OR Spectrum

, Volume 38, Issue 4, pp 849–876 | Cite as

Capacitated dynamic production and remanufacturing planning under demand and return uncertainty

Regular Article

Abstract

This paper considers a stochastic dynamic multi-product capacitated lot sizing problem with remanufacturing. Finished goods come from two sources: a standard production resource using virgin material and a remanufacturing resource that processes recoverable returns. Both the period demands and the inflow of returns are random. For this integrated stochastic production and remanufacturing problem, we propose a nonlinear model formulation that is approximated by sample averages and a piecewise linear approximation model. In the first approach, the expected values of random variables are replaced by sample averages. The idea of the piecewise linear approximation model is to replace the nonlinear functions with piecewise linear functions. The resulting mixed-integer linear programs are solved to create robust (re)manufacturing plans.

Keywords

Remanufacturing Stochastic demand Stochastic returns Robust optimization 

References

  1. Akçalı E, Cetinkaya S (2011) Quantitative models for inventory and production planning in closed-loop supply chains. Int J Prod Res 49(8):2373–2407CrossRefGoogle Scholar
  2. Aloulou MA, Dolgui A, Kovalyov MY (2014) A bibliography of non-deterministic lot-sizing models. Int J Prod Res 52:2293–2310CrossRefGoogle Scholar
  3. Bae H, Moon I, Yun W (2015) A time-varying lot sizes approach for the economic lot scheduling problem with returns. Int J Prod Res 160:1–17CrossRefGoogle Scholar
  4. Bayındır ZP, Erkip N, Güllü R (2007) Assessing the benefits of remanufacturing option under one-way substitution and capacity constraint. Comput Oper Res 34(2):487–514CrossRefGoogle Scholar
  5. Bookbinder J, Tan JY (1988) Strategies for the probabilistic lot-sizing problem with service-level constraints. Manag Sci 34(9):1096–1108CrossRefGoogle Scholar
  6. Buschkühl L, Sahling F, Helber S, Tempelmeier H (2010) Dynamic capacitated lot-sizing problems: a classification and review of solution approaches. OR Spectr 32:231–261CrossRefGoogle Scholar
  7. Dekker R, Fleischmann M, Inderfurth K (2004) Reverse logistics: quantitative models for closed-loop supply chains. Springer, BerlinGoogle Scholar
  8. Fazle Baki M, Chaouch BA, Abdul-Kader W (2014) A heuristic solution procedure for the dynamic lot sizing problem with remanufacturing and product recovery. Comput Oper Res 43:225–236CrossRefGoogle Scholar
  9. Fleischmann M, Bloemhof-Ruwaard JM, Dekker R, Van Der Laan E, Van Nunen JA, Van Wassenhove LN (1997) Quantitative models for reverse logistics: a review. Eur J Oper Res 103(1):1–17CrossRefGoogle Scholar
  10. Harris FW (1913) How many parts to make at once. Factor Mag Manag 10(2):135–136 (152)Google Scholar
  11. Helber S, Sahling F, Schimmelpfeng K (2013) Dynamic capacitated lot sizing with random demand and dynamic safety stocks. OR Spectr 35(1):75–105CrossRefGoogle Scholar
  12. Karimi B, Fatemi Ghomi SMT, Wilson JM (2003) The capacitated lot sizing problem: a review of models and algorithms. Omega 31:365–378CrossRefGoogle Scholar
  13. Kleywegt AJ, Shapiro A, de Mello TH (2002) The sample average approximation method for stochastic discrete optimization. SIAM J Optim 12(2):479–502CrossRefGoogle Scholar
  14. Li C, Liu F, Cao H, Wang Q (2009) A stochastic dynamic programming based model for uncertain production planning of re-manufacturing system. Int J Prod Res 47(13):3657–3668CrossRefGoogle Scholar
  15. Li X, Baki F, Tian P, Chaouch BA (2014) A robust block-chain based tabu search algorithm for the dynamic lot sizing problem with product returns and remanufacturing. Omega 42:75–87CrossRefGoogle Scholar
  16. Li Y, Chen J, Cai X (2006) Uncapacitated production planning with multiple product types, returned product remanufacturing, and demand substitution. OR Spectr 28(1):101–125CrossRefGoogle Scholar
  17. Li Y, Chen J, Cai X (2007) Heuristic genetic algorithm for capacitated production planning problems with batch processing and remanufacturing. Int J Prod Econ 105(2):301–317CrossRefGoogle Scholar
  18. Naeem M, Dias D, Tibrewal R, Chang P, Tiwari M (2013) Production planning optimization for manufacturing and remanufacturing system in stochastic environment. J Intell Manuf 24(4):717–728CrossRefGoogle Scholar
  19. Pan Z, Tang J, Liu O (2009) Capacitated dynamic lot sizing problems in closed-loop supply chain. Eur J Oper Res 198(3):810–821CrossRefGoogle Scholar
  20. Piñeyro P, Viera O (2010) The economic lot-sizing problem with remanufacturing and one-way substitution. Int J Prod Econ 124(2):482–488CrossRefGoogle Scholar
  21. Pokharel S, Mutha A (2009) Perspectives in reverse logistics: a review. Resour Conserv Recycl 53(4):175–182CrossRefGoogle Scholar
  22. Quadt D, Kuhn H (2008) Capacitated lot-sizing with extansions: a review. 4OR 6:61–83CrossRefGoogle Scholar
  23. Quariguasi Frota Neto J, Walther G, Bloemhof J, Van Nunen J, Spengler T (2009) A methodology for assessing eco-efficiency in logistics networks. Eur J Oper Res 193(3):670–682CrossRefGoogle Scholar
  24. Retel Helmrich MJ, Jans R, van den Heuvel W, Wagelmans AP (2014) Economic lot-sizing with remanufacturing: complexity and efficient formulations. IIE Trans 46(1):67–86CrossRefGoogle Scholar
  25. Richter K, Sombrutzki M (2000) Remanufacturing planning for the reverse wagner/whitin models. Eur J Oper Res 121(2):304–315CrossRefGoogle Scholar
  26. Rossi R, Kilic OA, Tarim SA (2015) Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing. Omega 50:126–140CrossRefGoogle Scholar
  27. Rubio S, Chamorro A, Miranda FJ (2008) Characteristics of the research on reverse logistics (1995–2005). Int J Prod Res 46(4):1099–1120CrossRefGoogle Scholar
  28. Sahling F (2013) A column-generation approach for a short-term production planning problem in closed-loop supply chains. BuR Bus Res 6(1):55–75CrossRefGoogle Scholar
  29. Sahling F (2016) Integration of vendor selection into production and remanufacturing planning subject to emission constraints. Int J Prod Res 1–15. doi:10.1080/00207543.2016.1148276
  30. Saliby E (1990) Descriptive sampling: a better approach to monte carlo simulation. J Oper Res Soc 41(12):1133–1142Google Scholar
  31. Sifaleras A, Konstantaras I, Mladenović N (2015) Variable neighborhood search for the economic lot sizing problem with product returns and recovery. Int J Prod Econ 160:133–143CrossRefGoogle Scholar
  32. Tang O, Teunter RH (2006) Economic lot scheduling problem with returns. Prod Oper Manag 15:488–497CrossRefGoogle Scholar
  33. Tempelmeier H (2013) Stochastic lot sizing. In: Smith MJ, Tan B (eds) Handbook of Stochastic Models and Analysis of Manufacturing System Operations, chap 10. Springer, New YorkGoogle Scholar
  34. Tempelmeier H, Hilger T (2015) Linear programming models for a stochastic dynamic capacitated lot sizing problem. Comput Oper Res 59:119–125CrossRefGoogle Scholar
  35. Teunter R, Kaparis K, Tang O (2008) Multi-product economic lot scheduling problem with separate production lines for manufacturing and remanufacturing. Eur J Oper Res 191:241–1253CrossRefGoogle Scholar
  36. Teunter RH, Bayindir ZP, Den Heuvel WV (2006) Dynamic lot sizing with product returns and remanufacturing. Int J Prod Res 44(20):4377–4400CrossRefGoogle Scholar
  37. Wagner HM, Whitin TM (1958) Dynamic version of the economic lot size model. Manag Sci 5(1):89–96CrossRefGoogle Scholar
  38. Zanoni S, Segerstedt A, Tang O, Mazzoldi L (2012) Multi-product economic lot scheduling problem with manufacturing and remanufacturing using a basic period policy. Comput Ind Eng 62(4):1025–1033CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Supply Chain Management and ProductionUniversity of CologneCologneGermany
  2. 2.Department of Production ManagementLeibniz Universität HannoverHannoverGermany

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