Minimum Fuel Resource Distribution in Multidimensional Logistic Networks Governed by Base-Stock Inventory Policy

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


The paper addresses the problem of fuel-efficient resource redistribution in logistic networks in the phase preceding the engagement of market relations. In the considered class of systems, two types of entities – external sources and controlled nodes – form a complex interconnection structure. The flow of resources is governed using the classical base-stock inventory policy deployed in a distributed way. The optimization objective is to dynamically adjust the reference stock level at the controlled nodes so that excessive goods traffic is avoided while preparing the network for the customer demand in a latter, active market phase. The discrete-time finite-horizon optimization problem is solved analytically, which allows one to express the pattern of reference stock adaptation in a straightforward to implement, closed form. The derivations are validated by numerical tests.


Optimal control Logistic networks Base-stock policy 


  1. 1.
    Kiesmüller, G.P., de Kok, A.G., Dabia, S.: Single item inventory control under periodic review and a minimum order quantity. Int. J. Prod. Econ. 133(1), 280–285 (2011)CrossRefGoogle Scholar
  2. 2.
    Ignaciuk, P., Bartoszewicz, A.: Dead-beat and reaching-law-based sliding-mode control of perishable inventory systems. Bull. Pol. Acad. Sci. Tech. Sci. 59(1), 39–49 (2011)zbMATHGoogle Scholar
  3. 3.
    Ignaciuk, P.: Discrete inventory control in systems with perishable goods – a time-delay system perspective. IET Control Theory Appl. 8(1), 11–21 (2014)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lai, X., Chen, Z., Giri, B.C., Chiu, C.H.: Two-echelon inventory optimization for imperfect production system under quality competition environment. Math. Probl. Eng. 2015 (2015). Article ID 326919, 11 pagesGoogle Scholar
  5. 5.
    Ignaciuk, P.: Dead-time compensation in continuous-review perishable inventory systems with multiple supply alternatives. J. Process Control 22(5), 915–924 (2012)CrossRefGoogle Scholar
  6. 6.
    Ignaciuk, P.: LQ optimal and robust control of perishable inventory systems with multiple supply options. IEEE Trans. Autom. Control 58(8), 2108–2113 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dominguez, R., Cannella, S., Framinan, J.M.: The impact of the supply chain structure on bullwhip effect. Appl. Math. Model. 39(23–24), 7309–7325 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bartoszewicz, A., Latosiński, P.: Sliding mode control of inventory management systems with bounded batch size. Appl. Math. Model. 66, 296–304 (2019)MathSciNetCrossRefGoogle Scholar
  9. 9.
    de Kok, T., Grob, C., Laumanns, M., Minner, S., Rambau, J., Schade, K.: A typology and literature review on stochastic multi-echelon inventory models. Eur. J. Oper. Res. 269(3), 955–983 (2018)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Cattani, K.D., Jacobs, F.R., Schoenfelder, J.: Common inventory modeling assumptions that fall short: arborescent networks, Poisson demand, and single-echelon approximations. J. Oper. Manag. 29(5), 488–499 (2011)CrossRefGoogle Scholar
  11. 11.
    Cannella, S.: Order-Up-To policies in information exchange supply chains. Appl. Math. Model. 38(23), 5553–5561 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lewis, F.L., Vrabie, D.L., Syrmos, V.L.: Optimal Control, 3rd edn. Wiley, Hoboken (2012)CrossRefGoogle Scholar
  13. 13.
    Ignaciuk, P., Wieczorek, L.: Networked base-stock inventory control in complex distribution systems. Math. Probl. Eng. 2019 (2019). Article ID 3754367, 14 pagesGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Lodz University of TechnologyŁódźPoland

Personalised recommendations