Economic Lot-Sizing Problem with Remanufacturing Option: Complexity and Algorithms

  • Kerem Akartunalı
  • Ashwin ArulselvanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10122)


In a single item dynamic lot-sizing problem, we are given a time horizon and demand for a single item in every time period. The problem seeks a solution that determines how much to produce and carry at each time period, so that we will incur the least amount of production and inventory cost. When the remanufacturing option is included, the input comprises of number of returned products at each time period that can be potentially remanufactured to satisfy the demands, where remanufacturing and inventory costs are applicable. For this problem, we first show that it cannot have a fully polynomial time approximation scheme (FPTAS). We then provide a pseudo-polynomial algorithm to solve the problem and show how this algorithm can be adapted to solve it in polynomial time, when we make certain realistic assumptions on the cost structure. We finally give a computational study for the capacitated version of the problem and provide some valid inequalities and computational results that indicate that they significantly improve the lower bound for a certain class of instances.


  1. 1.
    Akartunalı, K., Miller, A.: A computational analysis of lower bounds for big bucket production planning problems. Comput. Optim. Appl. 53(3), 729–753 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Atamtürk, A., Muñoz, J.C.: A study of the lot-sizing polytope. Math. Program. 99, 443–465 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Carnes, T., Shmoys, D.: Primal-dual schema for capacitated covering problems. Math. Program. 153(2), 289–308 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Erickson, R., Monma, C., Veinott, J.A.F.: Send-and-split method for minimum-concave-cost network flows. Math. Oper. Res. 12(4), 634–664 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Florian, M., Klein, M.: Deterministic production planning with concave costs and capacity constraints. Manage. Sci. 18, 12–20 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Florian, M., Lenstra, J., Rinnooy Kan, H.: Deterministic production planning: algorithms and complexity. Manag. Sci. 26(7), 669–679 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Garey, M., Johnson, D.: Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman & Co., New York (1979)zbMATHGoogle Scholar
  8. 8.
    Golany, B., Yang, J., Yu, G.: Economic lot-sizing with remanufacturing options. IIE Trans. 33(11), 995–1003 (2001)Google Scholar
  9. 9.
    Hoesel, C.V., Wagelmans, A.: Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems. Math. Oper. Res. 26, 339–357 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Korte, B., Schrader, R.: On the existence of fast approximation schemes. In: Magasarian, S.R.O., Meyer, R. (eds.) Nonlinear Programming, vol. 4, pp. 415–437. Academic Press, New York (1981)Google Scholar
  11. 11.
    Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization. Wiley-Interscience, New York (1988)CrossRefzbMATHGoogle Scholar
  12. 12.
    Padberg, M., van Roy, T., Wolsey, L.: Valid linear inequalities for fixed charge problems. Oper. Res. 33(4), 842–861 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Rardin, R., Wolsey, L.: Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems. Eur. J. Oper. Res. 71(1), 95–109 (1993)CrossRefzbMATHGoogle Scholar
  14. 14.
    Teunter, R., Bayındır, Z., van den Heuvel, W.: Dynamic lot sizing with product returns and remanufacturing. Int. J. Prod. Res. 44(20), 4377–4400 (2006)CrossRefzbMATHGoogle Scholar
  15. 15.
    van den Heuvel, W.: On the complexity of the economic lot-sizing problem with remanufacturing options. Econometric Institute Research Papers EI 2004-46, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute (2004)Google Scholar
  16. 16.
    Vazirani, V.: Approximation Algorithms. Springer-Verlag New York, Inc., New York (2001)zbMATHGoogle Scholar
  17. 17.
    Wagner, H., Whitin, T.: Dynamic version of the economic lot size model. Manage. Sci. 5, 89–96 (1958)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Management ScienceUniversity of StrathclydeGlasgowUK

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