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Inventory Routing Problem with Facility Location

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Algorithms and Data Structures (WADS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11646))

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Abstract

We study problems that integrate depot location decisions along with the inventory routing problem of serving clients from these depots over time balancing the costs of routing vehicles from the depots with the holding costs of demand delivered before they are due. Since the inventory routing problem is already complex, we study the version that assumes that the daily vehicle routes are direct connections from the depot thus forming stars as solutions, and call this problem the Star Inventory Routing Problem with Facility Location (SIRPFL). As a stepping stone to solving SIRPFL, we first study the Inventory Access Problem (IAP), which is the single depot, single client special case of IRP. The Uncapacitated IAP is known to have a polynomial time dynamic program. We provide an NP-hardness reduction for Capacitated IAP where each demand cannot be split among different trips. We give a 3-approximation for the case when demands can be split and a 6-approximation for the unsplittable case. For Uncapacitated SIRPFL, we provide a 12-approximation by rounding an LP relaxation. Combining the ideas from Capacitated IAP and Uncapacitated SIRPFL, we obtain a 24-approximation for Capacitated Splittable SIRPFL and a 48-approximation for the most general version, the Capacitated Unsplittable SIRPFL.

This material is based upon research supported in part by the U. S. Office of Naval Research under award number N00014-18-1-2099, and the U. S. National Science Foundation under award number CCF-1527032.

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Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA, 15213, USA

    Yang Jiao & R. Ravi

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  1. Yang Jiao
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  2. R. Ravi
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Correspondence to Yang Jiao .

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Editors and Affiliations

  1. Department of Computing Science, University of Alberta, Edmonton, AB, Canada

    Zachary Friggstad

  2. School of Computer Science, Carleton University, Manotick, ON, Canada

    Jörg-Rüdiger Sack

  3. Department of Computing Science, University of Alberta, Edmonton, AB, Canada

    Mohammad R Salavatipour

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Jiao, Y., Ravi, R. (2019). Inventory Routing Problem with Facility Location. In: Friggstad, Z., Sack, JR., Salavatipour, M. (eds) Algorithms and Data Structures. WADS 2019. Lecture Notes in Computer Science(), vol 11646. Springer, Cham. https://doi.org/10.1007/978-3-030-24766-9_33

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  • DOI: https://doi.org/10.1007/978-3-030-24766-9_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24765-2

  • Online ISBN: 978-3-030-24766-9

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