Reverse Logistics Modelling of Assets Acquisition in a Liquefied Petroleum Gas Company

  • Cristina LopesEmail author
  • Aldina Correia
  • Eliana Costa e Silva
  • Magda Monteiro
  • Rui Borges Lopes
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


In the business of liquefied petroleum gas (LPG), the LPG cylinder is the main asset and a correct planning of its needs is critical. This work addresses a challenge, proposed at an European Study Group with Industry by a Portuguese energy sector company, where the objective was to define an assets acquisition plan, i.e., to determine the amount of LPG cylinders to acquire, and when to acquire them, in order to optimize the investment. The used approach to find the solution of this problem can be divided in three phases. First, it is necessary to forecast demand, sales and the return of LPG bottles. Subsequently, this data can be used in a model for inventory management. Classical inventory models, such as the Wilson model, determine the Economic Order Quantity (EOQ) as the batch size that minimizes the total cost of stock management. A drawback of this approach is that it does not take into account reverse logistics, which in this challenge (i.e. the return of cylinders) plays a crucial role. At last, because it is necessary to consider the return rate of LPG bottles, reverse logistic models and closed loop supply chain models are explored.



COST Action TD1409, Mathematics for Industry Network (MI-NET), COST-European Cooperation in Science and Technology; CIDMA-Center for Research and Development in Mathematics and Applications; FCT-Portuguese Foundation for Science and Technology, project UID/MAT/04106/2013. We would like to thank Ana Sapata from University of Evora, and Claudio Henriques, Fabio Henriques e Mariana Pinto from University of Aveiro for their contributions during the European Study Group.


  1. 1.
    Alinovi, A., Bottani, E., Montanari, R.: Reverse logistics: a stochastic EOQ-based inventory control model for mixed manufacturing/remanufacturing systems with return policies. Int. J. Prod. Res. 50(5), 1243–1264 (2012)CrossRefGoogle Scholar
  2. 2.
    Ballou, R.H.: Business Logistics Management, 4th edn. Prentice Hall, Upper Saddle River (2006)Google Scholar
  3. 3.
    Cassettari, L., Bendato, I., Mosca, M., Mosca, R.: A new stochastic multi source approach to improve the accuracy of the sales forecasts. Foresight 19(1), 48–64 (2017)CrossRefGoogle Scholar
  4. 4.
    Harris, F.W.: Operations Cost, Factory Management Series. Shaw, Chicago (1915)Google Scholar
  5. 5.
    Lopes, I.C., Costa e Silva, E., Correia, A., Monteiro, M., Borges Lopes, R.: Combining data analysis methods for forecasting liquefied petroleum gas cylinders demand. V Workshop on Computational Data Analysis and Numerical Methods, ESTG, Instituto Politécnico do Porto, Portugal, (2018)Google Scholar
  6. 6.
    Richter, K.: The extended EOQ repair and waste disposal model. Int. J. Prod. Econ. 45(1–3), 443–447 (1996)CrossRefGoogle Scholar
  7. 7.
    Sousa, J.: Background of Portuguese domestic energy consumption at european level. In: IT4Energy International Workshop on Information Technology for Energy Applications (2012)Google Scholar
  8. 8.
    Teunter, R.H.: Economic ordering quantities for recoverable item inventory systems. Nav. Res. Logist. 48(6), 484–495 (2001)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Wilson, R.H.: A scientific routine for stock control. Harv. Bus. Rev. 13, 116–28 (1934)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Cristina Lopes
    • 1
    Email author
  • Aldina Correia
    • 2
  • Eliana Costa e Silva
    • 2
  • Magda Monteiro
    • 3
  • Rui Borges Lopes
    • 3
  1. 1.LEMA, CEOS.PPISCAP—Polytechnic of PortoPortoPortugal
  2. 2.CIICESIESTG—Polytechnic of PortoPortoPortugal
  3. 3.CIDMAUniversity of AveiroAveiroPortugal

Personalised recommendations