Abstract
This work studies a multi-echelon multi-item lot-sizing problem with remanufacturing and lost sales. The problem is formulated as a mixed-integer linear program. A new family of valid inequalities taking advantage of the problem structure is introduced and used in a customized branch-and-cut algorithm. The provided numerical results show that the proposed algorithm outperforms both the generic branch-and-cut algorithm embedded in a standard-alone mathematical solver and a previously published customized branch-and-cut algorithm.
This work was partially funded by the National Agency for Research and Development (ANID)/Scholarship Program/DOCTORADO BECAS CHILE/2018 - 72190160.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akartunalı, K., Arulselvan, A.: Economic lot-sizing problem with remanufacturing option: complexity and algorithms. In: Pardalos, P.M., Conca, P., Giuffrida, G., Nicosia, G. (eds.) MOD 2016. LNCS, vol. 10122, pp. 132–143. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-51469-7_11
Ali, S.A.S., Doostmohammadi, M., Akartunalı, K., van der Meer, R.: A theoretical and computational analysis of lot-sizing in remanufacturing with separate setups. Int. J. Prod. Econ. 203, 276–285 (2018)
Bansal, M.: Facets for single module and multi-module capacitated lot-sizing problems without backlogging. Discret. Appl. Math. 255, 117–141 (2019)
Brahimi, N., Absi, N., Dauzère-Pérès, S., Nordli, A.: Single-item dynamic lot-sizing problems: an updated survey. Eur. J. Oper. Res. 263(3), 838–863 (2017)
Cunha, J.O., Konstantaras, I., Melo, R.A., Sifaleras, A.: On multi-item economic lot-sizing with remanufacturing and uncapacitated production. Appl. Math. Model. 50, 772–780 (2017)
Guan, Y., Ahmed, S., Nemhauser, G.L.: Cutting planes for multistage stochastic integer programs. Oper. Res. 57(2), 287–298 (2009)
Leung, J.M., Magnanti, T.L., Vachani, R.: Facets and algorithms for capacitated lot sizing. Math. Program. 45(1), 331–359 (1989)
Loparic, M., Pochet, Y., Wolsey, L.A.: The uncapacitated lot-sizing problem with sales and safety stocks. Math. Program. 89(3), 487–504 (2001)
Miller, A.J., Nemhauser, G.L., Savelsbergh, M.W.: On the capacitated lot-sizing and continuous 0–1 knapsack polyhedra. Eur. J. Oper. Res. 125(2), 298–315 (2000)
Pochet, Y., Wolsey, L.A.: Polyhedra for lot-sizing with Wagner–whitin costs. Math. Program. 67(1), 297–323 (1994)
Pochet, Y., Wolsey, L.A.: Production Planning by Mixed Integer Programming. Springer Science & Business Media (2006). https://doi.org/10.1007/0-387-33477-7
Quezada, F., Gicquel, C., Kedad-Sidhoum, S., Vu, D.Q.: A multi-stage stochastic integer programming approach for a multi-echelon lot-sizing problem with returns and lost sales. Comput. Oper. Res. 116, 104865 (2020)
Retel Helmrich, M.J., Jans, R., van den Heuvel, W., Wagelmans, A.P.: Economic lot-sizing with remanufacturing: complexity and efficient formulations. IIE Trans. 46(1), 67–86 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Quezada, F., Gicquel, C., Kedad-Sidhoum, S. (2021). New Valid Inequalities for a Multi-echelon Multi-item Lot-Sizing Problem with Returns and Lost Sales. In: Mes, M., Lalla-Ruiz, E., Voß, S. (eds) Computational Logistics. ICCL 2021. Lecture Notes in Computer Science(), vol 13004. Springer, Cham. https://doi.org/10.1007/978-3-030-87672-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-87672-2_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-87671-5
Online ISBN: 978-3-030-87672-2
eBook Packages: Computer ScienceComputer Science (R0)