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Lagrangian Relaxation Bounds for a Production-Inventory-Routing Problem

  • Agostinho AgraEmail author
  • Adelaide Cerveira
  • Cristina Requejo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10122)

Abstract

We consider a single item Production-Inventory-Routing problem with a single producer/supplier and multiple retailers. Inventory management constraints are considered both at the producer and at the retailers, following a vendor managed inventory approach, where the supplier monitors the inventory at retailers and decides on the replenishment policy for each retailer. We assume a constant production capacity. Based on the mathematical formulation we discuss a classical Lagrangian relaxation which allows to decompose the problem into four subproblems, and a new Lagrangian decomposition which decomposes the problem into just a production-inventory subproblem and a routing subproblem. The new decomposition is enhanced with valid inequalities. A computational study is reported to compare the bounds from the two approaches.

Keywords

Inventory routing Lagrangian relaxation Lagrangian decomposition Lower bounds 

Notes

Acknowledgements

The research of the first and third authors was supported through CIDMA and FCT, the Portuguese Foundation for Science and Technology, within project UID/MAT/ 04106/2013. The research of the second author was financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”, and by FCT within project UID/EEA/50014/2013.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Agostinho Agra
    • 1
    Email author
  • Adelaide Cerveira
    • 2
    • 3
  • Cristina Requejo
    • 1
  1. 1.University of Aveiro and CIDMAAveiroPortugal
  2. 2.University of Trás-os-Montes e Alto-DouroVila RealPortugal
  3. 3.INESC TECPortoPortugal

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