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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| Veröffentlicht in: | Discrete Applied Mathematics Jg. 159; H. 9; S. 883 - 895 |
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06.06.2011
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| ISSN: | 0166-218X, 1872-6771 |
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| Abstract | 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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| AbstractList | 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. 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. |
| Author | Heilporn, Géraldine Cordeau, Jean-François Laporte, Gilbert |
| Author_xml | – sequence: 1 givenname: Géraldine surname: Heilporn fullname: Heilporn, Géraldine organization: Canada Research Chair in Logistics and Transportation and CIRRELT, HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, Canada H3T 2A7 – sequence: 2 givenname: Jean-François surname: Cordeau fullname: Cordeau, Jean-François organization: Canada Research Chair in Logistics and Transportation and CIRRELT, HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, Canada H3T 2A7 – sequence: 3 givenname: Gilbert surname: Laporte fullname: Laporte, Gilbert email: gilbert@crt.umontreal.ca, gilbert.laporte@cirrelt.ca organization: Canada Research Chair in Distribution Management and CIRRELT, HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, Canada H3T 2A7 |
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| Keywords | 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 |
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| References | Laporte, Louveaux, Mercure (br000085) 1994; 42 Cordeau (br000025) 2006; 54 Gendreau, Laporte, Séguin (br000060) 1996; 88 Psaraftis (br000095) 1980; 14 Ropke, Cordeau, Laporte (br000110) 2007; 49 Desrochers, Laporte (br000045) 1991; 10 Psaraftis (br000100) 1983; 17 Hjorring, Holt (br000065) 1999; 86 Cordeau, Laporte (br000030) 2007; 153 Cordeau, Laporte, Savelsbergh, Vigo (br000040) 2007 Ropke, Cordeau (br000105) 2009; 43 Savelsbergh (br000115) 1992; 4 Desrosiers, Dumas, Soumis (br000050) 1986; 6 Van Slyke, Wets (br000120) 1969; 17 Campbell, Thomas (br000020) 2009; 36 Gendreau, Laporte, Séguin (br000055) 1995; 29 Jaillet (br000075) 1988; 36 P. Jaillet, Probabilistic Traveling Salesman Problems, Ph.D. Thesis, Massachusetts Institute of Technology, 1985. Cordeau, Laporte, Potvin, Savelsbergh (br000035) 2007; vol. 14 E. Bartolini, Algorithms for Network Design and Routing Problems, Ph.D. Thesis, Università di Bologna, 2009. Campbell, Thomas (br000015) 2008; 42 Laporte, Louveaux, Van Hamme (br000090) 2002; 50 Laporte, Louveaux (br000080) 1993; 13 Benders (br000010) 1962; 4 |
| References_xml | – volume: 88 start-page: 3 year: 1996 end-page: 12 ident: br000060 article-title: Stochastic vehicle routing publication-title: European Journal of Operational Research – volume: 49 start-page: 258 year: 2007 end-page: 272 ident: br000110 article-title: Models and branch-and-cut algorithms for pickup and delivery problems with time windows publication-title: Networks – volume: 17 start-page: 638 year: 1969 end-page: 663 ident: br000120 publication-title: SIAM Journal of Applied Mathematics – reference: P. Jaillet, Probabilistic Traveling Salesman Problems, Ph.D. Thesis, Massachusetts Institute of Technology, 1985. – volume: 6 start-page: 301 year: 1986 end-page: 325 ident: br000050 article-title: A dynamic programming solution of the large scale single-vehicle dial-a-ride problem with time windows publication-title: American Journal of Mathematical Management Science – start-page: 367 year: 2007 end-page: 428 ident: br000040 article-title: Vehicle routing publication-title: Handbook in Operations Research & Management Science, vol. 14 – volume: 36 start-page: 1231 year: 2009 end-page: 1248 ident: br000020 article-title: Runtime reduction techniques for the probabilistic traveling salesman problem with deadlines publication-title: Computers & Operations Research – volume: 42 start-page: 1 year: 2008 end-page: 21 ident: br000015 article-title: Probabilistic traveling salesman problem with deadlines publication-title: Transportation Science – volume: 29 start-page: 143 year: 1995 end-page: 155 ident: br000055 article-title: An exact algorithm for the vehicle routing problem with stochastic demands and customers publication-title: Transportation Science – volume: vol. 14 start-page: 429 year: 2007 end-page: 466 ident: br000035 article-title: Transportation on demand publication-title: Handbook in Operations Research & Management Science – volume: 86 start-page: 569 year: 1999 end-page: 584 ident: br000065 article-title: New optimality cuts for a single-vehicle stochastic routing problem publication-title: Annals of Operations Research – volume: 10 start-page: 27 year: 1991 end-page: 36 ident: br000045 article-title: Improvements and extensions to the Miller–Tucker–Zemlin subtour elimination constraints publication-title: Operations Research Letters – volume: 42 start-page: 543 year: 1994 end-page: 549 ident: br000085 article-title: A priori optimization of the probabilistic traveling salesman problem publication-title: Operations Research – reference: E. Bartolini, Algorithms for Network Design and Routing Problems, Ph.D. Thesis, Università di Bologna, 2009. – volume: 4 start-page: 146 year: 1992 end-page: 154 ident: br000115 article-title: The vehicle routing problem with time windows: minimizing route duration publication-title: ORSA Journal on Computing – volume: 50 start-page: 415 year: 2002 end-page: 423 ident: br000090 article-title: An integer publication-title: Operations Research – volume: 13 start-page: 133 year: 1993 end-page: 142 ident: br000080 article-title: The integer publication-title: Operations Research Letters – volume: 17 start-page: 351 year: 1983 end-page: 357 ident: br000100 article-title: An exact algorithm for the single-vehicle many-to-many dial-a-ride problem with time windows publication-title: Transportation Science – volume: 36 start-page: 929 year: 1988 end-page: 936 ident: br000075 article-title: A priori solution of a traveling salesman problem in which a random subset of the customers are visited publication-title: Operations Research – volume: 4 start-page: 238 year: 1962 end-page: 252 ident: br000010 article-title: Partitioning procedures for solving mixed-variables programming problems publication-title: Numerische Mathematik – volume: 153 start-page: 29 year: 2007 end-page: 46 ident: br000030 article-title: The dial-a-ride problem: models and algorithms publication-title: Annals of Operations Research – volume: 54 start-page: 573 year: 2006 end-page: 586 ident: br000025 article-title: A branch-and-cut algorithm for the dial-a-ride problem publication-title: Operations Research – volume: 43 start-page: 267 year: 2009 end-page: 286 ident: br000105 article-title: Branch-and-cut-and-price for the pickup and delivery problem with time windows publication-title: Transportation Science – volume: 14 start-page: 130 year: 1980 end-page: 154 ident: br000095 article-title: A dynamic programming approach to the single-vehicle, many-to-many immediate request dial-a-ride problem publication-title: Transportation Science |
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| SubjectTerms | 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 |
| Title | An integer L -shaped algorithm for the Dial-a-Ride Problem with stochastic customer delays |
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