Lagrangian Formulation for Energy-efficient Warehouse Design

Ivan Derpich, Juan Sepulveda


Energy consumption in modern warehouses is today an important issue which has not received much attention in the scientific community. In this paper it is addressed the problem of warehouse design considering the energy costs incurred by vehicles and equipment in a fully or partially automated facility. Closed-form solutions are obtained by a formulating the Lagrangian of an operational cost function with equality constraints. The contribution of the paper is to develop formulas for reduced energy consumption and pollution, both relevant aspects in sustainable engineering systems. An example applied to a distributor of MRO items is presented. In this version the energy cost is integrated into the formula, modifying the method presented in [1].


Energy optimization, integrated facility design, green supply chains

Full Text:



I. Derpich and J. Sepulveda (2016), A Model for Storage Facility Design with Energy Costs, Computers Communications and Control (ICCCC), 2016 6th International Conference on, IEEE Xplore, e-ISSN 978-1-5090-1735-5, DOI: 10.1109/ICCCC.2016.7496753, 147 - 150.

Y. Bassan, Y. Roll and M.J. Rosenblatt (1980), Internal Layout Design of a Warehouse, IIE Transactions, 12(4): 317-322.

S. Onut, U.R.Tuzkaya, D. Bilgehan (2008), A particle swarm optimization algorithm for the multiple level warehouse layout design problem, Computers & Industrial Engineering, 54: 783-799.

P. Baker and M. Canessa (2009), Warehouse design: A structured approach, European Journal of Operational Research, 193: 425-436.

J. Gu, M.Goetschalckx and L.F. McGinnis (2010), Research on warehouse design and performance evaluation: A comprehensive review, European Journal of Operational Research, 203:539-549.

B. Rouwenhorst, B., B. Reuterb, V. Stockrahmb, G.J. van Houtumc, R.J. Mantela and W.H.M. Zijmc (2000), Warehouse design and control: Framework and literature review, European Journal of Operational Research, 122(3): 515-533.

S.S. Heragu, L. DU, R.J. Mantel and P.C. Schuur (2005), Mathematical model for warehouse design and product allocation International Journal of Production Research, 43(2):327-338.

S. Zhou, Y. Gong and R. De Koster(2016), Designing self-storage warehouses with customer choice, International Journal of Production Research, 54(10): 3080-3104.

K.J. Roodbergen and F.A. Vis (2006), A model for warehouse layout, IIE Transactions, 38:799-811.

J. Li, M. Moghaddam and S.Y. Nof (2016), Dynamic storage assignment with product affinity and ABC classification - a case study, Int J Adv Manuf Technol, 84:2179-2194.

R.L. Francis (1967), On some problems of rectangular warehouse design and layout, Journal of Industrial Engineering, 18: 595-604.

D. G. Luenberger (1989), Linear and non linear programming, Chapter 10, Addison Wesley Iberoamericana, 299-305.


Copyright (c) 2017 Ivan Derpich, Juan Sepulveda

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.


 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2);

SCImago Journal & Country Rank

Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.