Prognosis of product take-back for enhanced remanufacturing

  • Christos Aristeides TsiliyannisEmail author


Remanufacturing reduces final wastes to sinks, extraction of virgin materials and pollution from production processes by reinstating products taken back by end-users to satisfy part of overall demand. Product returns are delayed and possibly limited in periods of fast growth and excessive in the aftermath. Varying growth/demand and volatile take back by consumers and industrial end-users introduce uncertainty, regarding quantity and quality of returns. As remanufacturing expands, escalating competition for acquisition of high quality returns exacerbates uncertainty. Production planning and control for efficient remanufacturing depends on reliable prediction of quantity and quality of returns. A method is developed for prognosis of product return quantity and quality grades, as reflected by vintage flows. It is anchored on a law relating stock and end-of-life level, under random losses and arbitrary end-of-life distribution. Efficacy is tested via a model that describes stock and flows in reuse/remanufacturing, allowing for varying demand, random stock losses, random product returns with time-varying distributions and time-varying utilisation of product returns. Realisations are obtained by Marko-chain Monte-Carlo simulation. Inherently integral in nature, using scaled data and founded on rigorous balances, the method enables prognosis of returns and age-vintage flows, under realistic conditions, including unknown nonlinearities and non-stationarities. It features improved performance (mean absolute error less than one half) compared to leading methods in-use that employ black-box models with error-driven parameter adaptation (e.g. regression). Efficacy is particularly high at crucial peaks and lows (shortage or surplus periods) enabling resourceful planning of acquisition and inventory control of product returns towards sustainability.


Remanufacturing Reuse Product take-back Forecasting of product returns Closed loop supply chain Circular economy 



= Pt + Inet,t, Product inflow in period t, e.g. year t, (tons/period, e.g. t/y), a = steady state level


Autoregressive moving average, ARIMA AR integral MA


Overall sales, originals+remanufactured, consumption (t/y)


Polynomial of degree 2(N-κ) + μ + 1


Coefficient of order-k term in the polynomial D(x)


End-of-life (no further reusable product returns)


End-of-use (reusable product returns)


EoL flow (EoL product returns) or EoL exit in period t, e.g. year t, (tons/period)


= 1-g'1-g'2-…-g'k, complementary cumulative distribution of the EoL exit distribution, gi,

gi, t, i = 1, 2, ..., ν

Reusable product return distribution (gi, t= fraction returned in period t = t* + jκ-μ + i, i = 1,2,..,ν, j = 1,2,…,Ν-1,of an originally manufactured product in time period t*)


Expected value of the stochastic process gi, t, i = 1,2,..,ν,


Entries of vector \( \underset{\_}{h} \) given by eqs. 46 (or coefficients of polynomial eq. A3), Appendix A


Flow of original net imported products = imports -exports = Iprod,tExprod,t (t/period)


Maximum age in the reusable product return sample


Maximum age in the stock sample


Mean absolute percentage error


Mean residence time = mean lifespan, time periods, e.g. years


Minimum age in the EoL sample


Minimum age in the reusable product return sample


Number of manufacturing cycles (original plus N-1 remanufacturing cycles)


Original production flow (t/period), (original items made from virgin or recycled material)


Polynomial defined in eq. A4, Appendix A,


Coefficients of order-k term in the polynomial P(x) found from eqs. 7


Reusable return flow, Q = steady state value

Qs, t

Size (mass) of the reusable product return sample at time t

Qs, i, t

Size (mass) of vintage of age i in the reusable return sample at time t


Steady state product return flow rate with respect to inflow of original products = Q/a


Actually reused/remanufactured product flow, (t/period)


Early loss ratio = Ωt/(Ut + Ωt) = probability of early loss (prior to EoL exit) in period t


Time periods form production to centre axis of EoL exit (T = maximum lifetime for. products with non-distributed, deterministic exit in a single time period)


Product accumulation: quantity of product stock present at the end of time period t (tons)


=1-st = retention ratio = probability of remaining in the reuse/remanufacturing cycle in period t

yi, t

Mass fraction of vintage of age i in the reusable return flow in time period t


Ratio of mass of the vintage of age i in the reusable return flow in time period t over the mass of the same vintage in the corresponding product stock



=E/a = steady state EoL flow ratio with respect to inflow of originals = EoL rate or yield


=Stock mean age at time period t


=EoL flow mean age at time period t


=Mean cycle duration, time periods


Half spread of the take-back/EoL distribution, time periods


=2 μ + 1 = spread of the take-back/EoL distribution, time periods

Π (x)

Polynomial in x defined in Appendix A, eqs. A5, A6


Coefficients of Π(x), Eq. A5 given by Eq. 9 or Eq. A6


=U/a = mean residence time or mean product lifespan = MRT


Mean take-back fraction of reusable products with respect to reusable product stock


=Early loss flow (t/period)



Equal by definition.

< >

Mean sample path value (MSPV)



t is discrete time, t = 1: first time a product under consideration is launched in the market.





  1. 1.
    Abbey JD, Meloy MG, Guide VDR, Atalay S (2015) Remanufactured products in closed-loop supply chains for consumer goods. Prod Op Man 24(3):488–503Google Scholar
  2. 2.
    Atasu A, Cetinkaya S (2006) Lot sizing for optimal collection and use of remanufacturable returns over a finite life-cycle. Prod Oper Manag 15(4):473–487Google Scholar
  3. 3.
    Atasu A, Sarvary M, Van Wassenhove LN (2008) Remanufacturing as a marketing strategy. Manag Sci 54(10):1731–1174Google Scholar
  4. 4.
    Barquet, A., P, Rozenfeld, H, Fernando, A: An integrated approach to remanufacturing: model of a remanufacturing system Jnl Remanufacture 3:1 (2013)
  5. 5.
    Bulmus C, Zhu SX, Teunter RH (2014) Optimal core acquisition and pricing strategies for hybrid manufacturing and remanufacturing systems. Int J Prod Res 52(22):6627–6641Google Scholar
  6. 6.
    Canda A, Yuan XM, Wang FY (2016) Modeling and forecasting product returns: an industry case study. In: International Conf. On IEEM, 2016-January, vol 7385772, pp 871–875Google Scholar
  7. 7.
    Cooper DR, Gutowski TG (2017) The environmental impacts of reuse: a review. J Ind Ecol 21(1):38–56Google Scholar
  8. 8.
    Clottey T, Benton WC (2010) Core acquisitions planning in the automotive parts remanufacturing industry. The Ohio State UniversityGoogle Scholar
  9. 9.
    Clottey T, Benton WC Jr, Srivastava R (2012) Forecasting product returns for remanufacturing operations. Decis Sci 43(4):589–614Google Scholar
  10. 10.
    de Brito MP, Dekker R (2003) Modelling product returns, in inventory control - exploring the validity of general assumptions. Int J Prod Econ 81(82):225–241Google Scholar
  11. 11.
    de Brito M. P., Managing reverse logistics or reversing logistics management? Ph.D. Thesis, Research Institute of Management, Erasmus Univ., Rotterdam (2004)Google Scholar
  12. 12.
    Dindarian A, Gibson AP, Quariguasi-Frota-Neto J (2012) Electronic product returns and potential reuse opportunities: a microwave case study in the United Kingdom. J Clean Prod 32:22–31Google Scholar
  13. 13.
    Ding Y., Xu H, Tan BCY (2016) Predicting product return rate with tweets. Proceedings Pacific Asia Conference on Information Systems, paper 345Google Scholar
  14. 14.
    Ecoelastica (2013) Statistical data,
  15. 15.
    Fatimah YA, Biswas WK (2016) Sustainability assessment of remanufactured computers. Procedia CIRP 40:150–155. Google Scholar
  16. 16.
    Ferguson M, Toktay LB (2006) The effect of competition on recovery strategies. Prod Op Manag 15(3):351–368Google Scholar
  17. 17.
    Ferguson M, Guide VD Jr, Koca E, Souza GC (2009) The value of quality grading in remanufacturing. Prod Op Man 18(3):300–314Google Scholar
  18. 18.
    Ferguson ME, Souza GC (2010) Closed-loop supply chains: new developments to improve the sustainability of business practices. CRC Press Taylor & Francis GroupGoogle Scholar
  19. 19.
    Ferrao P, Ribeiro P, Silva P (2008) A management system for end-of-life tires: the Portuguese case study. Waste Manag 28(3):604–614Google Scholar
  20. 20.
    Ferrer G (1997) The economics of tire remanufacturing. Resour Conserv Recycl 19(4):221–255MathSciNetGoogle Scholar
  21. 21.
    Ferrer G (1997) The economics of personal computer remanufacturing. Resour Conserv Recycl 21:79–108Google Scholar
  22. 22.
    Fleischmann M (2000) Quantitative models for reverse logistics, Ph.D. thesis. Erasmus University Rotterdam. Rotterdam, The NetherlandsGoogle Scholar
  23. 23.
    Fleischmann M, Kuik R, Dekker R (2002) Controlling inventories with stochastic item returns: a basic model. Eur J Oper Res 138(1):63–75MathSciNetzbMATHGoogle Scholar
  24. 24.
    Galbreth MR, Blackburn JD (2006) Optimal acquisition and sorting policies for remanufacturing. Prod Op Man 15(3):384–392Google Scholar
  25. 25.
    Gallager R (2015) Discrete stochastic processes. Lecture Notes, MITGoogle Scholar
  26. 26.
    Gao WJ and Xing B (2013) Computational intelligence in remanufacturing. IG Global, ISBN: 9781466649088Google Scholar
  27. 27.
    Georgiadis P, Vlachos D, Tagaras G (2006) The impact of product lifecycle on capacity planning of closed-loop supply chains with remanufacturing. Prod Op Man 15(4):514–527Google Scholar
  28. 28.
    Goh TN, Varaprasad N (1986) A statistical methodology for the analysis of the life-cycle of reusable containers. IIE Trans 18(1):42–47Google Scholar
  29. 29.
    Govindan K, Soleimani H, Kannan D (2015) Reverse logistics and closed-loop supply chain: a comprehensive review to explore the future. Eur J Oper Res 240:603–626MathSciNetzbMATHGoogle Scholar
  30. 30.
    Guide VDR Jr (2000) Production planning and control for remanufacturing: industry practice and research needs. J Oper Manag 18:467–448Google Scholar
  31. 31.
    Guide VDR Jr, Van Wassenhove LN (2001) Managing product returns for remanufacturing. Prod Op Man 10(2):142–155Google Scholar
  32. 32.
    Hatcher G, Ijomah W, Windmill J (2013) Design for remanufacturing in China: a case study of electrical and electronic equipment. J Remanuf 3:3Google Scholar
  33. 33.
    Halstenberg FA. Steingrímsson JG and Stark R (2017) Material reutilization cycles across industries and production lines. Chapter in Sustainable Manufacturing, challenges, solutions and implementation perspectives, part of the series sustainable production, life cycle engineering and management, Springer, 163–173Google Scholar
  34. 34.
    Hanafi J, Sami K, Hartmut K (2007) Generating fuzzy coloured petri net forecasting model to predict the return of products. In: Electronics and the Environment, Proceedings of 2007 IEEE Intern. Symp, Orlando, FL, pp 245–250.
  35. 35.
    Hess JD, Mayhew GE (1997) Modeling merchandise returns in direct marketing. J Interact Mark 11(2):20–35Google Scholar
  36. 36.
    Ijomah W (2009) Addressing decision making for remanufacturing operations and design-for-remanufacture. Int J Sustain Eng 2(2):91–102. Google Scholar
  37. 37.
    Jayaraman V (2006) Production planning for closed-loop supply chains with product recovery and reuse: an analytical approach. Int J Prod Res 44(5):981–998zbMATHGoogle Scholar
  38. 38.
    Jayaraman V, Singh R, Anandnarayan A (2012) Impact of sustainable manufacturing practices on consumer perception and revenue growth: an emerging economy perspective. Int J Prod Res 50(5):1395–1410Google Scholar
  39. 39.
    Junior ML, Fihlo MG (2011) Production planning and control for remanufacturing: literature review and analysis. Prod Plan Control:419–435.
  40. 40.
    Kelle P, Silver EA (1989) Forecasting the returns of reusable containers. J Oper Manag 8(1):17–35Google Scholar
  41. 41.
    Kiesmuller PG, van der Laan AE (2001) An inventory model with dependent product demands and returns. Int J Prod Econ 72(1):73–87Google Scholar
  42. 42.
    Kumar DT, Soleimani H, Kannan G (2014) Forecasting return products in an integrated forward/reverse supply chain utilizing an ANFIS. Int J Appl Math Comput Sci 24(3):669–682MathSciNetzbMATHGoogle Scholar
  43. 43.
    Liang X, Jin X, Ni J (2014) Forecasting product returns for remanufacturing systems. J Remanufacturing 4(1):8 Google Scholar
  44. 44.
    Lyons DI (2007) A spatial analysis of loop closing among recycling, remanufacturing and waste treatment firms in Texas. J Ind Ecol 11(1):43–54Google Scholar
  45. 45.
    Mahadevan B, Pyke DF, Fleischmann M (2002) Periodic review, push inventory policies for remanufacturing. In: ERIM report series ERS-2002-35-LIS, Faculty of Business Administration, Erasmus University Rotterdam, The NetherlandsGoogle Scholar
  46. 46.
    Marx-Gómez J, Rautenstrauch C, Nürnberger A, Kruse R (2002) Neuro-fuzzy approach to forecast returns of scrapped products to recycling and remanufacturing. Knowl-Based Syst 15(1–2):119–128Google Scholar
  47. 47.
    Matsumoto M, Umeda Y (2011) An analysis of remanufacturing practices in Japan. J Remanuf 1(2):2. Google Scholar
  48. 48.
    Meinen GP, Verbiest P. de Wolf (1998) Perpetual inventory method service lives discard patterns and depreciation methods, Statistics Netherlands, Department of National AccountsGoogle Scholar
  49. 49.
    Mueller DB, Cao J, Kongar E, Altonji M, Weiner P-H, Graedel TE (2007) Service lifetimes of mineral end uses, U.S. Geological Survey. In: Minerals resources external research program award no: 06HQGR0174Google Scholar
  50. 50.
    Muller DB (2006) Stock dynamics for forecasting material flows-case study for housing in the Netherlands. Ecol Econ 59(1):142–156Google Scholar
  51. 51.
    Murakami S, Oguchi M, Tasaki T, Daigo I, Hashimoto S (2010) Lifespan of commodities, part I, the creation of a database and its review. J Ind Ecol 14(4):598–612Google Scholar
  52. 52.
    Mutha A, Bansal S, Guide VDR (2016) Managing demand uncertainty through core acquisition in remanufacturing. Prod Op Man 25(8):1449–1464Google Scholar
  53. 53.
    Neira J, Favret L, Fuji M, Miller R, Mahdavi S, Blass VD (2006) End-of-Life Management of Cell Phones in the United States. Theses, Univ. of California, S. BarbaraGoogle Scholar
  54. 54.
    OECD (1993) Methods used by OECD countries to measure stocks of fixed capital, national accounts: sources and methods, no. 2, ParisGoogle Scholar
  55. 55.
    Oguchi M, Murakami S, Tasaki T, Daigo I, Hashimoto S (2010) Lifespan of commodities, part II, methodologies for estimating lifespan distribution of commodities. J Ind Ecol 14(4):613–626Google Scholar
  56. 56.
    Opresnik D, Taisch M (2015) The manufacturer’s value chain as a service - the case of remanufacturing. J Remanuf 5(2).
  57. 57.
    Rathore P, Kota S, Chakrabarti A (2011) Sustainability through remanufacturing in India: a case study on mobile handsets. J Clean Prod 19(15):1709–1722Google Scholar
  58. 58.
    Rosado L, Niza S, Ferrao P (2014) A material flow accounting case study of the Lisbon metropolitan area using the urban metabolism analyst model. J Ind Ecol 18(1):84–101Google Scholar
  59. 59.
    Shang G (2014) Three essays on consumer product returns. (Doctoral dissertation). Retrieved from
  60. 60.
    Srivastava SK, Srivastava RK (2006) Managing product returns for reverse logistics. Intern J Phys Distr Logistics Manag 36(7):524–546Google Scholar
  61. 61.
    Steffens PR (2001) An aggregate sales model for consumer durables incorporating a time-varying mean replacement age. J Forecasting 20(1):63–77Google Scholar
  62. 62.
    Subramoniam R, Huisingh D, Chinnam R (2009) Remanufacturing for the automotive aftermarket – strategic factors: literature review and future research needs. J Clean Prod 17:1168–1174Google Scholar
  63. 63.
    Subramoniam R, Huisingh D, Chinnam RB (2010) Aftermarket remanufacturing strategic planning decision-making framework: theory & practice. J Clean Prod 18:1575–1586. Google Scholar
  64. 64.
    Sundin E, Dunbäck O (2013) Reverse logistics challenges in remanufacturing of automotive mechatronic devices. J Remanuf 3(2):2. Google Scholar
  65. 65.
    Teunter R, Vlachos D (2002) On the necessity of a disposal option for returned items that can be remanufactured. Int J Prod Econ 75(3):257–266Google Scholar
  66. 66.
    Toktay B, Wein LM, Zenios SA (2000) Inventory management of remanufacturable products. Manag Sci 46(11):1412–1426zbMATHGoogle Scholar
  67. 67.
    Toktay B (2003) Forecasting product returns, in business aspects of closed-loop supply chains. Carnegie Mellon University Press, Pittsburgh, PAGoogle Scholar
  68. 68.
    Toktay B, van der Laan EA, de Brito MP (2003) Managing product returns: the role of forecasting in. Dekker, R, Inderfurth, K., van Wassenhove, L. N., Fleischmann, M., (eds) 2004. Reverse logistics: quantitative models for closed-loop supply chains. Springer Verlag, New YorkGoogle Scholar
  69. 69.
    Toktay B, Wei D (2011) Cost allocation in manufacturing-remanufacturing operations. Prod Oper Manag 20(6):841–847Google Scholar
  70. 70.
    Tsiliyannis C (2005) Parametric analysis of environmental performance of reused/recycled packaging. Environ Sci Technol 39(24):9770–9777Google Scholar
  71. 71.
    Tsiliyannis CA (2015) Sustainability by cyclic manufacturing: assessment of resource preservation under uncertain growth and returns. Resour Conserv Recycl, 103:3055, 155–170Google Scholar
  72. 72.
    Tsiliyannis CA (2016) A fundamental law relating stock and end-of-life flow in cyclic manufacturing. J Clean Prod 127:461–474Google Scholar
  73. 73.
    Tsiliyannis CA (2017) Mean retention time and end-of-life rate identification in cyclic manufacturing. J Clean Prod 140:1553–1566Google Scholar
  74. 74.
    Vlachos D, Georgiadis P, Iakovou E (2007) A system dynamics model for dynamic capacity planning of remanufacturing in closed-loop supply chains. Comput Oper Res 34(2):367–394zbMATHGoogle Scholar
  75. 75.
    Wei S, Tang O, Sundin E (2015) Core (product) acquisition management for remanufacturing: a review. J Remanufacturing 5(4).

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.ANION Environmental LtdAthensGreece

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