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

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 t...

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Vydáno v:Discrete Applied Mathematics Ročník 159; číslo 9; s. 883 - 895
Hlavní autoři: Heilporn, Géraldine, Cordeau, Jean-François, Laporte, Gilbert
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier B.V 06.06.2011
Elsevier
Témata:
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
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Shrnutí: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.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2011.01.021