Article

# A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows

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## Abstract

A heuristic algorithm is described for a time-constrained version of the advance-request, multi-vehicle, many-to-many Dial-A-Ride Problem (DARP). The time constraints consist of upper bounds on: (1) the amount of time by which the pick-up or delivery of a customer can deviate from the desired pick-up or delivery time; (2) the time that a customer can spend riding in a vehicle. The algorithm uses a sequential insertion procedure to assign customers to vehicles and to determine a time schedule of pick-ups and deliveries for each vehicle. A flexible objective function balances the cost of providing service with the customers' preferences for pick-up and delivery times close to those requested, and for short ride times. Computational experience with the algorithm is described, including a run with a real database of 2600 customers and some 20 simultaneously active vehicles. The scenario for the application of the algorithm is also discussed in detail.

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... The study of dial-a-ride problems started with work of Wilson et al. [7] who examined solutions to dial-a-ride systems in North American cities (Haddonfield, NJ and Rochester NY). This work dates back to 1971 and was improved in a muchcited publication by Jaw et al. [8]. The authors consider time windows on departure or arrival and use an insertion heuristic which builds up schedules for the vehicles by the successive insertion of transportation requests. ...
... MCLIH solves a capacitated vehicle routing problem (CVRP) on the mini-clusters V. To that end, it links the miniclusters to a single traveling salesman tour that is then split into the respective vehicle routes. Subsequently, a greedy insertion heuristic (GIH) based on the ones in [8,9] is used to insert the chronic inbound trips. This GIH explores all possible insertions into the existing schedules and greedily chooses the one that minimizes a prespecified metric. ...
... From the obtained vehicle routes we can deduce the times when the appointments of the chronic patients can start and thus determine the time windows for the inbound 11 trips. By using the greedy insertion heuristic GIH based on [8,9] for the inbound trips, we finalize the schedules of the chronic patients. We assume that the number of vehicles is always large enough, such that this insertion is possible. ...
Preprint
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Patient transportation systems are instrumental in lowering access barriers in primary care by taking patients to their GPs. As part of this setting, each transportation request of a chronic or walk-in patient consists of an outbound trip to the GP and an inbound trip back home. The economic sustainability of patient transportation systems mainly depends on their utilization and how well transportation requests can be bundled through ride sharing. To ease the latter, we consider a flexible scheduling of chronic patients in which only a certain range for an appointment is fixed a priori while the exact time is determined by the scheduling of the outbound trip. This leads to a novel extension of the dial-a-ride problem that we call the dial-a-ride problem with combined requests and flexible scheduling (DARPCF). In this paper, we introduce two heuristics for the DARPCF that exploit this increased flexibility. Both approaches initially compute so-called mini-clusters of outbound requests. Then, the mini-clusters are linked by (i) solving a traveling salesman problem and creating routes of outbound rides with a splitting procedure or by (ii) using a rolling horizon approach and solving bipartite matching problems for the vehicle assignment. Our computational study shows that by using the presented algorithms with the flexible scheduling of chronic appointments, the average number of served requests can be increased by 16% compared to a non-flexible setting.
... Experimental Settings This study assumes that any commuter i, when requesting a commute trip for any day, would specify the desired arrival time at the destination of the inbound trip, at + i , and the desired departure time at the origin of the outbound trip, dt − i . This assumption is similar to that made in other literatures, e.g., Jaw et al. (1986), Cordeau and Laporte (2003b), Cordeau (2006). On top of that, it also assumes that each tolerates a maximum time shift of ±∆ to the desired times. ...
... This assumption is consistent with that made in other DARP literature, e.g. Jaw et al. (1986), Cordeau and Laporte (2003b), and Cordeau (2006). It is also assumed that the commuters are willing to tolerate a maximum shift of ±∆ to the desired times. ...
... Similar to Jaw et al. (1986), Cordeau and Laporte (2003b), and Cordeau (2006), this work assumes on any day, each commuter c would specify a desired arrival time at the destination of her inbound trip, at + c , and a desired departure time at the origin of her outbound trip, dt − c . It also assumes that each would tolerate a shift of ±∆ to the desired times. ...
Thesis
As cities struggle to cope with the ever-increasing demand on their transportation infrastructures, ride-hailing services have emerged as a potential remedy that promises to revolutionize urban mobility by making on-demand transportation available at the touch of a fingertip. The long-term sustainability of these services, however, can only be realized when their rides are aggregated by having individual vehicles serve multiple trips simultaneously to maximize the utilization of available seat capacity, i.e., by "true" ride sharing. While the community has long recognized ride sharing's potential for reducing traffic congestion, energy consumption, parking utilization, and greenhouse gas emissions, numerous unsolved challenges---from providing attractive mechanisms to incentivize modal shifts to building trust among unacquainted passengers---remain to hinder its widespread adoption. A key obstacle to ride sharing's ubiquity is the difficulty of coordinating rides with matching locations and schedules combined with the absence of algorithms capable of matching riders and drivers quickly and effectively. This research addresses this challenge by focusing on finding optimal routing plans for fleets of conventional and autonomous vehicles that maximize ride sharing for commute trips to power future ride-sharing platforms. The need to design routes that match trips to and from the workplace---that in turn, are dispersed spatially and temporally with schedules that may change every day---while respecting time-window, ride-duration, and vehicle-capacity constraints highlights the complexity of the problem. Driven by an original desire to investigate the potential of optimized ride-sharing platforms in relieving the parking pressure induced by the thousands of commuters traveling to the University of Michigan campus in Ann Arbor, Michigan, this research: (1) develops the mathematical framework for modeling the problem of seeking the optimal routing plan that maximizes ride sharing for commute trips for conventional and autonomous vehicles, (2) proposes techniques to decompose the problem and designs exact and approximate algorithms to tackle its computational complexity, and (3) quantifies the potential benefits and drawbacks of the generated plans and provides insight into the different factors that influence their performance through a real case study. Aside from investigating modeling and decomposition techniques that specifically exploit the structure imposed by the problem constraints and the spatio-temporal characteristics of the trips, this research also proposes solution approaches that leverage state-of-the-art linear-programming and combinatorial-optimization techniques, ranging from column generation to discover useful routes on demand to dynamic programming to efficiently find resource-constrained least-cost paths. The solution approaches share a common characteristic: Each produces a valid lower bound to the objective value which allows the calculation of an optimality gap to quantify its solution quality. These algorithms are further bolstered by the availability of a real-world dataset of the commute trips made by 15,000 drivers that use 15 university-operated parking structures in downtown Ann Arbor over April 2017; it not only allows the algorithms to be evaluated on real-world data, but analyses of its results provide invaluable insights into the performance characteristics of the optimized routing plans. This research demonstrates that through the optimal plans, the number of vehicles for these trips can be potentially reduced by 57% and 92% when using conventional and autonomous vehicles respectively. It also quantifies numerous other potential benefits and drawbacks from utilizing the plans, some of which include reductions in vehicle usage during peak hours, decreases in vehicle miles traveled, and increases in average commute times.
... For simplicity, we assume the passengers from one request cannot be split and serviced by different vehicles. Starting with an initial solution generated by a customised insertion heuristic based on (Jaw et al., 1986)'s sequential insertion heuristics (Section 4.1), the LS-H algorithm iterates between executing local search on the search space of user selection (Section 4.2.1) and the search space of routing optimisation (Section 4.2.2). The algorithm terminates when no better solution can be found and an overview of LS-H is detailed in Section 4.3. ...
... We name this alternative algorithm MATH-H and demonstrate it in detail in Section 4.4. (Jaw et al., 1986) proposed a sequential insertion heuristic, which we deem to be a decent starting point for generating initial solutions with a few modifications applied. Requests are indexed and sorted in an increasing order according to their earliest departure time. ...
... The remaining requests are inserted one by one following the adjusted insertion order in Algorithm 1. Initial solution 0 is instructed following (Jaw et al., 1986)'s insertion method: Schedule blocks (when vehicles are active) and slack periods (when vehicles are idling) of each vehicle are created at initialisation, and updated after each successful insertion. When inserting a request , the algorithm systematically scans all feasible insertions of the request into the existing work schedules of all vehicles, and choose the best insertion with minimum additional cost. ...
Article
The classic Dial-A-Ride Problem (DARP) aims at designing the minimum-cost routing that accommodates a set of user requests under constraints at an operations planning level, where users' preferences and revenue management are often overlooked. In this paper, we present a mechanism for accepting/rejecting user requests in a Demand Responsive Transportation (DRT) context based on the representative utilities of alternative transportation modes. We consider utility-maximising users and propose a mixed-integer programming formulation for a Chance Constrained DARP (CC-DARP), that captures users' preferences via a Logit model. We further introduce class-based user groups and consider various pricing structures for DRT services. A customised local search based heuristic and a matheuristic are developed to solve the proposed CC-DARP. We report numerical results for both DARP benchmarking instances and a realistic case study based on New York City yellow taxi trip data. Computational experiments performed on 105 benchmarking instances with up to 96 nodes yield average profit gaps of 2.59% and 0.17% using the proposed local search heuristic and matheuristic, respectively. The results obtained on the realistic case study reveal that a zonal fare structure is the best strategy in terms of optimising revenue and ridership. The proposed CC-DARP formulation provides a new decision-support tool to inform on revenue and fleet management for DRT systems on a strategic planning level.
... Dial-a-Ride [3] is a classic scheduling problem focused on planning or routing multiple rides requested by citizens simultaneously. Research using this approach can be divided into two types of operating models: single-vehicle models [4,5] and multi-vehicle models [6,7]. In the former, a single vehicle provides different types of services. ...
... Later, Desrosiers et al. [8] presented a solution using forward dynamic programming in conjunction with two-dimensional labeling and claimed that their approach could effectively increase the number of fulfilled citizen requests. Recently, Sexton and Boldin [5,6] proposed heuristic algorithms and demonstrated the validity of their proposed approach through experiments. Unfortunately, these methods cannot be directly applied to the problem considered in this study, which involves more than one vehicle providing different services. ...
... Unfortunately, these methods cannot be directly applied to the problem considered in this study, which involves more than one vehicle providing different services. The paratransit service issue discussed in this study resembles the multi-vehicle model [6,7], in which multiple vehicles provide the same service at the same time. The first multi-vehicle Dial-a-Ride models were developed by Jaw et al. [6] and Bodin and Sexton [7]; both studies proposed heuristic algorithms as solutions. ...
Article
Full-text available
As aging populations increase worldwide, many governments have introduced the concept of paratransit services to assist individuals with limited mobility with transportation. A successful paratransit service must be able to satisfy most requests to the system; this success is typically related to the allocation of vehicles to dispatch stations. A suitable configuration can reduce unnecessary travel time and thus serve more people. This resembles the classic Dial-a-Ride problem, which previous studies have solved using heuristic algorithms. Most of these algorithms, however, incur heavy computational costs and, therefore, cannot be operated online, especially when there are many conditions to consider, many configuration requirements, or many vehicles requested. Therefore, this paper proposes an approach based on the generative adversary network (GAN), which can reduce computation significantly. In online environments, this approach can be implemented in just a few seconds. Furthermore, the amount of computation is not affected by the number of conditions, configuration requirements, or vehicles requested. This approach is based on three important concepts: (1) designing a GAN to solve the target problem; (2) using an improved Voronoi diagram to divide the overall service area to generate the input of the GAN generator; (3) using well-known system simulation software Arena to swiftly generate many conditions for the target problem and their corresponding best solutions to train the GAN. The efficiency of the proposed approach was verified using a case study of paratransit services in Yunlin, Taiwan.
... L'algorithme ne peut résoudre de manière optimale que des instances relativement petites soit environ une dizaine de passagers. [Jaw et al. 1986] [Parragh et al. 2010] ont proposé une heuristique de recherche à voisinage variable pour la résolution du DARP statique multi-véhicule. Cet algorithme est appliqué sur deux variantes du problème où la seule différence est relative à la fonction d'évaluation. ...
... Comme dans [Jaw et al. 1986], le passager fixe soit la plus tôt heure de son ramassage ou la plus tard heure de son débarquement. Sur la base de son choix ainsi que l'écart maximum acceptable , la durée de trajet direct entre le noeud de charge et de décharge et la durée de trajet maximum acceptable entre le noeud de ramassage et de débarquement , des fenêtres de temps sont définis comme suit : -pour les demandes dont la plus tôt heure de ramassage ( ) est déterminée : Notons que l'écart maximum acceptable est un laps de temps que le client peut négliger en attente de son service. ...
... Ces agents sont créés et initialisés par l'agent Décideur. La construction se base sur une heuristique qui essaie d'insérer toutes les demandes dans un itinéraire à la fois [Jaw et al. 1986]. En effet, la méthode commence par trier les demandes dans l'ordre croissant de leurs heures de ramassage. ...
Thesis
Full-text available
Ce manuscrit présente une synthèse des travaux de recherche que j’ai effectués de 2007 à 2018 en tant que Maître Assistante, et chercheur depuis 1999 au sein de l’unité de recherche URIASIS qui était ensuite promue Laboratoire SOIE (et actuellement SMART) à l’ISG de Tunis et à partir de 2016-2018 au sein du Laboratoire COSMOS (Complex Outstanding Systems Modeling Optimization and Supervision) à l’ENSI, Université de la Manouba.
... Attracted by the characteristics of flex-route transit, both academia and industry have shown great interest. In the early years, scholars [20][21][22][23] provided fixed service and dial-a-ride service for common passengers and special demands, respectively. Later, many studies [24][25][26][27][28][29][30][31][32] designed flex-route transit to serve static-station-based demands and dynamicstation-related demands. ...
... If the trip j accepts the real-time demand n * (z j,n * = 1), it must meet the requirement of station sequence, as constraints (2) to (7) show, maintain the service for reserved demands, as constraints (8) to (10) show, and build the temporal and spatial relationship with the real-time demand n * , as constraints (18) to (21) show. ...
Article
Full-text available
Flex-route transit is regarded as the feasible solution to provide flexible service for various demands. To improve the service of flex-route transit, this paper proposes a design framework with the input of multi-type demands. Firstly, according to the multi-feature-based classification method, static stations and dynamic stations are divided by hierarchical clustering algorithm based on historical demands. Secondly, in the two-stage planning method, an offline plan is generated by multi-route design model and route-design-oriented genetic algorithm based on the classified stations and the flexible combination of reserved demands and regular travel patterns. Then, an online plan is adjusted by route modification model and greedy algorithm based on the offline plan and real-time demands. Numerical experiments demonstrate the applicability of flex-route transit in the realistic road network and show that flex-route transit can transport demands more effectively and save nearly 40% of cost compared with traditional transit.
... It is worth noting that imposing a time window at the origin and destination points of a user is a contested issue. Although DARP models typically let users impose a time window on both their departure and arrival times, the service provider might be capable of improving the operational efficiency if this constraint is partially relaxed [14]. ...
... Constraints (7) ensure that if a vehicle k serves arc (i, j) the passenger load upon leaving vertex j is greater than or equal to the load at vertex i plus q j . Constraints (14) ensure that the in-vehicle passenger load w k i upon leaving vertex i is at least max{0, q i } and, at the same time, does not exceed the vehicle capacity min{Q k , Q k + q i }. ...
Conference Paper
Full-text available
The Dial-A-Ride Problem (DARP) has received significant attention during the COVID-19 pandemic. During the pandemic's peak, public transport ridership was reduced up to 90% in several countries and many public transport users had to seek less crowded alternatives in DARP services. Such alternatives are flexible modes that do not operate on fixed lines (i.e., on-demand minibuses, shared vehicles). However, the standard Dial-A-Ride Problem (DARP) does not consider the in-vehicle crowding as long as the capacity of the vehicle is not exceeded. To rectify this, this study proposes a new formulation of the DARP that considers also the inconvenience of passengers due to the in-vehicle crowding levels in the objective function of the problem. In our formulation, we consider a progressive penalization of the increase of in-vehicle crowding to account for social distancing. This is modeled with piecewise linear functions that map the inconvenience of passengers to the in-vehicle crowding levels. The proposed model is a MINLP and it is reformulated as a MILP that can be solved with branch-and-bound and linear programming. This model is implemented in numerical experiments with benchmark DARP datasets to investigate the increases of the vehicle route costs when seeking to reduce the in-vehicle crowdedness.
... The P2P ride-matching problem is a generalization of the dial-a-ride problem (DARP). DARP was originally designed to model para-transit systems (Madsen et al., 1995;Healy and Moll, 1995;Fu, 2002); however, it has evolved through several years to model the operation of ride-sourcing systems (Jaw et al., 1986;Cordeau, 2006;Wang and Yang, 2019). The P2P ride-matching problem has a fundamental difference from ride-sourcing and shared-taxi services, in that in a P2P ridesharing system drivers are also customers who are willing to share their rides while completing their own trips. ...
... In recent decades, with the advent of advanced communication technologies and computational tools, the dynamic form of this problem has been the main focus of research. Jaw et al. (1986) were among the first to consider a dynamic DARP with time constraints. They proposed a simple and efficient insertion heuristic that influenced the work of many others afterwards. ...
Thesis
In the last decade, ubiquity of the internet and proliferation of smart personal devices have given rise to businesses that are built on the foundation of the sharing economy. The mobility market has implemented the sharing economy model in many forms, including but not limited to, carsharing, ride-sourcing, carpooling, taxi-sharing, ridesharing, bikesharing, and scooter sharing. Among these shared-use mobility services, ridesharing services, such as peer-to-peer (P2P) ridesharing and ride-pooling systems, are based on sharing both the vehicle and the ride between users, offering several individual and societal benefits. Despite these benefits, there are a number of operational and economic challenges that hinder the adoption of various forms of ridesharing services in practice. This dissertation attempts to address these challenges by investigating these systems from two different, but related, perspectives. The successful operation of ridesharing services in practice requires solving large-scale ride-matching problems in short periods of time. However, the high computational complexity and inherent supply and demand uncertainty present in these problems immensely undermines their real-time application. In the first part of this dissertation, we develop techniques that provide high-quality, although not necessarily optimal, system-level solutions that can be applied in real time. More precisely, we propose a distributed optimization technique based on graph partitioning to facilitate the implementation of dynamic P2P ridesharing systems in densely populated metropolitan areas. Additionally, we combine the proposed partitioning algorithm with a new local search algorithm to design a proactive framework that exploits historical demand data to optimize dynamic dispatching of a fleet of vehicles that serve on-demand ride requests. The main purpose of these methods is to maximize the social welfare of the corresponding ridesharing services. Despite the necessity of developing real-time algorithmic tools for operation of ridesharing services, solely maximizing the system-level social welfare cannot result in increasing the penetration of shared mobility services. This fact motivated the second stream of research in this dissertation, which revolves around proposing models that take economic aspects of ridesharing systems into account. To this end, the second part of this dissertation studies the impact of subsidy allocation on achieving and maintaining a critical mass of users in P2P ridesharing systems under different assumptions. First, we consider a community-based ridesharing system with ride-back guarantee, and propose a traveler incentive program that allocates subsidies to a carefully selected set of commuters to change their travel behavior, and thereby, increase the likelihood of finding more compatible and profitable matches. We further introduce an approximate algorithm to solve large-scale instances of this problem efficiently. In a subsequent study for a cooperative ridesharing market with role flexibility, we show that there may be no stable outcome (a collusion-free pricing and allocation scheme). Hence, we introduced a mathematical formulation that yields a stable outcome by allocating the minimum amount of external subsidy. Finally, we propose a truthful subsidy scheme to determine matching, scheduling, and subsidy allocation in a P2P ridesharing market with incomplete information and a budget constraint on payment deficit. The proposed mechanism is shown to guarantee important economic properties such as dominant-strategy incentive compatibility, individual rationality, budget-balance, and computational efficiency. Although the majority of the work in this dissertation focuses on ridesharing services, the presented methodologies can be easily generalized to tackle related issues in other types of shared-use mobility services.
... Most practical applications use heuristic techniques to find solutions. Jaw et al. (20) presented one of the earliest heuristics for solving the static, multi-vehicle DARP, although their approach is limited by inserting requests sequentially -leaving it susceptible to myopic behavior. While many on-demand routing algorithms make use of an insertion type heuristic (e.g. ...
... Because the feasibility check is performed repeatedly, and because the computation time of each feasibility calculation scales with problem size, an efficient feasibility check is highly valuable. The feasibility check used in Jaw et al. (20) builds its schedules as blocks of continuous service, shifting and merging them as needed to find feasible solutions. Other feasibility approaches use the concept of "forward time slack" to track, for each node, the amount of time the node can be delayed while still satisfying all constraints. ...
Article
Full-text available
The coronavirus pandemic changed paratransit service dramatically, with most operators eliminating shared rides to halt disease transmission. This paper applies an estimate of disease contact exposure to actual data from New York City's Access-A-Ride (AAR) paratransit system. Scenario analyses performed using insertion heuristic trip construction show that eliminating rideshare on the AAR system increases operating miles by 70%. We also show contact exposure can be significantly limited (by ~50-60%) by reducing vehicle capacity from 4 to 2 passengers. Manipulating the maximum ride time factor also shows the potential to reduce contact exposure, with a 50% increase of the ratio from 2 to 3 leading to a 40% increase in contact exposure. Contact exposure was relatively insensitive to changes in the max wait time policy.
... Most practical applications use heuristic techniques to find solutions. Jaw et al. (20) presented one of the earliest heuristics for solving the static, multi-vehicle DARP, although their approach is limited by inserting requests sequentially -leaving it susceptible to myopic behavior. While many on-demand routing algorithms make use of an insertion type heuristic (e.g. ...
... Because the feasibility check is performed repeatedly, and because the computation time of each feasibility calculation scales with problem size, an efficient feasibility check is highly valuable. The feasibility check used in Jaw et al. (20) builds its schedules as blocks of continuous service, shifting and merging them as needed to find feasible solutions. Other feasibility approaches use the concept of "forward time slack" to track, for each node, the amount of time the node can be delayed while still satisfying all constraints. ...
Preprint
Full-text available
The coronavirus pandemic changed paratransit service dramatically, with most operators eliminating shared rides to halt disease transmission. This paper applies an estimate of disease contact exposure to actual data from New York City's Access-A-Ride (AAR) paratransit system. Scenario analyses performed using insertion heuristic trip construction show that eliminating rideshare on the AAR system increases operating miles by 70%. We also show contact exposure can be significantly limited (by ~50-60%) by reducing vehicle capacity from 4 to 2 passengers. Manipulating the maximum ride time factor also shows the potential to reduce contact exposure, with a 50% increase of the ratio from 2 to 3 leading to a 40% increase in contact exposure. Contact exposure was relatively insensitive to changes in the max wait time policy.
... Early work is carried out by Jaw, Odoni, Psaraftis, & Wilson (1986) , who develop one of the first heuristics for the multi-vehicle DARP. Depending on the users' earliest possible pick-up times, the heuristic determines the cheapest insertion position in an existing route in terms of user satisfaction and operator costs. ...
... Depending on the users' earliest possible pick-up times, the heuristic determines the cheapest insertion position in an existing route in terms of user satisfaction and operator costs. Desrosiers, Dumas, Soumis, Taillefer, & Villeneuve (1991) ; Dumas, Desrosiers, & Soumis (1989) and Ioachim, Desrosiers, Dumas, Solomon, & Villeneuve (1995) first identify groups of users to be served within the same area and time. In a second step, these 'clusters' are combined to obtain feasible vehicle routes. ...
Article
Ride-hailing services require efficient optimization algorithms to simultaneously plan routes and pool users in shared rides. We consider a static dial-a-ride problem (DARP) where a series of origin-destination requests have to be assigned to routes of a fleet of vehicles. Thereby, all requests have associated time windows for pick-up and delivery, and may be denied if they can not be serviced in reasonable time or at reasonable cost. Rather than using a spatial representation of the transportation network we suggest an event-based formulation of the problem. While the corresponding MILP formulations require more variables than standard models, they have the advantage that capacity, pairing and precedence constraints are handled implicitly. The approach is tested and validated using a standard IP-solver on benchmark data from the literature. Moreover, the impact of, and the trade-off between, different optimization goals is evaluated on a case study in the city of Wuppertal (Germany).
... Jaw et al. [75] proposed a heuristic algorithm for a static, multi vehicle demandaware transit problem. The algorithm uses a sequential insertion procedure to assign customers to vehicles and to determine a time schedule of pick-ups and deliveries for each vehicle. ...
... Also, several types of vehicles are used to provide the service and it may become unavailable due to breakdowns. The authors develop an insertion algorithm based on [75]. Authors report results for an instance with 300 requests and 24 vehicles. ...
Thesis
Full-text available
Public transit systems have been constantly plagued by the inherent connectivity gap due to fixed routes and schedules of feeder bus services. Demand-aware bus transit systems that rely on real-time scheduling of flexible routes have gained popularity as an alternative to bridge the connectivity gap, thereby enhancing user experience and operator profitability. In this research, scalable techniques have been proposed to realize citywide deployment of a demand-aware bus transit system to replace the conventional fixed-route based feeder bus services. In Chapter 3, a graph-based representation has been proposed to model demand-aware flexible route generation. The mixed integer programming model for generating the optimal flexible routes incorporates real-life scenarios including actual distances of the road network and asymmetric distance/time matrices that represent the different `to and fro' distance/travelling times between two given points. The proposed model can successfully generate optimal flexible routes to enhance the travel times of passengers (user experience) or vehicle miles travelled by the fleet (operator profitability). In particular, the normalized weighted technique has been introduced to facilitate trade-off analysis based on user requirements to ensure that the flexible routes are sensitive to both the user experience and operator profitability. The proposed model has been successfully employed to prune the design space to speed up route computations without compromising optimality. Experimental results demonstrate the capability of the model in performing diverse what-if analyses by varying different input parameters. A heuristic routing technique has been proposed in Chapter 4 to accelerate the flexible route generation process by combining both the Ꜫ-constraint method and a genetic algorithm. The technique incorporates nearest neighbour heuristic to generate superior initial solutions, selection of genetic operators for fast convergence, and a hybrid parent selection algorithm for balancing solution quality and diversity. Experimental results confirm that routes generated by the proposed technique deviate only 3% from the optimal values. The rapid convergence of the proposed technique results in a 26% reduction in runtime when compared to a widely-used baseline algorithm. A directionality-centric technique has been proposed for the systematic segmentation of bus transit network in Chapter 5. The network segmentation technique generates sub-zones based on the feasible shortest path routes from its bus stops to the destination. Heuristic technique proposed in Chapter 4 has been employed to generate the flexible routes of the size limited sub-zones. This has led to notable speed-up of flexible route computations that can also benefit from parallel computations, thereby paving the way for a highly scalable technique without compromising the responsiveness demanded by demand-aware bus transit systems. The outlier bus stops of sub-zones are incorporated into the neighbouring sub-zones on-the-fly to minimize vehicle detours. Moreover, dynamic methods for demand-aware allocation of EVs and workload balancing among sub-zones improves the overall responsiveness of a large-scale deployment. Experimental results confirm that the routes generated using the proposed technique achieves over 7x speed-up when compared to a global, heuristic routing technique without compromising on solution quality. A similar performance improvement was also evident for the case of sporadic demands, highlighting the applicability of the proposed network segmentation technique to real-life scenarios. In Chapter 6, applicability of the proposed methods to a large scale deployment of demand-aware bus transit system has been demonstrated. This necessitated the systematic segmentation of feeder bus services into sub-zones and outlier bus stops as well as point-to-point trunk services. Identification of independent transit hub regions of a large scale transit system as well as segmenting each transit hub into workload balanced zones has notably improved the responsiveness of route computations. Experimental results confirm that, compared to a widely-used unsupervised learning algorithm, the zone-wise runtime has improved by 83% while also improving the quality of routes. A demand-aware scheduling technique to improve the user experience and operator profitability of trunk bus services has also been proposed in this chapter. In Chapter 7, the various techniques proposed in this thesis have been integrated into a framework to realize the citywide deployment of demand-aware flexible routing. The model for demand prediction was trained using multi-modal sensing inputs from mobile apps and vision-based crowd counting. This has paved the way for estimating near-future demand at each bus stop to schedule flexible routes in real-time. Runtime performance of citywide route generation process has also been improved by the offline processing of a significant component of the workload and by limiting the generation of sub-zones, based on near-future demand estimation, to online. Experiments confirm that the flexible routes can be computed in 20 and 24 seconds for workloads of 50 and 65 passengers respectively, when implemented on a 4-core Xeon E5-1630 V4 CPU running at 3.70 GHz. The proposed sensing methods also lend well for the periodic generation of offline schedules for trunk bus services. Finally, real-life deployment of the proposed techniques for the city-wide replacement of fixed-route based bus transit systems has been successfully demonstrated to minimise the connectivity gap inherent in current implementations.
... We now present the mathematical programming model for addressing the elastic logistics service proposed in this study. The objective of this problem is to determine the direct and indirect tours that minimize the total direct and indirect [16] DARP [17] Customer allocation (to bus stop) Integer Modified ADARTW [18] Engelen et al. [19] DARP [17] Stop order Integer Dynamic insertion algorithm Archetti et al. [20] Periodic VRP Customer visited period Mixed-integer MILP formulation Archetti et al. [21] Periodic VRP Periodic demand Mixed-integer Tabu search heuristic Wang et al. [22] TDSP [23] Trip assignment Integer Gaussian mixture model Tas et al. [24] EVRPTW [25] Time window Integer Column generation Shi et al. [26] HHCRSP [27] Travel and service times Mixed-integer Simulated annealing Ours TSP with facility locations Delivery type and Station activation Integer Memetic algorithm ...
... We now present the mathematical programming model for addressing the elastic logistics service proposed in this study. The objective of this problem is to determine the direct and indirect tours that minimize the total direct and indirect [16] DARP [17] Customer allocation (to bus stop) Integer Modified ADARTW [18] Engelen et al. [19] DARP [17] Stop order Integer Dynamic insertion algorithm Archetti et al. [20] Periodic VRP Customer visited period Mixed-integer MILP formulation Archetti et al. [21] Periodic VRP Periodic demand Mixed-integer Tabu search heuristic Wang et al. [22] TDSP [23] Trip assignment Integer Gaussian mixture model Tas et al. [24] EVRPTW [25] Time window Integer Column generation Shi et al. [26] HHCRSP [27] Travel and service times Mixed-integer Simulated annealing Ours TSP with facility locations Delivery type and Station activation Integer Memetic algorithm ...
Article
In this study, we present a flexible delivery routing problem faced by logistics service providers in which some customers may receive their packages indirectly. Customers are supposed to get their packages directly from a delivery service provider or be delivered to indirectly using a nearby station drop and a subsequent separate last-mile delivery service provider that finally delivers their goods. We address the problem of determining whether deliveries to customers should be fulfilled directly or indirectly in this situation. We present the mathematical programming model and propose a near-optimal heuristic approach based on a memetic algorithm. In addition, we evaluate the numerical performance of the proposed algorithm and perform various parametric analyses to gain managerial insights from the model.
... An insertion-based heuristic was provided for solving a DARP with customized constraints in [Markovic et al. 2015] [44]. The heuristic was based on the parallel insertion heuristic of Jaw et al. (1986) [60]. Some customer oriented constraints are improved to fulfill various users requirements. ...
... An insertion-based heuristic was provided for solving a DARP with customized constraints in [Markovic et al. 2015] [44]. The heuristic was based on the parallel insertion heuristic of Jaw et al. (1986) [60]. Some customer oriented constraints are improved to fulfill various users requirements. ...
Chapter
The interest of on demand transport systems is constantly growing. This trend is accompanied by increased customer’s expectations in the quality of the service provided. In this regard, the quality of service must meet the needs for more customer-oriented features. This article summarizes recent developments in Dial-A-Ride Problems which integrate customer service quality. We provide a classification of the variants examined, as well as the available resolution methodologies and references on the instances used. A discussion on the sate of the art is given with perspectives for future researches.
... Other heuristics and metaheuristics were further developed to handle large-size DARP. For example, simple insertion heuristics were proposed to quickly find feasible solutions where each request is inserted in the vehicle's schedule by the cheapest insertion criterion (Jaw et al. 1986;Wong et al. 2014;Xiang et al. 2008). Cordeau and Laporte (2003) introduced Tabu search by locating requests in different neighbors with additional heuristic diversification strategies. ...
Preprint
On-demand peer-to-peer ride-sharing services provide flexible mobility options, and are expected to alleviate congestion by sharing empty car seats. An efficient matching algorithm is essential to the success of a ride-sharing system. The matching problem is related to the well-known dial-a-ride problem, which also tries to find the optimal pickup and delivery sequence for a given set of passengers. In this paper, we propose an efficient dynamic tree algorithm to solve the on-demand peer-to-peer ride-sharing matching problem. The dynamic tree algorithm benefits from given ride-sharing driver schedules, and provides satisfactory runtime performances. In addition, an efficient pre-processing procedure to select candidate passenger requests is proposed, which further improves the algorithm performance. Numerical experiments conducted in a small network show that the dynamic tree algorithm reaches the same objective function values of the exact algorithm, but with shorter runtimes. Furthermore, the proposed method is applied to a larger size problem. Results show that the spatial distribution of ride-sharing participants influences the algorithm performance. Sensitivity analysis confirms that the most critical ride-sharing matching constraints are the excess travel times. The network analysis suggests that small vehicle capacities do not guarantee overall vehicle-kilometer travel savings.
... Interest in efficient operational schemes for autonomous vehicle fleet that can provide door-to-door transportation has been another motivator for the recent revival of interest in the dynamic DARP (Hyland and Mahmassani, 2018;Zhang et al., 2020;Jayakrishnan, 2016, 2017a). Jaw et al. (1986) were among the first to consider a dynamic DARP with time constraints. They proposed a simple and efficient insertion heuristic that influenced the work of many others afterwards. ...
Article
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The problem of dispatching shuttles to serve trip requests can be mathematically formulated as a dial-a-ride problem (DARP). With on-demand mobility services gaining more popularity due to the recent developments in the gig economy, communication technologies, and urbanization, the real-time application of DARP is attracting ever more interest. However, the fact that the size of DARP grows exponentially with number of requests and number of available seats renders the current solution methodologies inadequate for online applications. In order to tackle this issue, we propose a general framework that shifts much of the computational burden of the optimization problems that need to be solved into an offline phase, thereby addressing on-demand requests with fast and high-quality solutions in real time. Using numerical experiments, we demonstrate the benefits of the proposed method. Furthermore, we conduct a sensitivity analyses to show the performance of our methodology under different parameter settings.
... Other heuristics and metaheuristics were further developed to handle large-size DARP. For example, simple insertion heuristics were proposed to quickly find feasible solutions where each request is inserted in the vehicle's schedule by the cheapest insertion criterion (Jaw et al. 1986;Wong et al. 2014;Xiang et al. 2008). Cordeau and Laporte (2003) introduced Tabu search by locating requests in different neighbors with additional heuristic diversification strategies. ...
Article
Full-text available
On-demand peer-to-peer ridesharing services provide flexible mobility options and are expected to alleviate congestion by sharing empty car seats. An efficient matching algorithm is essential to the success of a ridesharing system. The matching problem is related to the well-known dial-a-ride problem, which also tries to find the optimal pickup and delivery sequence for a given set of passengers. In this paper, we propose an efficient dynamic tree algorithm to solve the on-demand peer-to-peer ridesharing matching problem. The dynamic tree algorithm benefits from given ridesharing driver schedules and provides satisfactory runtime performances. In addition, an efficient pre-processing procedure to select candidate passenger requests is proposed, which further improves the algorithm performance. Numerical experiments conducted in a small network show that the dynamic tree algorithm reaches the same objective function values of the exact algorithm, but with shorter runtimes. Furthermore, the proposed method is applied to a larger size problem. Results show that the spatial distribution of ridesharing participants influences the algorithm performance. Sensitivity analysis confirms that the most critical ridesharing matching constraints are the excess travel times. The network analysis suggests that small vehicle capacities do not guarantee overall vehicle-kilometer travel savings.
... Transport and network researchers have studied on-demand systems for a long time. The DAR (dial-a-ride) problem was analyzed widely during the seventies and eighties (for example Wilson et al., 1976;Psaraftis, 1983;and Jaw et al., 1986), usually assuming trips requested by phone. In the past few years, the problem has gained new attention due to the massive coordination abilities provided by online (real-time) apps (as shown by Uber or Cabify), which changes the problem as now there are many more requests, and they arrive more often. ...
Article
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Within the context of a shared on-demand transport system, we study the problem of selecting the stopping points from which passengers should walk to their exact destinations (or from their exact origins). We focus on the single-vehicle case that must follow a predefined order of requests, posing the mathematical program, showing that it can be solved in polynomial time and proposing a heuristic that runs faster. We compare the optimal algorithm, the heuristic, and the routes that visit the exact request points, and we show that avoiding detours can reduce total costs by almost one fifth and vehicle costs by more than one third. The heuristic yields competitive results. Simulations over the real street network from Manhattan show that the time reduction achieved by the heuristic might be crucial to enable the system to operate in real-time.
... Multiple objectives and constraints had to be considered. They started their work based on an algorithm by Jaw et al. (1986). Again, their approach falls into the class of random insertion heuristics, where a known schedule is improved. ...
Article
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Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational (tactical) tools for dynamic (online, real-time) routing. Several types and scopes of dynamics are proposed. Particular attention is given to sequential dynamics. The balanced dynamic closest vehicle heuristic (BD-CVH) and the balanced dynamic assignment vehicle heuristic (BD-AVH) are applied to this type of dynamics. The algorithms are applied to a wide range of test instances. Taxi services and palette transfers in warehouses demonstrate how to use the BD-mTSP algorithms in real-world scenarios. Continuous approximation models for the BD-mTSP’s are derived and serve as strategic tools for dynamic routing. The models express route lengths using vehicles, customers, and dynamic scopes without the need of running an algorithm. A machine learning approach was used to obtain regression models. The mean absolute percentage error of two of these models is below 3%.
... However, small distance cannot correspond to optimal matches because inserting customers into some vehicles' schedule would influence vehicles' current customers' routes. Hence, many people [177][178][179] first try to insert a customer's route into candidate vehicles and then select the vehicle with the least cost to actually insert the customer's route. Considering that the time complexity of trying all candidates is too large, Huang et al. [180] design the kinetic tree (KT) to improve the efficiency. ...
Article
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Intelligent transportation (e.g., intelligent traffic light) makes our travel more convenient and efficient. With the development of mobile Internet and position technologies, it is reasonable to collect spatio-temporal data and then leverage these data to achieve the goal of intelligent transportation, and here, traffic prediction plays an important role. In this paper, we provide a comprehensive survey on traffic prediction, which is from the spatio-temporal data layer to the intelligent transportation application layer. At first, we split the whole research scope into four parts from bottom to up, where the four parts are, respectively, spatio-temporal data, preprocessing, traffic prediction and traffic application. Later, we review existing work on the four parts. First, we summarize traffic data into five types according to their difference on spatial and temporal dimensions. Second, we focus on four significant data preprocessing techniques: map-matching, data cleaning, data storage and data compression. Third, we focus on three kinds of traffic prediction problems (i.e., classification, generation and estimation/forecasting). In particular, we summarize the challenges and discuss how existing methods address these challenges. Fourth, we list five typical traffic applications. Lastly, we provide emerging research challenges and opportunities. We believe that the survey can help the partitioners to understand existing traffic prediction problems and methods, which can further encourage them to solve their intelligent transportation applications.
... In the literature, dynamic variants of DARP can be found, although in practice pure dynamic DARPs rarely exist because a subset of requests is often known in advance, according to [15], who reports some examples of dynamic DARP. [17] developed an insertion algorithm, RE-BUS, based on the ADARTW procedure of [18] for a real-life problem involving services to elderly and disabled people in Copenhagen. Requests arrive dynamically along a time horizon and are inserted in existing routes considering the difficulty of insertion. ...
Article
On-Demand Transport (ODT) systems have attracted increasing attention in recent years. Traditional centralized dispatching can achieve optimal solutions, but NP-Hard complexity makes it unsuitable for online and dynamic problems. Centralized and decentralized heuristics can achieve fast, feasible solution at run-time with no guarantee on the quality. Starting from a feasible not optimal solution, we present in this paper a new solution model (ORNInA) consisting of two parallel coordination processes. The first one is a decentralized insertion-heuristic based algorithm to build vehicle schedules in order to solve a particular case of the dynamic Dial-A-Ride-Problem (DARP) as an ODT system, in which vehicles communicate via Vehicle-to-vehicle communication (V2V) and make decentralized decisions. The second coordination scheme is a continuous optimization process namely Pull-demand protocol, based on combinatorial auctions, in order to improve the quality of the global solution achieved by decentralized decision at run-time by exchanging resources between vehicles (k-opt). In its simplest implementation, k is set to 1 so that vehicles can exchange only one resource at a time. We evaluate and analyze the promising results of our contributed techniques on synthetic data for taxis operating in Saint-Étienne city, against a classical decentralized greedy approach and a centralized one that uses a classical mixed-integer linear program (MILP) solver.
... A lot of research has been influenced by real-life problems in the transportation of elderly, handicapped or ill passengers (Jorgensen et al. 2007;Heilporn et al. 2011;Detti et al. 2017). Nevertheless, especially for urban areas dial-a-ride problems have also been studied in the context of commercial ride-sharing and demand responsive transport systems (Jaw et al. 1986;Parragh et al. 2015). Muelas et al. (2013) consider a dial-a-ride problem for on-demand transportation in large cities, but they use routing cost minimization as their objective. ...
Article
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The paper investigates the static dial-a-ride problem with ride and waiting time minimization. This is a new problem setting of significant practical relevance because several ride-sharing providers launched in recent years in large European cities. In contrast to the standard dial-a-ride problem, these providers focus on the general public. Therefore, they are amongst others in competition with taxis and private cars, which makes a more customer-oriented objective necessary. We present an adaptive large neighbourhood search (ALNS) as well as a dynamic programming algorithm (DP), which are tested in comprehensive computational studies. Although the DP can only be used for a single tour and, due to the computational effort, as a restricted version or for small instances, the ALNS also works efficiently for larger instances. The results indicate that ride-sharing proposals may help to solve the trade-off between individual transport, profitability of the provider, and reduction of traffic and pollution.
... While important theoretical work has been undertaken to find exact solutions for the DARP, these approaches are small in scale, with solutions limited to the single-vehicle case for under fifty requests(Cordeau & Laporte, 2007). Most practical applications use heuristic techniques to find solutions.Jaw et al. (1986) presented one of the earliest heuristics for solving the static, multi-vehicle DARP, although their approach is limited by inserting requests sequentially -leaving it vulnerable to myopic behavior. A number of authors have useAs transportation network companies (TNCs) have debuted on-demand ride hailing with shared rides for the general ...
Thesis
The coronavirus pandemic changed paratransit service dramatically, with most operators eliminating shared rides to halt disease transmission. This paper applies an estimate of disease contact exposure to actual data from New York City's Access-A-Ride (AAR) paratransit system. Scenario analyses performed using insertion heuristic trip construction show that eliminating rideshare on the AAR system increases operating miles 70%. I also show contact exposure can be significantly limited by reducing vehicle capacity to 2 passengers down from 4. Finally, this paper puts forward a hospital-based system design that offers the potential to both reduce costs and also improve ride quality for riders' hospital trips.
... In addition to this, the following assumptions are made in order to define the time windows and ride-duration limits of each trip. Consistent with past works on the DARP (e.g., Jaw et al. (1986), Cordeau and Laporte (2003b), Cordeau (2006)), each rider i specifies a desired arrival time at + i at the destination of her inbound trip and a desired departure time dt − i at the origin of her outbound trip when requesting a trip. Riders also tolerate a maximum shift of ±∆ to the desired times. ...
Preprint
This paper studies the benefits of autonomous vehicles in ride-sharing platforms dedicated to serving commuting needs. It considers the Commute Trip Sharing Problem with Autonomous Vehicles (CTSPAV), the optimization problem faced by a reservation-based platform that receives daily commute-trip requests and serves them with a fleet of autonomous vehicles. The CTSPAV can be viewed as a special case of the Dial- A-Ride Problem (DARP). However, this paper recognizes that commuting trips exhibit special spatial and temporal properties that can be exploited in a branch and cut algorithm that leverages a redundant modeling approach. In particular, the branch and cut algorithm relies on a MIP formulation that schedules mini routes representing inbound or outbound trips. This formulation is effective in finding high-quality solutions quickly but its relaxation is relatively weak. To remedy this limitation, the mini-route MIP is complemented by a DARP formulation which is not as effective in obtaining primal solutions but has a stronger relaxation. The benefits of the proposed approach are demonstrated by comparing it with another, more traditional, exact branch and cut procedure and a heuristic method based on mini routes. The methodological contribution is complemented by a comprehensive analysis of a CTSPAV platform for reducing vehicle counts, travel distances, and congestion. In particular, the case study for a medium-sized city reveals that a CTSPAV platform can reduce daily vehicle counts by a staggering 92% and decrease vehicles miles by 30%. The platform also significantly reduces congestion, measured as the number of vehicles on the road per unit time, by 60% during peak times. These benefits, however, come at the expense of introducing empty miles. Hence the paper also highlights the tradeoffs between future ride-sharing and car-pooling platforms.
... Since PDPTW has been proved to be NP-hard, many scholars study heuristic algorithms to solve the problems on a larger scale. Insertion heuristics were developed by Jaw et al. (1986) for the multi-vehicle PDPTW. Tabu search is also widely used (Li and Lim, 2003;Nanry and Barnes, 2000). ...
Article
Shared mobility has attracted increasing attention due to its advantages in relieving traffic congestion and low-carbon environmental protection. This paper studies the dynamic shared-taxi problem of the on-demand shared-taxi system, where we introduce a rescheduling ratio to measure the proportion of requests that can be rescheduled in the total scheduled requests. To match vehicles and passengers in the on-demand platforms with high quality and efficiency, we formulate the problem into a mixed-integer model and develop two optimality-guaranteed algorithms, the branch-and-price algorithm and the Lagrangian relaxation algorithm. The two algorithms share a common subproblem which is solved by dynamic programming in parallel to speed up the solving. Computational results reveal that the branch-and-price algorithm and the Lagrangian relaxation algorithm are significantly superior to the commercial solver (Gurobi) in terms of the solution quality, solvable problem size, and the computational time. Specifically, the branch-and-price algorithm is superior in solution quality, while the Lagrangian relaxation algorithm can obtain high-quality solutions for several large-scale instances faster. After that, we further compare the proposed algorithms with several commonly used heuristic algorithms to verify the necessity of developing optimality-guaranteed algorithms. Finally, sensitivity analyses of the rescheduling ratio factor are carried out to provide several insights for the shared-taxi platform on balancing the relationship between the system-wide profit and user experience.
... Because ride requests are not known in advance, the dynamic dial-a-ride literature has focused on heuristic and metaheuristic methods for both assignment and routing decisions (Ho et al. 2018). This study adopts and modifies construction heuristics developed by Jaw et al. (1986); Ota et al. (2016) for both shuttle assignment and routing because the computation time required for more advanced metaheuristics is often too high for real-world applications (Ho et al. 2018;Wang 2019). These construction heuristics have been shown to produce strong results in real-world settings (Madsen et al. 1995;Markovic et al. 2015). ...
Article
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First-mile last-mile (FMLM) mobility services that connect riders to public transit can lead to improved transit accessibility and network efficiency if such services are convenient and reliable. However, many current FMLM services are inefficient and costly because they are inflexible (e.g., fixed supply of shuttles) and do not leverage collected data for optimized decision making. At the same time, new forms of shared mobility can provide added flexibility and real-time analytics to FMLM systems when carefully integrated. This study evaluates performance and cost implications of public/private coordination between transit shuttles and transportation network companies (TNC) in the FMLM context. A real-time operations model was developed to simulate daily operations for an existing FMLM system using real-world demand data. Three supply strategies were tested with varying levels of flexibility: (1) Status Quo (two 23-passenger on-demand shuttles), (2) Hybrid (one 23-passenger on-demand shuttle + TNC), and (3) TNC Only (exclusively use TNC services). Results indicated that the added flexibility of the Hybrid service design (using shuttles and TNCs) improved service performance (a 7.7% improvement), reduced daily operating costs (− 6.0%), and improved service reliability (95th percentile travel times decreased by up to 40% during peak periods). In addition, the Hybrid service design was more robust to variations in demand. The Hybrid service was significantly cheaper to operate (− 31.6%) at reduced demand levels (50% of normal), and improved service performance (a 10.2% improvement) when demand levels were increased (150% of normal). These findings emphasize the importance of flexibility in FMLM service designs, especially when demand is sparse and variable.
... Jaw et al. proposed a time-constrained heuristic algorithm for many-to-many DART problems. This algorithm describes the Advanced Dial-a-Ride Time Window Problem (ADARTW) with quality of service constraints and can determine the feasibility of passenger insertion in the vehicle's work schedule [7]. Barr et al. provided reporting guidelines for computational experiments using heuristic methods [8]. ...
Article
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Route deviation transit is a flexible “door-to-door” service method that combines the efficiency of conventional public transport modes and the flexibility of demand response modes, meeting the travel needs of people with low travel density and special groups. In this paper, the minimum value of the sum of vehicle operating cost and passenger travel cost was the optimal goal, and the RDT multi-vehicle operation scheduling model was constructed. Taking the available relaxation time as the control parameter of the RDT system and considering the insertion process of the random travel demand of the passengers during the operation process, we used a heuristic search algorithm to solve the scheduling model. This paper took Suburb No. 5 Road of Harbin as an example, using MATLAB to simulate the RDT operation scheduling model to verify the stability and feasibility of the RDT system under different demands. The results showed that under different demand conditions, the system indicators such as passenger travel time, waiting time, and vehicle mileage in the RDT system fluctuated very little, and the system performance was relatively stable. Under the same demand conditions, the per capita cost of the RDT system was 5.9% to 10.8% less than that of the conventional bus system. When the demand ρ is 20~40 person/hour, the RDT system is more effective than the conventional bus for the 5 bus in the suburbs of Harbin.
... In addition to humanitarian logistics, the Vehicle Routing Problem (VRP) is dedicated to the assignment and routing of vehicles (Dantzig and Ramser, 1959;Jaw et al., 1986;Lee et al., 2006;Bräysy and Gendreau, 2005;Chen et al., 2011). Adrang et al. (2020) planed for EMS vehicles during disasters through a location-routing model, formulated as a bi-objective mixed-integer linear programming, for urgent therapeutic services. ...
Article
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The response efficiency of Emergency Medical Service (EMS) is related to the survival rate of patients in Mass Casualty Incidents (MCIs). This study aims to reduce delays caused by congestions in the transportation network and also that in hospitals. A patient transportation and assignment model is proposed considering routing of ambulances and operational conditions of hospitals for an efficient MCI response. The proposed model is composed of a Cell Transmission Model (CTM) and a nonlinear treatment impedance function. A Lagrangian heuristic is utilized to expedite model solution by decomposing the problem into two relatively tractable sub-problems: one linear and the other nonlinear. The linear sub-problem is solved by the simplex algorithm, and is related to ambulance routing, while the nonlinear sub-problem is solved by a gradient projection algorithm for the optimization of patients’ hospital assignment. A case study and several benchmark networks were tested, and the proposed methodology outperformed a typical Lagrangian Relaxation approach. This work has the potential to enable a more efficient patient assignment in MCIs.
... A first attempt to consider real-time requests can be found in Jaw et al. (1986), where a sequential insertion procedure is used to handle new demands. After that work, DVRP starts to gain ground and many variants were studied. ...
Article
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In this paper, we investigate the Pollution Routing Problem in dynamic environments (DPRP). It consists in determining the routing plan of a fleet of vehicles supplying a set of customers, while minimizing the traveled distance and CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CO_2$$\end{document} emissions. The dynamic character of the problem is manifested by the occurrence of new customer demands when the working plan is in progress. Consequently, the planned routes have to be adapted in real time to include the locations of the new customers. In order to efficiently manage the trade-off between the two considered objectives, a new vector evaluated evolutionary algorithm augmented with an exploitation phase and hyper-mutation is proposed. This combination aims to reinforce the refinement of compromised solutions, and to speed up adaptation after the occurrence of a change in the problem inputs. An experimental study is conducted to test the proposed approaches on mono-objective and bi-objective test problems, and against well known approaches from the literature. The obtained results show that our proposal performs well and is highly competitive compared with the competing meta-heuristics.
... Furthermore, dynamic programming [12,13], nonlinear integer programming [14,15], and column generation [16] were used to solve variants of the fundamental problem. In addition, several heuristics were also investigated [17][18][19]. Many additional techniques were reviewed in Savelsbergh and Sol's published survey [20]. ...
Article
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In this study, we propose a general method for tackling the Pickup and Drop-off Problem (PDP) using Hybrid Pointer Networks (HPNs) and Deep Reinforcement Learning (DRL). Our aim is to reduce the overall tour length traveled by an agent while remaining within the truck's capacity restrictions and adhering to the node-to-node relationship. In such instances, the agent does not allow any drop-off points to be serviced if the truck is empty; conversely, if the vehicle is full, the agent does not allow any products to be picked up from pickup points. In our approach, this challenge is solved using machine learning-based models. Using HPNs as our primary model allows us to gain insight and tackle more complicated node interactions, which simplified our objective to obtaining state-of-art outcomes. Our experimental results demonstrate the effectiveness of the proposed neural network, as we achieve the state-of-art results for this problem as compared with the existing models. We deal with two types of demand patterns in a single type commodity problem. In the first pattern , all demands are assumed to sum up to zero (i.e., we have an equal number of backup and drop-off items). In the second pattern, we have an unequal number of backup and drop-off items, which is close to practical application, such as bike sharing system rebalancing. Our data, models, and code are publicly available at https://github.com/AhmedStohy/Solving-Pickup-and-Dropoff-Problem-Using-Hybrid-Pointer-Networks-with-Deep-Reinforcement-Learning
... Jaw et al. [8] looked at multi-vehicle DARP with pick-up and drop-off windows, and in this case, vehicles cannot be idle while transporting passengers. Healy et al. suggested a new extension of the local search technique to solve the DARP in 1995 [9]. ...
Preprint
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The provision of paratransit services is one option to meet the transportation needs of Vulnerable Road Users (VRUs). Like any other means of transportation, paratransit has obstacles such as high operational costs and longer trip times. As a result, customers are dissatisfied, and paratransit operators have a low approval rating. Researchers have undertaken various studies over the years to better understand the travel behaviors of paratransit customers and how they are operated. According to the findings of these researches, paratransit operators confront the challenge of determining the optimal route for their trips in order to save travel time. Depending on the nature of the challenge, most research used different optimization techniques to solve these routing problems. As a result, the goal of this study is to use Graph Convolutional Neural Networks (GCNs) to assist paratransit operators in researching various operational scenarios in a strategic setting in order to optimize routing, minimize operating costs and minimize their users' travel time. The study was carried out by using a randomized simulated dataset to help determine the decision to make in terms of fleet composition and capacity under different situations. For the various scenarios investigated, the GCN assisted in determining the minimum optimal gap.
... In online mode, insertion [25] is the state-of-the-art operation of the existing works [26,27] in route planning, which inserts the pickup and drop-off locations of a new request into the vehicle's schedule without reordering. Tong et al. [16] proposed an insertion method based on dynamic programming, which checks the constraints in constant time and dispatches requests in linear time. ...
Article
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Ridesharing services aim to reduce travel costs for users and optimize revenue for drivers and platforms by sharing available seats. Existing works can be roughly classified into two types, i.e., online-based and batch-based methods. The former mainly focuses on responding quickly to the requests, and the latter focuses on meticulously enumerating request combinations to improve service quality. However, online-based methods perform poorly in service quality due to the neglect of the sharing relationship between requests, while batch-based methods fail in terms of efficiency. To obtain better service quality more efficiently, we propose a shareability prediction-based framework P-Ride. Specifically, we first introduce the k-clique listing strategy in graph theory based on the shareability graph to reduce the infeasible request combinations. Moreover, we extend the shareability graph to the hypergraph structure to represent the higher-order shareable relationships among requests. Furthermore, we devise a shareability prediction model that supports the prediction of sharable relationships for request combinations of an arbitrary size, which helps further filtering of candidate request combinations with GPU devices acceleration. The extensive experimental results demonstrate the efficiency and effectiveness of our proposed P-Ride framework.
Article
Emergency Medical Services (EMS) first mission is to reach people requiring urgent medical attention and transport them to hospitals or care facilities. In many cases, EMS also provide a second mission, which concerns the non-emergency transportation of patients. These services have different characteristics and goals from a managerial standpoint and in practice, most EMS organisations split their fleet into two sub-fleets that are managed independently. However, both missions are in most of the cases carried out by the same types of ambulances and crews, suggesting that managing both fleets together might bring potential advantages. This study explores the potential advantages of a new management strategy that allows sharing resources between two separated ambulance fleets. In particular, the proposed strategy allows for dynamically modifying the size of each fleet considering that a subset of ambulances can change their mission during the day to better adapt to the system's state. This strategy offers an incomplete integration of the fleets, but has the worthy advantages of improving the overall system performance and being simple to implement by an EMS organisation. Numerical experiments on realistic instances demonstrate, using a discrete event simulation tool, the feasibility and benefits of the proposed strategy.
Chapter
The paper focuses on the static dial-a-ride problem with ride and waiting time minimization. This is an important problem setting of significant practical relevance, as several ridesharing providers launched in recent years in large cities. In contrast to the standard dial-a-ride problem, these providers focus on the general public. Therefore, they are amongst others in competition with taxis and private cars, which makes a more customer-oriented objective necessary. We minimize the sum of relative detours of all customers. The paper introduces upper bounds for the arrival times and an initial lower bound for the objective value. Our approach is tested in a computational study with realistic test instances.
Article
This work reconsiders the concept of community-based trip sharing proposed by Hasan et al. (2018) that leverages the structure of commuting patterns and urban communities to optimize trip sharing. It aims at quantifying the benefits of autonomous vehicles for community-based trip sharing, compared to a car-pooling platform where vehicles are driven by their owners. In the considered problem, each rider specifies a desired arrival time for her inbound trip (commuting to work) and a departure time for her outbound trip (commuting back home). In addition, her commute time cannot deviate too much from the duration of a direct trip. Prior work motivated by reducing parking pressure and congestion in the city of Ann Arbor, Michigan, showed that a car-pooling platform for community-based trip sharing could reduce the number of vehicles by close to 60%. This paper studies the potential benefits of autonomous vehicles in further reducing the number of vehicles needed to serve all these commuting trips. It proposes a column-generation procedure that generates and assembles mini routes to serve inbound and outbound trips, using a lexicographic objective that first minimizes the required vehicle count and then the total travel distance. The optimization algorithm is evaluated on a large-scale, real-world dataset of commute trips from the city of Ann Arbor, Michigan. The results of the optimization show that it can leverage autonomous vehicles to reduce the daily vehicle usage by 92%, improving upon the results of the original Commute Trip Sharing Problem by 34%, while also reducing daily vehicle miles traveled by approximately 30%. These results demonstrate the significant potential of autonomous vehicles for the shared commuting of a community to a common work destination.
Article
Ride-hailing sharing involves grouping ride-hailing customers with similar trips and time schedules to share the same ride-hailing vehicle to reduce their total travel cost. With the current information and communication technology, ride-hailing customers and drivers can be matched in real-time via a ride-hailing platform. This paper formulates a dynamic ride-hailing sharing problem that simultaneously maximizes the number of served customers, minimizes the travel cost and travel time ratios, and considers the capacity, time window, and travel cost constraints. The travel cost ratio is the ratio of actual passengers’ fare to the passengers’ fare without ride-hailing sharing, whereas the travel time ratio is defined as the actual travel time (including waiting time) over the maximum allowable travel time. To solve the dynamic problem, it is divided into many small and continuous static subproblems with an equal time interval. Each subproblem is solved by a modified artificial bee colony (MABC) algorithm with path relinking, while the contraction hierarchies and vantage point tree are used to determine the shortest path and accelerate the algorithm, respectively. Problem properties and the performance of the proposed solution method are demonstrated using large-scale real-time data from Didi that is the largest ride-hailing company in China. The proposed method is shown to outperform the benchmark, i.e., greedy randomized adaptive search procedure (GRASP) with path relinking. The proposed method also performs better when the length of each time interval is longer, and the tolerance for the incremental travel time caused by detours is higher. We also demonstrate that (a) considering both travel cost and travel time ratios in the objective can achieve a better sharing percentage, and balance the increase in the travel time ratio and the decrease in the travel cost ratio compared with the objective that misses either travel time or the travel cost ratio; and (b) the passengers can gain a large out-of-pocket cost saving in the case of ride-hailing sharing while enduring a relatively small increase in travel time compared with the case without ride-hailing sharing.
Chapter
The research paper analyses the level of stress and functional state of the drivers in urban traffic congestion. Therefore, the primary objective of this research is to describe patterns to assess fatigue of the driver during urban traffic congestion. The Electrocardiography (ECG) data is used to assess fatigue of the driver. The model comprising of influence of traffic congestion on the functional state of the average driver, allows us to predict changes to the driver’s state depending on the age, the duration of the traffic congestion and initial state prior to congestion. The value of the initial functional state affects the driver’s functional state during his/her stay in a traffic congestion in different ways. The rising of tension during staying in traffic jam is 10–12% after 7–10 min. The research uses system analysis for data analysis; electrophysiological methods in determining the functional state of the driver and mathematical statistics methods were used during the development of model for analysis of the functional state of the driver.
Article
There has been a dramatic growth of shared mobility applications such as ride-sharing, food delivery, and crowdsourced parcel delivery. Shared mobility refers to transportation services that are shared among users, where a central issue is route planning . Given a set of workers and requests, route planning finds for each worker a route, i.e., a sequence of locations to pick up and drop off passengers/parcels that arrive from time to time, with different optimization objectives. Previous studies lack practicability due to their conflicted objectives and inefficiency in inserting a new request into a route, a basic operation called insertion . In addition, previous route planning solutions fail to exploit the appearance patterns of future requests hidden in historical data for optimization. In this paper, we present a unified formulation of route planning called URPSM. It has a well-defined parameterized objective function which eliminates the contradicted objectives in previous studies and enables flexible multi-objective route planning for shared mobility. We propose two insertion-based frameworks to solve the URPSM problem. The first is built upon the plain-insertion widely used in prior studies, which processes online requests only, whereas the second relies on a new insertion operator called prophet-insertion that handles both online and predicted requests. Novel dynamic programming algorithms are designed to accelerate both insertions to only linear time. Theoretical analysis shows that no online algorithm can have a constant competitive ratio for the URPSM problem under the competitive analysis model, yet our prophet-insertion-based framework can achieve a constant optimality ratio under the instance-optimality model. Extensive experimental results on real datasets show that our insertion-based solutions outperform the state-of-the-art algorithms in both effectiveness and efficiency by a large margin (e.g., up to 30 $$\times$$ more effective in the objective and up to 20 $$\times$$ faster).
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The dial-a-ride problem (DARP) deals with the transportation of people from source to destination locations. One of the most common use cases is in the transportation of elderly or sick people, and as such it represents an important problem to consider. Since DARP is NP-hard, it most often has to be solved using various heuristic methods. Previous studies demonstrated that metaheuristics are suitable for solving this kind of problem. However, in most cases, basic metaheuristics have been considered without any adaptation to the problem, which could potentially limit their performance. Therefore, in this study a GA is proposed and several of its elements adapted for solving DARP. The obtained results show that the proposed algorithm can achieve better results than similar methods from previous studies. Moreover, the experiments demonstrate that the results can be improved by considering some constraints as soft constraints and including them in the cost function to give the algorithm more flexibility in the search.
Thesis
Nos travaux de recherche ont été motivés par une problématique réelle d'optimisation du transport logistique du Centre Hospitalier de Troyes (CHT). Le CHT s'inscrit actuellement dans la revue et l'amélioration des processus et l'implémentation des techniques de recherche opérationnelle afin d’apporter des solutions aux problèmes conjoints de transports de produits et planification des chauffeurs. L'objectif de cette étude est de proposer des solutions efficaces afin d'assurer au quotidien le transport des chariots de repas, de linge, de produits pharmaceutiques et de produits magasiniers. Après la formalisation du problème, nous avons proposé une démarche de résolution composée de trois phases : la première traite du problème connu de collectes et livraisons avec fenêtre de temps et flotte homogène de véhicules, la seconde considère une flotte hétérogène de véhicules, et la troisième phase intègre l'affectation et le dimensionnement de l'équipe des chauffeurs. Nous avons abouti au développement et à la mise en place un outil d'aide à la décision. Nous avons suite à nos travaux, développé et mis en place en partenariat avec la start-up OPTA-LP un logiciel au CHT. Tout au long de nos travaux, nous avons développé des méthodes de résolution exactes et approchées, et aussi élaborer des techniques pour diminuer le temps de résolution dans une approche de résolution exacte, ou encore pour améliorer une solution donnée dans le cas d'une méthode approchée.
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Public transportation is a shared transportation service and includes urban public transit and intercity public transportation. The main transportation modes in urban public transit are buses, trams, trolleybuses, trains, and the metro. Ferries also appear in some cities in the world as an urban transportation mode. Airlines, buses, intercity rail, and, in some countries, high-speed rail are the transportation modes that appear in intercity public transportation. Some of the biggest transit operators in the world operate a few thousand buses and serve a few hundred bus routes. They employ thousands of drivers. The world’s largest airline serves approximately 100 airports in 41 countries with a fleet of nearly 700 aircraft. This chapter considers planning and operations in public transportation systems and includes public transportation network design, service frequencies determination, vehicle and crew scheduling, disruption management, and revenue management problems. The chapter deals with urban public transit systems, interurban road transport systems, and air transportation.
Article
Mobility-On-Demand (MoD) services have been transforming the urban mobility ecosystem. However, they raise a lot of concerns for their impact on congestion, Vehicle Miles Traveled (VMT), and competition with transit. There are also questions about their long-term survival because of inherent inefficiencies in their operations. Considering the popularity of the MoD services, increasing ride-pooling is an important means to address these concerns. Shareability depends not only on riders’ attitudes and preferences but also on operating models deployed by providers. The paper introduces an advance requests operating model for ride pooling, users may request rides in advance of their desired departure times. A platform with efficient algorithms for request matching, vehicle routing, rebalancing, and flexible user preferences is developed. Data from Chengdu, China, and New York, United States are used to evaluate the performance of the advance requests system. The impact of various design aspects of the system (e.g. advance requests horizon, vehicle capacity) on its performance is investigated. The sensitivity of the results to user preferences in terms of the level of service (time to be served and excess trip time), willingness to share and place requests in advance, and traffic conditions are explored. The results suggest that significant benefits in terms of sustainability, level of service, and fleet utilization can be realized when advance requests are along with an increased willingness to share. Furthermore, even “near-on-demand” (relative short planning horizons) operations can offer benefits for all stakeholders (users, operators, cities).
Article
Taxi ride-sharing based on autonomous vehicles (AVs) is seen as a new and promising mode of urban mobility to promise a huge social and environmental benefits, such as conserving fuel, mitigating traffic congestions, reducing air pollution. Although a number of studies have focused on taxipooling or taxi ride-sharing, majority of these studies just concerned about the vehicle routing problem. Limited studies were conducted to excavate and understand the potential benefits of this new mobility mode through a comprehensively designed taxi ride-sharing system. To fill this gap, this study tries to design an autonomous taxi ride-sharing system for commuting trips from the perspective of energy consumption, in which schedule (i.e., taxi type, taxi path, feet size) and depot location are optimized within a unified model. Based on this, we further evaluate its effectiveness in reductions of energy consumption and vehicle usage, and analyze the influences of several key factors on the system efficiency. Case studies show that the taxi ride-sharing service mode needs fewer vehicles than the private car travel mode, and outperforms the traditional taxi service mode in terms of fuel consumption. Moreover, it is found that trip density is an important influence factor on the benefits of taxi ride-sharing system. This study aims to provide transportation managers a good understanding of the energy benefits of well-designed autonomous taxi ride-sharing system.
Article
Socio-demographic trends and recent economic development patterns have resulted in travel behavior changes that call for more flexible and accessible public transit options. Because flexible transit services vary in scope, size, and service type, new data-informed methods are useful to optimize services based on the specific needs of local communities and riders. In this study, real-world demand and vehicle trajectory data were used to evaluate and optimize system performance for an existing first-mile–last-mile (FMLM) service in Robinson Township, PA. A general FMLM model for arbitrary demand and service supply was then developed to quantify system performance—both travel time costs and day-to-day reliability—for various operational polices considering spatio-temporal demand variation and transportation network dynamics. Heuristics were used for optimal real-time vehicle routing in sizable real-world networks accommodating various service types and scopes. In this case study, total user costs were reduced by 18.6% when rides were coordinated with mainline fixed-route transit. Predictive routing strategies were shown to marginally improve system performance under sparse and variable spatio-temporal demand. The case study also highlights potentially large travel time and user reliability improvements—reductions of 51% and 53.8%, respectively—when trip requests were made in advance of their desired pickup time. Finally, we show that travel time reliability can be improved for time-inflexible trips with trip prioritization without increasing total user costs. These results were stable to changes in demand density.
Thesis
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In this thesis, the vehicle routing problem and one of its variants, the vehicle routing problem with simultaneous pick up and deliveries (VRPSPD) are studied. The traditional vehicle routing problem (VRP) consists of constructing minimum cost routes for the vehicles to follow so that the set of customers are visited only once. A lot of effort has been devoted to research on developing fast and effective solution methods for many different versions of this problem by different majors of engineering profession. Thus, a structuring effort is needed to organize and document the vast literature so far has accumulated in this field. Over its lifespan the VRP literature has become quite disjointed and disparate. Keeping track of its development has become difficult because its subject matter transcends several academic disciplines and professions that range from algorithm design to traffic management. Consequently, this dissertation begins with defining VRP’s domain in its entirety, accomplishes an all-encompassing taxonomy for the VRP literature, and delineates all of VRP’s facets in a parsimonious and discriminating manner. Sample articles chosen for their disparity are classified to illustrate the descriptive power and parsimony of the taxonomy. Next, a more detailed version of the original problem, the VRPSPD is examined and a more abstract taxonomy is proposed. Additionally, two other existing classification methodologies are used to distinguish all published VRPSPD papers on their respective research strategies and solution methods. By using well-organized methods this study provides a solid multidimensional identification of all VRPSPD studies’ attributes thus synthesizing knowledge in the filed. Finally, a hybrid meta-heuristic solution algorithm for the VRPSPD problem is presented. To solve this NP-hard vehicle routing problem a GRASP initiated hybrid genetic algorithm is developed. The algorithm is tested on two sets of benchmark problems from the literature with respect to computational efficiency and solution quality. The effect of starting with a better initial population for the genetic algorithm is further investigated by comparing the current results with previously generated ones. The experimental results indicate that the proposed algorithm produces relatively good quality solutions and a better initial population yields a reduction in processing cycles.
Article
Full-text available
An investigation of the single-vehicle, many-to-many, immediate-request dial-a-ride problem is developed in two parts. Part I focuses on the ″static″ case of the problem. A generalized objective function is examined, the minimization of a weighted combination of the time to service all customers and of the total degree of ″dissatisfaction″ experienced by them while waiting for service. A dynamic programming approach is developed. The algorithm exhibits a computational effort. Part II extends this approach to solving the equivalent ″dynamic″ case. Example in both ″static″ and ″dynamic″ cases are presented.
Thesis
Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Civil Engineering.
Article
Discusses the problem of routing or scheduling vehicles in the presence of time window constraints on customer delivery times. An algorithm is presented based upon a time-oriented formulation of the traveling salesman problem. The procedure is designed to exploit the structure provided by the time windows to reduce the computational requirements of a branch and bound solution process. A demonstration of the algorithm is given using several vehicle scheduling problems adapted from the literature. -Author
Article
This paper modifies the exact Dynamic Programming algorithm developed by the author for the single vehicle many-to-many immediate request Dial-A-Ride problem to solve the problem where each customer has specified upper and lower bounds for his pickup and delivery times and where the objective is to minimize the time needed to service all customers. The major difference between the two algorithms is the substitution of backward recursion with forward recursion. The new algorithm requires the same computational effort as the old one and is able to recognize infeasible problem instances.
Article
Certain ″Bus Problems″ are defined as generalizations of the traveling salesman problem. The simplest result concerns the length of the tour required by a single bus to pick up and deliver n passengers from random locations to random destinations in a bounded region of the plane. It is shown that the length of the tour divided by the square root of n converges almost surely to the square root of slightly more than twice the area of the region as n goes to infinity. When several buses are available, the length of the tour is simply divided by the number of buses. The bus problems have been motivated by the practical problem of scheduling dial-a-ride transportation systems.
Article
An analytic investigation into the fundamental aspects of scheduling ″Dial-a-Ride″ transportation systems is conducted. Based upon simple mathematical models that focus on the combinatorial nature of the problem, a class of algorithms is derived for which performance can be measured in a precise asymptotic probabilistic sense. It is concluded that the approach yields many qualitative insights and the resulting transportation schemes have modest computational requirements, are decentralized, and are easy to visualize and implement.
Article
This paper presents an analytic model to predict average waiting and ridingtimes in urban transportation systems (such as dial-a-bus and taxicabs), which provide non-transfer door-to-door transportation with a dynamically dispatched fleet of vehicles. Three different dispatching algorithms are analyzed with a simple deterministic model, which is then generalized to capture the most relevant stochastic phenomena. The formulae obtained have been successfully compared with simulated data and are simple enough for hand calculation. They are, thus, tools which enable analysts to avoid cumbersome simulation models when contemplating implementing or modifying many-to-many demand responsive transportation systems.
Article
Thesis (Ph.D.)--University of Pennsylvania, 1984. Bibliography: leaves [180]-187. Includes index. Microfiche. s
Article
We develop an O(N2) heuristic to solve the single vehicle many-to-many Euclidean Dial-A-Ride problem. The heuristic is based on the Minimum Spanning Tree of the modes of the problem. The algorithm's worst case performance is four times the length of the optimal Dial-A-Ride tour. An analysis of the algorithm's average performance reveals that in terms of sizes of single-vehicle problems that are likely to be encountered in the real world (up to 100 nodes) and in terms of computational complexity, the O(N2) heuristic performs equally well, or, in many cases, better than heuristics described earlier by Stein for the same problem. The performance of the heuristic exhibits statistical stability over a broad range of problem sizes.
Article
We develop k-interchange procedures to perform local search in a precedence-constrained routing problem. The problem in question is known in the Transportation literature as the single vehicle many-to-many Dial-A-Ride Problem, or DARP. The DARP is the problem of minimizing the length of the tour traveled by a vehicle to service N customers, each of whom wishes to go from a distinct origin to a distinct destination. The vehicle departs from a specified point and returns to that point upon service of all customers. Precedence constraints in the DARP exist because the origin of each customer must precede his/her destination on the route. As in the interchange procedure of Lin for the Traveling Salesman Problem (TSP), a k-interchange is a substitution of k of the links of an initial feasible DARP tour with k other links, and a DARP tour is k-optimal if it is impossible to obtain a shorter tour by replacing any k of its links by k other links. However, in contrast to the TSP where each individual interchange takes O(1) time, checking whether each individual DARP interchange satisfies the origin-destination precedence constraints normally requires O(N2) time. In this paper we develop a method which still finds the best k-interchange that can be produced from an initial feasible DARP tour in O(Nk) time, the same order of magnitude as in the Lin heuristic for the TSP. This method is then embedded in a breadth-first or a depth-first search procedure to produce a k-optimal DARP tour. The paper focuses on the k = 2 and k = 3 cases. Experience with the procedures is presented. in which k-optimal tours are produced by applying a 2-opt or 3-opt search to initial DARP tours produced either randomly or by a fast O(N2) heuristic. The breadth-first and depth-first search modes are compared. The heuristics are seen to produce very good or near-optimal DARP tours.
A Heuristic Aigorithm for Routing and Scheduling Dial-a-Ride Vehicles
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A Heuristic Algorithm for Routing and Scheduling Dial-a-Ride Vehicles
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