Lauri Häme

An adaptive insertion algorithm for the single-vehicle dial-a-ride problem with narrow time windows

The dial-a-ride problem (DARP) is a widely studied theoretical challenge related to dispatching vehicles in demand-responsive transport services, in which customers contact a vehicle operator requesting to be carried from specified origins to specified destinations. An important subproblem arising in dynamic dial-a-ride services can be identified as the single-vehicle DARP, in which the goal is to determine the optimal route for a single vehicle with respect to a generalized objective function. The main result of this work is an adaptive insertion algorithm capable of producing optimal solutions for a time constrained version of this problem, which was first studied by Psaraftis in the early 1980s. The complexity of the algorithm is analyzed and evaluated by means of computational experiments, implying that a significant advantage of the proposed method can be identified as the possibility of controlling computational work smoothly, making the algorithm applicable to any problem size.

Dynamic journeying under uncertainty

We introduce a journey planning problem in multi-modal transportation networks under uncertainty. The goal is to find a journey, possibly involving transfers between different transport services, from a given origin to a given destination within a specified time horizon. Due to uncertainty in travel times, the arrival times of transport services at public transport stops are modeled as random variables. If a transfer between two services is rendered unsuccessful, the commuter has to reconsider the remaining path to the destination. The problem is modeled as a Markov decision process in which states are defined as paths in the transport network. The main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time. By assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem. Analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination, the proposed approximations may be useful for practical purposes due to their computational simplicity. In addition to on-time arrival probability, we show how travel and overdue costs can be taken into account, making the model applicable to freight transportation problems.

Dynamic Journeying in Scheduled Networks

We study a dynamic-journey planning problem for multimodal transportation networks. The goal is to find a journey, possibly involving transfers between different transport modes, from a given origin to a given destination within a specified time horizon. Transport services are represented as sequences of scheduled legs between nodes in the transportation network. Due to uncertainty in transport services, we assume for each pair of adjacent legs i and j a probability of a successful transfer from i to j. If a transfer between two legs is unsuccessful, the customer needs to reconsider the remaining path to the destination. The problem is modeled as a Markov decision process, and the main contribution is a backward induction algorithm that generates an optimal policy for traversing the public transport network in terms of a given objective, e.g., reliability, ride time, waiting time, walking time, or the number of transfers. A straightforward method for maximizing reliability is also suggested, and the algorithms are tested on real-life Helsinki area public transport data. Computational examples show that, with a given input, the proposed algorithms rapidly solve the journeying problem.

Simulation of a large scale dynamic pickup and delivery problem

We study a variant of dynamic vehicle routing problem with pickups and deliveries where a vehicle is allocated to each service (i.e., trip) request immediately upon the arrival of the request. Solutions to this problem can be characterized as dynamic policies that define how each customer is handled by operating a fleet of vehicles. Evaluation of such policies is beyond the grasp of analytical studies and requires extensive simulations. We present an efficient and modular simulation tool developed for studying the performance of a large scale system with different policies under given trip arrival process. Numerical and analytical observations on the model are utilized to provide guidelines for solving the routing problem efficiently, and to support the validation of the simulation results. Application of the developed framework is demonstrated by several numerical examples, e.g., policy parameter optimization, which all give insight on the viability of this type of transportation system.

A Maximum Cluster Algorithm for Checking the Feasibility of Dial-A-Ride Instances

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.

Routing by ranking

The dial-a-ride problem involves the dispatching of a fleet of vehicles in order to transport a set of customers from specific pick-up nodes to specific drop-off nodes. Using a modified version of hyperlink-induced topic search (HITS), we characterize hubs as nodes with many out-links to other hubs and calculate a hub score for each pick-up and drop-off node. Ranking the nodes by hub score gives guidance to a backtracking algorithm for efficiently finding feasible solutions to the dial-a-ride problem.