Ride Time Constraints Research Articles

Impact of soft ride time constraints on the complexity of scheduling in Dial-A-Ride Problems

The Dial-a-Ride problem can contain various constraints for pickup-delivery requests, such as time windows and ride time constraints. Given a tour as a sequence of pickups and deliveries, there exist polynomial time algorithms to find a schedule respecting these constraints (provided that there exists one). However, if no such schedule exists, it is natural to ask for a schedule minimising constraint violations. We model a generic fixed-sequence scheduling problem, which we call Min Pickup-Delivery Scheduling, that allows violation of time window constraints (by late visits) and ride time constraints, both penalised with linear penalty functions. Although our model only considers these two types of time constraints, we show that it can express other common time constraints such as earliness and waiting times. We prove that Min Pickup-Delivery Scheduling is APX-hard, even in the very restrictive case where only the ride time constraints can be violated and the time windows have the same length. Conversely, when only the time window constraints can be violated (by late visits), we present a polynomial time algorithm to solve the problem. Then we focus on instances with some specific structural properties and present two polynomial-time algorithms: one for the case where all the ride time constraints are bounded by a constant, and a second one for the case where all the pickups precede all the deliveries in the sequence of stops.

Hybrid and approximate algorithms for the dial-a-ride problem with adaptive ride times considering different service strategies

The dial-a-ride problem (DARP) is that of satisfying a number of pickup and drop-off customer requests, using a fleet of vehicles. In real life, traffic conditions can affect expected travel times, and hence the satisfaction of rigid pickup/drop-off time windows and scheduled ride times. This article considers the DARP with customer-adaptive ride times under different service conditions and strategies. The problem is formulated as a mixed integer linear programming model that minimizes service cost and customer inconvenience. A hybrid genetic–variable neighbourhood search algorithm (GAVNS) is proposed to solve the problem. Experiments are conducted to compare the performance of GAVNS with that of an approximate column generation algorithm, and to evaluate the application of different strategies on service efficiency and customer satisfaction. The results demonstrate the efficiency of GAVNS, and that limited violations of time-window and ride-time constraints can improve the service efficiency while preserving customer satisfaction levels.

A New Formulation for the Dial-a-Ride Problem

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.

A hybrid algorithm for the multi-depot heterogeneous dial-a-ride problem

Vehicle routing problems arise in many practical situations in the context of transportation logistics. Among them, we can highlight the problem of transporting customers from origin to destination locations, which is known as the dial-a-ride problem (DARP). This problem consists of designing least-cost routes to serve pickup-and-delivery requests, while meeting capacity, time window, maximum route duration, and maximum ride time constraints. This work proposes a hybrid algorithm to solve single and multi-depot DARP variants where both the demands and vehicle fleet are heterogeneous. The method combines the iterated local search metaheuristic with an exact procedure based on a set partitioning approach. In addition, several procedures were implemented to speedup the local search phase. Extensive computational experiments were conducted on existing and newly proposed benchmark instances in order to evaluate the impact of the different components of the algorithm, and to compare its performance against the best existing method. The results obtained suggest that the proposed algorithm is capable of producing highly competitive results regarding both solution quality and CPU time, and of improving several best known solutions.

Time-Dependent Vehicle Routing of Free Pickup and Delivery Service in Flight Ticket Sales Companies Based on Carbon Emissions

The time-dependent pollution-routing problem of free pickup and delivery of passengers to the airport service (TDFPDS) is an extension of the time-dependent pollution-routing problems, arising in flight ticket sales companies for the service of free pickup and delivery of airline passengers to the airport. The problem consists of routing a fleet of vehicles in order to deliver a set of customers to the airport considering the traffic congestion, time window constraints, and maximum ride time constraints. The cost function includes fuel consumption and driver costs. We provide an analytical characterization of the optimal solutions for a fixed route and propose a novel heuristic for a given route based on the analysis of the illustrative examples. The heuristic algorithm is embedded into a set-partitioning model to produce high-quality routing plans. Finally, using wide variety of random instances, we present results on the computational performance of the heuristic and also on the impact of the congestion and the maximum ride time constraints.

The traveling salesman problem with pickup, delivery, and ride-time constraints

In the traveling salesman problem with pickup, delivery, and ride-time constraints (TSPPD-RT), a vehicle located at a depot is required to service a number of requests where the requests are known before the route is formed. Each request consists of (i) a pickup location (origin), (ii) a delivery location (destination), and (iii) a maximum allowable travel time from the origin to the destination (maximum ride-time). The problem is to design a tour for the vehicle that (i) starts and ends at the depot, (ii) services all requests, (iii) ensures that each request's ride-time does not exceed its maximum ride-time, and (iv) minimizes the total travel time required by the vehicle to service all requests (objective function). A capacity constraint that may be present is that the weight or volume of the undelivered requests on the vehicle must always be no greater than the vehicle's capacity. In this article, we concurrently analyze the TSPPD-RT with capacity constraints and without capacity constraints. We describe two mathematical formulations of the problem. These formulations are used to derive new lower bounds on the solution to the problem. Then, we provide two exact methods for finding the optimal route that minimizes the total travel cost. Our extensive computational analysis on both versions of the TSPPD-RT shows that the proposed algorithms are capable of solving to optimality instances involving up to 50 requests. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(2), 95–110 2016

A comparison of column-generation approaches to the Synchronized Pickup and Delivery Problem

In the Synchronized Pickup and Delivery Problem (SPDP), user-specified transportation requests from origin to destination points have to be serviced by a fleet of homogeneous vehicles. The task is to find a set of minimum-cost routes satisfying pairing and precedence, capacities, and time windows. Additionally, temporal synchronization constraints couple the service times at the pickup and delivery locations of the customer requests in the following way: a request has to be delivered within prespecified minimum and maximum time lags (called ride times) after it has been picked up. The presence of these ride-time constraints severely complicates the subproblem of the natural column-generation formulation of the SPDP so that it is not clear if their integration into the subproblem pays off in an integer column-generation approach. Therefore, we develop four branch-and-cut-and-price algorithms for the SPDP based on column-generation formulations that use different subproblems. Two of these subproblems are considered for the first time in this paper have not been studied before. We derive new dominance rules and labeling algorithms for their effective solution. Extensive computational results indicate that integrating either both types of ride-time constraints or only the maximum ride-time constraints into the subproblem results in the strongest overall approach.

Evaluating the performance of a dial-a-ride service using simulation

In this paper we study the effects of changes to a paratransit system operated as a dynamic dial-a-ride service. The scheduling of requests is limited by time window constraints and maximum ride time constraints; costs for customer discomfort in form of waiting time and excess ride time are considered in the planning of the service. The parameters defining these constraints and costs are evaluated based on simulations of a real-world scenario. Several different criteria, both regarding customer level of service and operational costs, are used to evaluate the simulation results. By showing which parameters have a large impact on the different evaluation criteria, we can give guidelines to operators of public transport of how to design their dial-a-ride services. Numerical results are presented and from these results conclusions are drawn regarding which parameters are most important in dynamic dial-a-ride services.

The Dial-A-Ride Problem with Transfers

The Dial-A-Ride Problem with Transfers (DARPT) consists in defining a set of routes that satisfy transportation requests of users between a set of pickup points and a set of delivery points, in the presence of ride time constraints. Users may change vehicles during their trip. This change of vehicle, called a transfer, is made at specific locations called transfer points. Solving the DARPT involves modeling and algorithmic difficulties. In this paper we provide a solution method based on an Adaptive Large Neighborhood Search (ALNS) metaheuristic and explain how to check the feasibility of a request insertion. The method is evaluated on real-life and generated instances. Experiments show that savings due to transfers can be up to 8% on real-life instances.

Analysis of the dial-a-ride problem of Hunsaker and Savelsbergh

Hunsaker and Savelsbergh [B. Hunsaker, M. Savelsbergh, Efficient feasibility testing for dial-a-ride problems, Operations Research Letters 30 (2002) 169–173] discussed feasibility testing for a dial-a-ride problem under maximum wait time and maximum ride time constraints. We show that this feasibility test can be expressed as a shortest path problem in vertex-weighted interval graphs, which leads to a simple linear time algorithm.

A note on “Efficient feasibility testing for dial-a-ride problems”

Hunsaker and Savelsbergh [B. Hunsaker, M.W.P. Savelsbergh, Efficient feasibility testing for dial-a-ride problems, Operations Research Letters 30 (2002) 169–173.] developed a linear-time algorithm to verify the feasibility for dial-a-ride problems. However, this algorithm may incorrectly declare infeasibility due to ride time constraints in some cases. We propose a revised procedure to address this flaw, but in an O ( n 2 ) worst-case time.

A Branch-and-Cut Algorithm for the Dial-a-Ride Problem

In the dial-a-ride problem, users formulate requests for transportation from a specific origin to a specific destination. Transportation is carried out by vehicles providing a shared service. The problem consists of designing a set of minimum-cost vehicle routes satisfying capacity, duration, time window, pairing, precedence, and ride-time constraints. This paper introduces a mixed-integer programming formulation of the problem and a branch-and-cut algorithm. The algorithm uses new valid inequalities for the dial-a-ride problem as well as known valid inequalities for the traveling salesman, the vehicle routing, and the pick-up and delivery problems. Computational experiments performed on randomly generated instances show that the proposed approach can be used to solve small to medium-size instances.

Efficient feasibility testing for dial-a-ride problems

Dial-a-ride systems involve dispatching a vehicle to satisfy demands from a set of customers who call a vehicle-operating agency requesting that an item be picked up from a specific location and delivered to a specific destination. Dial-a-ride problems differ from other routing and scheduling problems, in that they typically involve service-related constraints. It is common to have maximum wait time constraints and maximum ride time constraints. In the presence of maximum wait time and maximum ride time restrictions, it is not clear how to efficiently determine, given a sequence of pickups and deliveries, whether a feasible schedule exists. We demonstrate that this, in fact, can be done in linear time.