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Shared mobility services involving electric autonomous shuttles have increasingly been implemented in recent years. Because of various restrictions, these services are currently offered on fixed circuits and operated with fixed schedules. This study introduces a service variant with flexible stopping patterns and schedules. Specifically, in the electric dial-a-ride problem on a fixed circuit (eDARP-FC), a fleet of capacitated electric shuttles operates on a given circuit consisting of a recharging depot and a sequence of stations where passengers can be picked up and dropped off. The shuttles may perform multiple laps, between which they may need to recharge. The goal of the problem is to determine the vehicles' stopping sequences and schedules, including recharging plans, so as to minimize a weighted sum of the total passenger excess time and the total number of laps. The eDARP-FC is formulated as a nonstandard lap-based mixed integer linear programming and is shown to be NP-Hard. Efficient polynomial time algorithms are devised for two special scheduling subproblems. These algorithms and several heuristics are then applied as subroutines within a large neighborhood search metaheuristic. Experiments on instances derived from a real-life system demonstrate that the flexible service results in a 32%–75% decrease in the excess time at the same operational costs. Funding: This work was supported by the Fonds Wetenschappelijk Onderzoek [Project Data-Driven Logistics: Grant S007318N; Project Optimizing the Design of a Hybrid Urban Mobility System: Grant G020222N; and Grant OR4Logistics]. Y. Molenbruch is partially funded by the Fonds Wetenschappelijk Onderzoek [Grant 1202719N]. The computational resources and services used in this work were provided by the Flemish Supercomputer Center funded by the Fonds Wetenschappelijk Onderzoek and the Flemish Government. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/trsc.2023.1208. [ABSTRACT FROM AUTHOR]

In this paper, we study a paratransit application in which children are transported every day from their homes to their special schools or medical-social establishments. To optimize this transportation system, the establishments collaborate to propose a joint transportation plan. We propose a new algorithm to jointly build vehicle routes that visit several establishments and simultaneously set the establishments' opening hours. This algorithm combines a large neighborhood search, the resolution of a route-based model, and the progressive shrinkage of the planning window. It is applied to a real case from the area of Lyon in France, including 34 schools and 575 heterogeneous users served by a heterogeneous fleet of reconfigurable vehicles. On average, we show that in addition to the 10% of saving that can be expected by sharing vehicle routes between schools, 7% of additional savings can be achieved by school bell adjustment. This cost saving also decreases average user ride times and the number of vehicles required, creating longer routes that are more attractive for driver services. Funding: This work was supported by the European Union through the European Regional Development Fund [Grant RA0012500] and by the French Région Auvergne-Rhône-Alpes through the NOMAd project. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1160. [ABSTRACT FROM AUTHOR]

When demand for transportation is low or sparse, traditional transit cannot provide efficient and good-quality service, because of its fixed structure. For this reason, mass transit is evolving toward some degree of flexibility. Although the extension of Dial-a-Ride systems to general public meets such need of adaptability, it presents several drawbacks mostly related to the their extreme flexibility. Consequently, new transportation alternatives, such as demand-adaptive systems (DASs), combining characteristics from both the traditional transit and Dial-a-Ride, have been introduced. For their twofold nature, DASs require careful planning. We focus on tactical aspects of the planning process by formalizing the single-line DAS design problem with stationary demand and proposing two alternative hierarchical decomposition approaches for its solution. The main motivation behind this work is to provide a general methodology suitable to be used as a tool to build the tactical DAS plan in real-life conditions. We provide an experimental study where the two proposed decomposition methods are compared and the general behavior of the systems is analyzed when altering some design parameters. Furthermore, we test the versatility of our methods on a variety of situation that may be encountered in real-life conditions. [ABSTRACT FROM AUTHOR]

This paper proposes a new mixed integer programming formulation and branch and cut (BC) algorithm to solve the dial-a-ride problem (DARP). The DARP is a route-planning problem where several vehicles must serve a set of customers, each of which has a pickup and delivery location, and includes time window and ride time constraints. We develop "restricted fragments," which are select segments of routes that can represent any DARP route. We show how to enumerate these restricted fragments and prove results on domination between them. The formulation we propose is solved with a BC algorithm, which includes new valid inequalities specific to our restricted fragment formulation. The algorithm is benchmarked on existing and new instances, solving nine existing instances to optimality for the first time. In comparison with current state-of-the-art methods, run times are reduced between one and two orders of magnitude on large instances. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an extension of the R-DARP recently proposed by [Liu M, Luo Z, Lim A (2015) A branch-and-cut algorithm for a realistic dial-a-ride problem. Transporation Res. Part B: Methodological 81(1):267–288.]. The R-DARP, as a variant of the classic dial-a-ride problem (DARP), consists of determining a set of minimum-distance trips for vehicles to transport a set of clients from their origins to their destinations, subject to side constraints, such as capacity constraints, time window constraints, maximum riding time constraints, and manpower planning constraints. Our problem extends the R-DARP by (1) changing its objective to first maximizing the number of requests satisfied and then minimizing the total travel distance of the vehicles, and (2) generalizing the lunch break constraints of staff members. To solve this problem, we propose a two-phase branch-and-price-and-cut algorithm based on a strong trip-based model. The trip-based model is built on a set of nondominated trips, which are enumerated by an ad hoc label-setting algorithm in the first phase. Then we decompose the trip-based model by Benders decomposition and propose a branch-and-price-and-cut algorithm to solve the decomposed model in the second phase. Our two-phase exact algorithm is tested on the R-DARP benchmark instances and a set of new instances generated according to the same real-world data set as the R-DARP instances. Our algorithm quickly solves all of the R-DARP instances to optimality and outperforms the branch-and-cut proposed by Liu, Luo, and Lim. On the 42 new test instances, our algorithm solves 27 instances to optimality in four hours with the largest instance consisting of 36 requests. The online appendix is available at https://doi.org/10.1287/trsc.2017.0772. [ABSTRACT FROM AUTHOR]

In this paper we propose and study a new paratransit transportation system that integrates accessible taxi (or private hire) services, the most widely used form of disabled transport, with semiflexible public bus services that deviate from their nominal route to provide door-to-door transport. The scope of this system is to serve all paratransit orders received and minimize the overall transport cost under practical service quality imperatives. The proposed system and its design aspects are studied by modeling the related planning problem as a mixed integer-linear program. The program incorporates important cost and service-level considerations, and it is solved to optimality by a new exact branch-and-price approach that leverages two types of subproblems, one per mode. An extensive experimental study has been performed to (a) assess the advantage of integrating the two modes, (b) assess the efficiency of the proposed solution method, and (c) provide system design guidelines for achieving an appropriate balance between system operating costs and service quality. [ABSTRACT FROM AUTHOR]

The dial-a-ride problem (DARP) involves the dispatching of a fleet of vehicles to transport customers requesting service and is one of the most challenging tasks of combinatorial optimization. We study the DARP as a constraint satisfaction problem, where the goal is to find a feasible solution with respect to the time, capacity, and precedence constraints, or to prove infeasibility. The main contribution of our work is a new robust method for this problem formulation. The algorithm is based on a dynamic subroutine that finds for any set of customers a maximum cluster, that is, a maximal set of customers that can be served by a single vehicle. The performance of the algorithm is analyzed and evaluated by means of computational experiments, justifying the efficiency of the solution method. [ABSTRACT FROM AUTHOR]

This paper presents a methodology based on generic evolutionary algorithms to solve a dynamic pickup and delivery problem formulated under a hybrid predictive control approach. The solution scheme is designed to support the dispatcher of a dial-a-ride service, where quick and efficient real-time solutions are needed. The scheme considers different configurations of particle swarm optimization and genetic algorithms within a proposed ad-hoc methodology to solve in real time the nonlinear mixed-integer optimization problem related with the hybrid predictive control approach. These consist of different techniques to handle the operational constraints (penalization, Baldwinian, and Lamarckian repair) and encodings (continuous and integer). For parameter tuning, a new approach based on multiobjective optimization is proposed and used to select and study some of the evolutionary algorithms. The multiobjective feature arises when deciding the parameters with the best trade-off between performance and computational effort. Simulation results are presented to compare the different schemes proposed and to advise conditions for the application of the method in real instances. [ABSTRACT FROM AUTHOR]

A dynamic time window relates to two operations that must be executed within a given time meaning that the difference between the points in time when the two operations are performed is bounded from above. The most prevalent context of dynamic time windows is when precedence is given for the two operations so that it is a priori specified that one operation must take place before the other. A prominent vehicle routing problem with dynamic time windows and precedence is the dial-a-ride problem (DARP), where user-specified transportation requests from origin to destination points must be serviced. The paper presents a new branch-and-cut-and-price solution approach for the DARP, the prototypical vehicle-routing problem with ordinary and dynamic time windows. For the first time (to our knowledge), both ordinary and dynamic time windows are handled in the column-generation subproblem. For the solution, an effective column-generation pricing procedure is derived that allows fast shortest-path computations due to new dominance rules. The new approach is compared with alternative column-generation algorithms that handle dynamic time windows either as constraints of the master program or with less effective labeling procedures. Computational experiments indicate the superiority of the new approach. [ABSTRACT FROM AUTHOR]

In this paper we introduce the dial-a-ride problem with split requests and profits (DARPSRP). Users place transportation requests, specifying a pickup location, a delivery location, and a time window for either of the two. Based on maximum user ride time considerations, the second time window is generated. A given fleet of vehicles, each with a certain capacity, is available to serve these requests, and maximum route duration constraints have to be respected. Each request is associated with a revenue and the objective is to maximize the total profit, that is, the total revenue minus the total costs. Transportation requests involving several persons may be split if it is beneficial to do so. We formulate the DARPSRP as a mixed-integer program using position variables and in terms of a path-based formulation. For the solution of the latter, we design a branch-and-price algorithm. The largest instance solved to optimality, when applied to available instances from the literature, has 40 requests; when applied to newly generated instances, the largest instance solved to optimality consists of 24 requests. To solve larger instances a variable neighborhood search algorithm is developed. We investigate the impact of request splitting under different geographical settings, assuming favorable settings for request splitting in terms of the number of people per request. The largest benefits from request splitting are obtained for problem settings exhibiting clustered customer locations. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of a new optimization problem designated as the express minibus problem, which intends to form small groups of clients with compatible boarding/exiting points in time and space for a new type of urban mobility service. This new transport option, as a competitive alternative to the private car, aims to provide almost direct services between dispersed demand poles in places where high-capacity and efficient public transport options are scarce, thus combining the major strengths of both public transport and private vehicles. Conventional public transport systems can present efficient space and energy consumption, whereas private vehicles have high levels of flexibility, are fast, and are always available. The proposed algorithm aims at assessing the potential demand of this new service by developing a clustering algorithm in which the groups of clients formed for each minibus route should present the following characteristics: there is a small number of boarding and exiting points, where in each point there is only boarding or alighting; boarding points should be close to each other, as well as the exiting points; there must be a reasonable distance between the last boarding point and the first exiting point; the average load factor must be high; and for all clients the overall detour time relative to the direct service should be small. This paper presents the rationale and structure of the clustering algorithm, followed by an application for the Lisbon metropolitan area during the morning peak, which could be adapted to the afternoon peak with some slight modifications. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the importance of introducing stochastic elements into service network design formulations. To offer insights into this issue, we take a basic version of the problem in which periodic schedules are built for a number of vehicles and where only the demand may vary stochastically. We study how solutions based on uncertain demand differ from solutions based on deterministic demand and provide qualitative descriptions of the structural differences. Some of these structural differences provide a hedge against uncertainty by using consolidation. This way we get consolidation as output from the model rather than as an a priori required property. Service networks with such properties are robust, as seen by the customers, by providing operational flexibility. [ABSTRACT FROM AUTHOR]

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 (0(N²3N) for N customers) and is able to recognize infeasible problem instances. [ABSTRACT FROM AUTHOR]

An investigation of the single-vehicle, many-to-many, immediate-request dial-a-ride problem is developed in two parts (I and II). Part I focuses on the "static" case of the problem. In this case, intermediate requests that may appear during the execution of the route are not considered. 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. This dissatisfaction is assumed to be a linear function of the waiting and riding times of each customer. Vehicle capacity constraints and special priority rules are part of the problem. A Dynamic Programming approach is developed. The algorithm exhibits a computational effort which, although an exponential function of the size of the problem, is asymptotically lower than the corresponding effort of the classical Dynamic Programming algorithm applied to a Traveling Salesman Problem of the same size. Part II extends this approach to solving the equivalent "dynamic" case. In this case, new customer requests are automatically eligible for consideration at the time they occur. The procedure is an open-ended sequence of updates, each following every new customer request. The algorithm optimizes only over known inputs and does not anticipate future customer requests. Indefinite deferment of a customer's request is prevented by the priority rules introduced in Part L Examples in both "static" and "dynamic" cases are presented. [ABSTRACT FROM AUTHOR]

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. The approach yields many qualitative insights and the resulting transportation schemes have many attractive practiced features. For example, they have modest computational requirements, are decentralized, and are early to visualize and implement. [ABSTRACT FROM AUTHOR]