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Probabilistic a priori routing‐location problems

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  • Igor Averbakh
  • Oded Berman
  • David Simchi‐Levi

Abstract

In many routing‐location models customers located at nodes of a network generate calls for service with known probabilities. The customers that request service in a particular day are served by a single server that performs a service tour visiting these customers. The order of providing service to customers for each potential list of calls is uniquely defined by some a priori fixed basic sequence of all the customers (a priori tour). The problems addressed in this article are to find an optimal home location or an optimal basic sequence for the server so as to minimize the expectation of a criterion. The following criteria are considered: the total waiting time of all the customers, the total length of the tour, the maximal waiting time of a customer, the average traveled length per customer, and the average waiting time per customer. We present polynomial‐time algorithms for the location problems. For the routing problems we present lower bounds that can be calculated efficiently (in polynomial time) and used in a branch‐and‐bound scheme. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Igor Averbakh & Oded Berman & David Simchi‐Levi, 1994. "Probabilistic a priori routing‐location problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(7), pages 973-989, December.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:7:p:973-989
    DOI: 10.1002/1520-6750(199412)41:73.0.CO;2-H
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    References listed on IDEAS

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    1. Oded Berman & David Simchi-Levi, 1988. "Finding the Optimal a Priori Tour and Location of a Traveling Salesman with Nonhomogeneous Customers," Transportation Science, INFORMS, vol. 22(2), pages 148-154, May.
    2. Dimitris J. Bertsimas, 1989. "Traveling Salesman Facility Location Problems," Transportation Science, INFORMS, vol. 23(3), pages 184-191, August.
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    Cited by:

    1. Ahmadi-Javid, Amir & Amiri, Elahe & Meskar, Mahla, 2018. "A Profit-Maximization Location-Routing-Pricing Problem: A Branch-and-Price Algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 866-881.

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