A column generation and Combinatorial Benders Decomposition algorithm for the Selective Dial-A-Ride-Problem. (April 2022)

• Record Type: Journal Article
• Authors: Rist, Yannik; Forbes, Michael
• Is Part Of: Computers & operations research. Volume 140(2022)
• Publication Date: 2022-04
• Subjects: Transportation -- Vehicle routing -- Dial-a-Ride Problem -- Dantzig–Wolfe decomposition -- Benders decomposition -- Time discretisation -- Variable fixing; Operations research -- Periodicals; Electronic digital computers -- Periodicals; 004.05
• DOI: 10.1016/j.cor.2021.105649
• Languages: English
• ISSNs: 0305-0548

Abstract

Abstract: In Pickup-and-Delivery Problems (PDP), one must design a set of vehicle routes that visit matching pickup and delivery locations. The Selective Dial-A-Ride Problem (SDARP) is a PDP which aims to serve as many pickup–delivery pairs as possible, where each pair has a time window and a maximum ride time. This paper introduces Extended Fragments to solve the SDARP. Extended Fragments stem from a subclass of vehicle routes which can be directly enumerated. An Extended Fragment formulation for the SDARP is proposed and solved using Combinatorial Benders Decomposition, augmented by a time discretisation and a novel variable-fixing technique. This algorithm, along with other recent 'fragment'-based methods for PDP, is an a priori column generation method, combined with Combinatorial Benders Decomposition. The new method solves the existing benchmark for the SDARP, including 11 previously-unsolved instances. Highlights: Column generation and Benders decomposition to solve the Selective Dial-A-Ride Problem. Exploiting symmetry and integrality of objective function with variable fixing. Algorithm outperforms current best methods on existing benchmark instances.