# Prognosis of product take-back for enhanced remanufacturing

- 23 Downloads

## Abstract

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.

## Keywords

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

*a*_{t}=

*P*_{t}+*I*_{net},_{t}, Product inflow in period*t*, e.g. year*t*, (tons/period, e.g.*t*/y),*a*= steady state level- ARMA
Autoregressive moving average, ARIMA AR integral MA

- C
_{f,t} Overall sales, originals+remanufactured, consumption (

*t*/y)*D*(*x*)Polynomial of degree 2(N-κ) + μ + 1

*d*_{k}Coefficient of order-k term in the polynomial

*D*(*x*)- EoL
End-of-life (no further reusable product returns)

- EoU
End-of-use (reusable product returns)

*E*_{t}EoL flow (EoL product returns) or EoL exit in period

*t*, e.g. year*t*, (tons/period)*G*'_{c,k}= 1-

*g'*_{1}-*g'*_{2}-…-*g'*_{k}, complementary cumulative distribution of the EoL exit distribution,*g*_{i},*g*_{i, t},*i*= 1, 2, ...,*ν*Reusable product return distribution (

*g*_{i, 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**)*g*_{i}Expected value of the stochastic process

*g*_{i, t},*i*= 1,2,..,*ν*,*h*_{i}Entries of vector \( \underset{\_}{h} \) given by eqs. 4–6 (or coefficients of polynomial eq. A3), Appendix A

*I*_{net}Flow of original net imported products = imports -exports =

*I*_{prod,t}–*Ex*_{prod,t}(*t*/period)*k*_{Q}Maximum age in the reusable product return sample

*k*_{U}Maximum age in the stock sample

- MAPE
Mean absolute percentage error

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

*m*_{E}Minimum age in the EoL sample

*m*_{Q}Minimum age in the reusable product return sample

*N*Number of manufacturing cycles (original plus

*N*-1 remanufacturing cycles)*P*_{t}Original production flow (

*t*/period), (original items made from virgin or recycled material)*P*(*x*)Polynomial defined in eq. A4, Appendix A,

*p*_{k}Coefficients of order-k term in the polynomial

*P*(*x*) found from eqs. 7*Q*_{t}Reusable return flow,

*Q*= steady state value*Q*_{s, t}Size (mass) of the reusable product return sample at time

*t**Q*_{s, i, t}Size (mass) of vintage of age

*i*in the reusable return sample at time*t**q*Steady state product return flow rate with respect to inflow of original products =

*Q/a**RU*_{t}Actually reused/remanufactured product flow, (

*t*/period)*s*_{t}Early loss ratio =

*Ω*_{t}/(*U*_{t}+*Ω*_{t}) = probability of early loss (prior to EoL exit) in period*t**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)*U*_{t}Product accumulation: quantity of product stock present at the end of time period

*t*(tons)*x*_{t}=1-

*s*_{t}= retention ratio = probability of remaining in the reuse/remanufacturing cycle in period*t**y*_{i, t}Mass fraction of vintage of age

*i*in the reusable return flow in time period*t**y**_{,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

## Greek

- ε
=

*E/a*= steady state EoL flow ratio with respect to inflow of originals = EoL rate or yield*η*_{t}=Stock mean age at time period

*t**θ*_{t}=EoL flow mean age at time period

*t**κ*=Mean cycle duration, time periods

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

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

*Π*(*x*)Polynomial in

*x*defined in Appendix A, eqs. A5, A6*π*_{i}- τ
=

*U/a*= mean residence time or mean product lifespan = MRT*φ*Mean take-back fraction of reusable products with respect to reusable product stock

*Ω*_{t}=Early loss flow (

*t*/period)

## Symbols

- =:
Equal by definition.

- < >
Mean sample path value (MSPV)

## Subscripts

_{t}*t*is discrete time,*t*= 1: first time a product under consideration is launched in the market._{s}Sample.

## Notes

## References

- 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.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.Atasu A, Sarvary M, Van Wassenhove LN (2008) Remanufacturing as a marketing strategy. Manag Sci 54(10):1731–1174Google Scholar
- 4.Barquet, A., P, Rozenfeld, H, Fernando, A: An integrated approach to remanufacturing: model of a remanufacturing system Jnl Remanufacture 3:1 (2013) https://doi.org/10.1186/2210-4690-3-1
- 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.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.Cooper DR, Gutowski TG (2017) The environmental impacts of reuse: a review. J Ind Ecol 21(1):38–56Google Scholar
- 8.Clottey T, Benton WC (2010) Core acquisitions planning in the automotive parts remanufacturing industry. The Ohio State UniversityGoogle Scholar
- 9.Clottey T, Benton WC Jr, Srivastava R (2012) Forecasting product returns for remanufacturing operations. Decis Sci 43(4):589–614Google Scholar
- 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.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.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.Ding Y., Xu H, Tan BCY (2016) Predicting product return rate with tweets. Proceedings Pacific Asia Conference on Information Systems, paper 345Google Scholar
- 14.Ecoelastica (2013) Statistical data, www.ecoelastika.gr
- 15.Fatimah YA, Biswas WK (2016) Sustainability assessment of remanufactured computers. Procedia CIRP 40:150–155. https://doi.org/10.1016/j.procir.2016.01.087 Google Scholar
- 16.Ferguson M, Toktay LB (2006) The effect of competition on recovery strategies. Prod Op Manag 15(3):351–368Google Scholar
- 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.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.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.Ferrer G (1997) The economics of tire remanufacturing. Resour Conserv Recycl 19(4):221–255MathSciNetGoogle Scholar
- 21.Ferrer G (1997) The economics of personal computer remanufacturing. Resour Conserv Recycl 21:79–108Google Scholar
- 22.Fleischmann M (2000) Quantitative models for reverse logistics, Ph.D. thesis. Erasmus University Rotterdam. Rotterdam, The NetherlandsGoogle Scholar
- 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.Galbreth MR, Blackburn JD (2006) Optimal acquisition and sorting policies for remanufacturing. Prod Op Man 15(3):384–392Google Scholar
- 25.Gallager R (2015) Discrete stochastic processes. Lecture Notes, MITGoogle Scholar
- 26.Gao WJ and Xing B (2013) Computational intelligence in remanufacturing. IG Global, ISBN: 9781466649088Google Scholar
- 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.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.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.Guide VDR Jr (2000) Production planning and control for remanufacturing: industry practice and research needs. J Oper Manag 18:467–448Google Scholar
- 31.Guide VDR Jr, Van Wassenhove LN (2001) Managing product returns for remanufacturing. Prod Op Man 10(2):142–155Google Scholar
- 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.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.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. https://doi.org/10.1109/ISEE.2007.369402
- 35.Hess JD, Mayhew GE (1997) Modeling merchandise returns in direct marketing. J Interact Mark 11(2):20–35Google Scholar
- 36.Ijomah W (2009) Addressing decision making for remanufacturing operations and design-for-remanufacture. Int J Sustain Eng 2(2):91–102. https://doi.org/10.1080/19397030902953080 Google Scholar
- 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.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.Junior ML, Fihlo MG (2011) Production planning and control for remanufacturing: literature review and analysis. Prod Plan Control:419–435. https://doi.org/10.1080/09537287.2011.561815
- 40.Kelle P, Silver EA (1989) Forecasting the returns of reusable containers. J Oper Manag 8(1):17–35Google Scholar
- 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.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.Liang X, Jin X, Ni J (2014) Forecasting product returns for remanufacturing systems. J Remanufacturing 4(1):8 http://www.journalofremanufacturing.com/4/1/8 Google Scholar
- 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.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.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.Matsumoto M, Umeda Y (2011) An analysis of remanufacturing practices in Japan. J Remanuf 1(2):2. https://doi.org/10.1186/2210-4690-1-2 Google Scholar
- 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.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.Muller DB (2006) Stock dynamics for forecasting material flows-case study for housing in the Netherlands. Ecol Econ 59(1):142–156Google Scholar
- 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.Mutha A, Bansal S, Guide VDR (2016) Managing demand uncertainty through core acquisition in remanufacturing. Prod Op Man 25(8):1449–1464Google Scholar
- 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.OECD (1993) Methods used by OECD countries to measure stocks of fixed capital, national accounts: sources and methods, no. 2, ParisGoogle Scholar
- 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.Opresnik D, Taisch M (2015) The manufacturer’s value chain as a service - the case of remanufacturing. J Remanuf 5(2). https://doi.org/10.1186/s13243-015-0011-x
- 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.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.Shang G (2014) Three essays on consumer product returns. (Doctoral dissertation). Retrieved from http://scholarcommons.sc.edu/etd/2884
- 60.Srivastava SK, Srivastava RK (2006) Managing product returns for reverse logistics. Intern J Phys Distr Logistics Manag 36(7):524–546Google Scholar
- 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.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.Subramoniam R, Huisingh D, Chinnam RB (2010) Aftermarket remanufacturing strategic planning decision-making framework: theory & practice. J Clean Prod 18:1575–1586. https://doi.org/10.1016/j.jclepro.2010.07.022 Google Scholar
- 64.Sundin E, Dunbäck O (2013) Reverse logistics challenges in remanufacturing of automotive mechatronic devices. J Remanuf 3(2):2. https://doi.org/10.1186/2210-4690-3-2 Google Scholar
- 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.Toktay B, Wein LM, Zenios SA (2000) Inventory management of remanufacturable products. Manag Sci 46(11):1412–1426zbMATHGoogle Scholar
- 67.Toktay B (2003) Forecasting product returns, in business aspects of closed-loop supply chains. Carnegie Mellon University Press, Pittsburgh, PAGoogle Scholar
- 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.Toktay B, Wei D (2011) Cost allocation in manufacturing-remanufacturing operations. Prod Oper Manag 20(6):841–847Google Scholar
- 70.Tsiliyannis C (2005) Parametric analysis of environmental performance of reused/recycled packaging. Environ Sci Technol 39(24):9770–9777Google Scholar
- 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.Tsiliyannis CA (2016) A fundamental law relating stock and end-of-life flow in cyclic manufacturing. J Clean Prod 127:461–474Google Scholar
- 73.Tsiliyannis CA (2017) Mean retention time and end-of-life rate identification in cyclic manufacturing. J Clean Prod 140:1553–1566Google Scholar
- 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.Wei S, Tang O, Sundin E (2015) Core (product) acquisition management for remanufacturing: a review. J Remanufacturing 5(4). https://doi.org/10.1186/s13243-015-0014-7