Models and algorithms for the heterogeneous dial-a-ride problem with driver-related constraints

Abstract

This paper introduces models and algorithms for a static dial-a-ride problem arising in the transportation of patients by non-profit organizations such as the Austrian Red Cross. This problem is characterized by the presence of heterogeneous vehicles and patients. In our problem, two types of vehicles are used, each providing a different capacity for four different modes of transportation. Patients may request to be transported either seated, on a stretcher or in a wheelchair. In addition, some may require accompanying persons. The problem is to construct a minimum-cost routing plan satisfying service-related criteria, expressed in terms of time windows, as well as driver-related constraints expressed in terms of maximum route duration limits and mandatory lunch breaks. We introduce both a three-index and a set-partitioning formulation of the problem. The linear programming relaxation of the latter is solved by a column generation algorithm. We also propose a variable neighborhood search heuristic. Finally, we integrate the heuristic and the column generation approach into a collaborative framework. The column generation algorithm and the collaborative framework provide tight lower bounds on the optimal solution values for small-to-medium-sized instances. The variable neighborhood search algorithm yields high-quality solutions for realistic test instances.

The pickup and delivery problem with time windows and scheduled lines

“…The author proposes a Branch & Cut (B&C) and a variable neighbourhood search (VNS) algorithm to solve the DARP. Parragh et al (2012) extend the heterogeneous DARP to consider driver-related constraints and propose a hybrid column generation and VNS heuristic algorithm.…”

A memetic algorithm for the patient transportation problem

“…These constraints have been examined in ambulance routing problems [36,26]. For example, Parragh et al [37] proposed a heterogeneous DARP that considers the requirements of assistants (referred to as attendants in their paper) and lunch break constraints. They implemented a branch-and-price algorithm to solve the problem.…”

The Dial-a-Ride Problem with Split Requests and Profits

“…The two resources w and f are needed to compute the minimum possible duration of a route. They are based on the notion of forward time slack (Savelsbergh 1992) and have also been used in Parragh et al (2012).…”