An integer L -shaped algorithm for the Dial-a-Ride Problem with stochastic customer delays

• Published in: Discrete Applied Mathematics Vol. 159; no. 9; pp. 883 - 895
• Main Authors: Heilporn, Géraldine, Cordeau, Jean-François, Laporte, Gilbert
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 06.06.2011; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Calculus of variations and optimal control; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Cost engineering; Delay; Dial-a-Ride Problem; Exact sciences and technology; Integer [formula omitted]-shaped algorithm; Integers; Mathematical analysis; Mathematical models; Mathematics; Optimization; Sciences and techniques of general use; Stochastic programming; Stochasticity; Theoretical computing; Tours; Vehicles; Dial-a-Ride Problem; Integer L -shaped algorithm; Stochastic programming; Costs; Computer theory; Optimal algorithm; Optimization; Delay; Integer; Experience; Integer L-shaped algorithm; Optimal solution; Combinatorics; Hamiltonian
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2011.01.021

This paper considers a single-vehicle Dial-a-Ride Problem in which customers may experience stochastic delays at their pickup locations. If a customer is absent when the vehicle serves the pickup location, the request is fulfilled by an alternative service (e.g., a taxi) whose cost is added to the total cost of the tour. In this case, the vehicle skips the corresponding delivery location, which yields a reduction in the total tour cost. The aim of the problem is to determine an a priori Hamiltonian tour minimizing the expected cost of the solution. This problem is solved by means of an integer L -shaped algorithm. Computational experiments show that the algorithm yields optimal solutions on several instances within reasonable CPU times. It is also shown that the actual cost of an optimal solution obtained with this algorithm can be significantly smaller than that of an optimal solution obtained with a deterministic formulation.