On the one-commodity pickup-and-delivery traveling salesman problem with stochastic demands |
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Authors: | François Louveaux Juan-José Salazar-González |
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Institution: | (1) Louvain School of Management, FUNDP, University of Namur, Namur, Belgium;(2) Departamento de Estadística, Investigación Operativa y Computación. Facultad de Matemáticas, Universidad de La Laguna, Av. Astrofísico Francisco Sánchez, 38271 La Laguna, Tenerife, Spain |
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Abstract: | This paper studies how to set the vehicle capacity for traveling Salesman Problems where some of the customer demands are
stochastic. The analyses are done for the one-commodity pickup-and-delivery TSP, as this problem also includes the setting
of the initial load. The paper first considers feasibility issues. This includes finding the smallest vehicle capacity and
some initial load such that a given tour is feasible for all scenarios. Different variants are considered as a function of
the time when information becomes available. The paper then analyzes the case where some penalties are paid for routing a
tour unable to handle customer demands. Various types of penalties are considered. The paper studies properties of the minimal
expected penalty of a given tour, which are then used to provide approaches to find near-optimal tours. Computational results
are presented. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 90C15 90C27 90C90 |
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