The inventory routing problem (IRP) is a challenging optimization problem underlying the vendor managed inventory policy. In this paper, we focus on a particular case of this problem, namely, the long-term single-vehicle IRP with stable demand rates. The objective is thus to develop an optimal cyclical distribution plan, of a single product, from a single distribution center to a set of selected customers. After an analysis of the problem’s features, we propose and discuss a hybrid approximation algorithm to solve the problem. The approach is then tested on some randomly generated problems to evaluate its performance.


Cycle Time Demand Rate Vendor Manage Inventory Inventory Rout Problem Minimal Cycle Time 
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  1. 1.
    Campbell, Melissa, A., Savelsbergh, M.W.P.: A Decomposition Approach for the Inventory-Routing Problem. Transportation Science 38(4), 488–502 (2004)CrossRefGoogle Scholar
  2. 2.
    Aghezzaf, E.H., Raa, B., Van Landeghem, H.: Modeling Inventory Routing Problem in Supply Chain of High Consumption Products. European Journal of Operation Research 169, 1048–1063 (2006)CrossRefzbMATHGoogle Scholar
  3. 3.
    Aghezzaf, E.H.: Robust distribution planning for supplier-managed inventory agreements when demand rates and travel times are stationary. Journal of the Operational Research Society (2007)Google Scholar
  4. 4.
    Raa, B.: Models and Algorithms for the Cyclic Inventory Routing Problem. PhD thesis, Gent University, Belgium, pp. 16–48 (2006)Google Scholar
  5. 5.
    Frank, M., Wolfe, P.: An Algorithm for Quadratic Programming. Naval Research Logistics Quarterly 3, 95–110 (1956)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chryssoverghi, I., Bacopoulos, A., Kokkinis, B., Coletsos, J.: Mixed Frank-Wolfe Penalty Method with Applications to Nonconvex Optimal Control Problems. Journal of Optimization Theory and Applications 94(2), 311–334 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    ZhiQuan, L., SuZhong, Zh.: On Extensions of the Frank-Wolfe Theorems. Computational Optimization and Applications 13, 87–110 (1999)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yiqing Zhong
    • 1
  • El-Houssaine Aghezzaf
    • 1
  1. 1.Department of Industrial ManagementGhent UniversityZwijnaardeBelgium

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