility of each line. We propose a branch and price cutting algorithm, whose pricing problem is a robust resource-constrained shortest path problem. In addition, we take the Wenchuan Earthquake as an example to verify the practicability of the method. The robust model is simulated under different uncertainty levels and distributions and compared with the scheme obtained by the deterministic problem. The results show that the robust model can run successfully and maintain its robustness, and the robust model provides better protection against demand uncertainty. In addition, we find that cost is more sensitive to uncertainty level than protection level, and our proposed model also allows controlling the robustness level of the solution by adjusting the protection level. In all experiments, the cost of robustness is that the routing cost increases by an average of 13.87%.

Optimal Electric Bus Scheduling under Travel Time Uncertainty: A Robust Model and Solution Method

With the increasing adoption of electric buses (e-buses), e-bus scheduling problem has become an essential part of transit operation planning. As e-buses have a limited battery capacity, e-bus scheduling problem aims to assign vehicles to timetabled service trips on the bus routes considering their charging demand. Affected by the dynamic operation environment, the travel time and energy consumption of the e-buses often display considerable randomness, resulting in unexpected trip start delays and battery energy shortages. In this paper, we addressed the e-bus scheduling problem under travel time uncertainty by robust optimization approaches. We consider the cardinality constrained uncertainty set to formulate a robust multidepot EVSP model considering trip time uncertainty and partial recharging. The model is developed based on the dynamic programming equations that we formulated for trip chain robustness checking. A branch-and-price (BP) algorithm is devised to generate provably high-quality solutions for large-scale instances. In the BP algorithm, an efficient label setting algorithm is developed to solve the robust resource-constrained shortest path subproblem. Comprehensive numerical experiments are conducted based on the bus routes in Shenzhen to demonstrate the effectiveness of the suggested methodology. The robustness of the schedules was evaluated through Monte Carlo simulation. The results show that the trip start delay and battery energy shortage caused by the travel time uncertainty can be effectively reduced at the expense of an increase in the operational cost. A trade-off should be made between the reduction in infeasibility rate and increase in operational cost to choose a proper uncertainty budget.

A heuristics pulse algorithm with relaxation pruning strategy for resources re-initialized UAV path planing

Path planning is the basis and prerequisite for unmanned aerial vehicle (UAV) to perform tasks, and it is important to achieve precise location in path planning. This paper focuses on solving the UAV path planning problem under the constraint of system positioning error. Some nodes can re-initiate the accumulated flight error to zero and this type of scenario can be modeled as the resource-constrained shortest path problem with re-initialization (RCSPP-R). The additional re-initiation conditions expand the set of viable paths for the original constrained shortest path problem and increasing the search cost. To solve the problem, an effective preprocessing method is proposed to reduce the network nodes. At the same time, a relaxed pruning strategy is introduced into the traditional Pulse algorithm to reduce the search space and avoid more redundant calculations on unfavorable scalable nodes by the proposed heuristic search strategy. To evaluate the accuracy and effectiveness of the proposed algorithm, some numerical experiments were carried out. The results indicate that the three strategies can reduce the search space by 99%, 97% and 80%, respectively, and in the case of a large network, the heuristic algorithm combining the three strategies can improve the efficiency by an average of 80% compared to some classical solution.

Shift Planning Under Delay Uncertainty at Air France: A Vehicle-Scheduling Problem with Outsourcing

Airlines must operate many jobs in airports, such as passenger check-in or runway tasks. In airlines’ hubs, airlines generally choose to perform these jobs with their own agents. Shift planning aims at building the sequences of jobs operated by the airline agents and has been widely studied given its impact on operating costs. The impact of delayed flights is generally not taken into account despite the propagation of flight delays along these sequences: If a flight is late, then the agents doing the corresponding jobs are delayed, and may arrive late to their next jobs and delay the corresponding flights. Since delay costs are much higher than the costs of outsourcing jobs, if the agent who is supposed to operate a job is still working elsewhere when the job begins, then airlines tend to outsource the job to their own dedicated team or to a third party. We introduce a stochastic version of the shift-planning problem that takes into account outsourcing costs due to delay. It can be seen as a natural stochastic generalization of the vehicle-scheduling problem in which delayed jobs are outsourced. We propose a column-generation approach to solve it, whose key element is the pricing subproblem algorithm, modeled as a stochastic resource-constrained shortest-path problem. Numerical results on Air France industrial instances show the benefits of using our stochastic version of the shift-planning problem and the efficiency of the solution method. Moving to the stochastic version enables Air France to reduce total operating costs by 3.5%–4.8% on instances with more than 200 jobs, and our algorithm can solve to near optimality instances with up to 400 jobs.

On Accuracy of Approximation for the Resource Constrained Shortest Path Problem

The paper we considers the Resource Constrained Shortest Path problem (RCSP). This problem is NP- hard extension of a well-known shortest path problem in the directed graph G = (V;E). In the RCSP problem each arc e from E has a cost w(e) and additional weight functions ri(e); i = 1; : : : ; k, which specifying its requirements from a finite set of resource. A polynomial time ϵ-approximation algorithm RevTree based on node labeling method is presented in the paper. The main advantage of the RevTree algorithm over existing ones is its ability to produce ϵ approximation of the RCSP problem in O(jV j2) time. The present paper provides a proof of complexity and aproximation of RevTree algorithm