A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

[EN] This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the vehicles are not required to return to the depot after completing a service. In this new problem, the demands of customers are fulfilled by a heterogeneous fixed fleet of vehicles having various capacities, fixed costs and variable costs. This problem is an important variant of the open vehicle routing problem (OVRP) and can cover more practical situations in transportation and logistics. Since this problem belongs to NP-hard Problems, An approach based on column generation (CG) is applied to solve the HFFOVRP. A tight integer programming model is presented and the linear programming relaxation of which is solved by the CG technique. Since there have been no existing benchmarks, this study generated 19 test problems and the results of the proposed CG algorithm is compared to the results of exact algorithm. Computational experience confirms that the proposed algorithm can provide better solutions within a comparatively shorter period of time.Yousefikhoshbakht, M.; Dolatnejad, A. (2017). A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem. International Journal of Production Management and Engineering. 5(2):55-71. doi:10.4995/ijpme.2017.5916SWORD557152Aleman, R. E., & Hill, R. R. (2010). A tabu search with vocabulary building approach for the vehicle routing problem with split demands. International Journal of Metaheuristics, 1(1), 55. doi:10.1504/ijmheur.2010.033123Anbuudayasankar, S. P., Ganesh, K., Lenny Koh, S. C., & Ducq, Y. (2012). Modified savings heuristics and genetic algorithm for bi-objective vehicle routing problem with forced backhauls. Expert Systems with Applications, 39(3), 2296-2305. doi:10.1016/j.eswa.2011.08.009Brandão, J. (2009). A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem. 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PASA: A Priori Adaptive Splitting Algorithm for the Split Delivery Vehicle Routing Problem

The split delivery vehicle routing problem (SDVRP) is a relaxed variant of the capacitated vehicle routing problem (CVRP) where the restriction that each customer is visited precisely once is removed. Compared with CVRP, the SDVRP allows a reduction in the cost of the routes traveled by vehicles. The exact methods to solve the SDVRP are computationally expensive. Moreover, the complexity and difficult implementation of the state-of-the-art heuristic approaches hinder their application in real-life scenarios of the SDVRP. In this paper, we propose an easily understandable and effective approach to solve the SDVPR based on an a priori adaptive splitting algorithm (PASA). The idea of a priori split strategy was first introduced in Chen et al. (2017). In this approach, the demand of the customers is split into smaller values using a fixed splitting rule in advance. Consequently, the original SDVRP instance is converted to a CVRP instance which is solved using an existing CVRP solver. While the proposed a priori splitting rule in Chen et al. (2017) is fixed for all customers regardless of their demand and location, we suggest an adaptive splitting rule that takes into account the distance of the customers to the depot and their demand values. Our experiments show that PASA can generate solutions comparable to the state-of-the-art but much faster. Furthermore, our algorithm outperforms the fixed a priori splitting rule proposed by Chen et al. (2017)

A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups

The Vehicle Routing Problem with Discrete Split Deliveries and Pickups is a variant of the Vehicle Routing Problem with Split Deliveries and Pickups, in which customers’ demands are discrete in terms of batches (or orders). It exists in the practice of logistics distribution and consists of designing a least cost set of routes to serve a given set of customers while respecting constraints on the vehicles’ capacities. In this paper, its features are analyzed. A mathematical model and Tabu Search algorithm with specially designed batch combination and item creation operation are proposed. The batch combination operation is designed to avoid unnecessary travel costs, while the item creation operation effectively speeds up the search and enhances the algorithmic search ability. Computational results are provided and compared with other methods in the literature, which indicate that in most cases the proposed algorithm can find better solutions than those in the literature

Robust vehicle routing in disaster relief and ride-sharing: models and algorithms

In this dissertation, the variants of vehicle routing problems (VRPs) are specifically considered in two applications: disaster relief routing and ride-sharing. In disaster relief operations, VRPs are important, especially in the immediate response phase, as vehicles are an essential part of the supply chain for delivering critical supplies. This dissertation addresses the capacitated vehicle routing problem (CVRP) and the split delivery vehicle routing problem (SDVRP) with uncertain travel times and demands when planning vehicle routes for delivering critical supplies to the affected population in need after a disaster. A robust optimization approach is used for the CVRP and the SDVRP considering the five objective functions: minimization of the total number of vehicles deployed (minV), the total travel time/travel cost (minT), the summation of arrival times (minS), the summation of demand-weighted arrival times (minD), and the latest arrival time (minL), out of which we claim that minS, minD, and minL are critical for deliveries to be fast and fair for relief efforts, while minV and minT are common cost-based objective functions in the traditional VRP. In ride-sharing problem, the participants\u27 information is provided in a short notice, for which driver-rider matching and associated routes need to be decided quickly. The uncertain travel time is considered explicitly when matching and route decisions are made, and a robust optimization approach is proposed to handle it properly. To achieve computational tractability, a new two-stage heuristic method that combines the extended insertion algorithm and tabu search (TS) is proposed to solve the models for large-scale problems. In addition, a new hybrid algorithm named scoring tabu search with variable neighborhood (STSVN) is proposed to solve the models and compared with TS. The solutions of the CVRP and the SDVRP are compared for different examples using five different metrics in which the results show that the latter is not only capable of accommodating the demand greater than the vehicle capacity but also is quite effective to mitigate demand and travel time uncertainty, thereby outperforms CVRP in the disaster relief routing perspective. The results of ride-sharing problem show the influence of parameters and uncertain travel time on the solutions. The performance of TS and STSVN are compared in terms of solving the models for disaster relief routing and ride-sharing problems and the results show that STSVN outperforms TS in searching the near-optimal/optimal solutions within the same CPU time

A dynamic ridesharing dispatch and idle vehicle repositioning strategy with integrated transit transfers

We propose a ridesharing strategy with integrated transit in which a private on-demand mobility service operator may drop off a passenger directly door-to-door, commit to dropping them at a transit station or picking up from a transit station, or to both pickup and drop off at two different stations with different vehicles. We study the effectiveness of online solution algorithms for this proposed strategy. Queueing-theoretic vehicle dispatch and idle vehicle relocation algorithms are customized for the problem. Several experiments are conducted first with a synthetic instance to design and test the effectiveness of this integrated solution method, the influence of different model parameters, and measure the benefit of such cooperation. Results suggest that rideshare vehicle travel time can drop by 40-60% consistently while passenger journey times can be reduced by 50-60% when demand is high. A case study of Long Island commuters to New York City (NYC) suggests having the proposed operating strategy can substantially cut user journey times and operating costs by up to 54% and 60% each for a range of 10-30 taxis initiated per zone. This result shows that there are settings where such service is highly warranted