Optimal production-inventory policy for closed-loop supply chain with remanufacturing under random demand and return

  • Bimal Kumar Mawandiya
  • J. K. Jha
  • Jitesh J. Thakkar
Original Paper


This paper presents a centralized production-inventory model for an infinite planning horizon of a two-echelon closed-loop supply chain (CLSC) consisting a retailer, manufacturer, and remanufacturer. The demand at the retailer is satisfied through the new and remanufactured products received from the manufacturer and remanufacturer, respectively. The proposed model considers demand at the retailer and return at the remanufacturer as random. The manufacturer and remanufacturer produce the products at a finite rate, and they deliver to the retailer alternatively in multiple batches. An algorithm is developed to find the optimal-lot sizing and shipment policies of each entity of the CLSC by minimizing the expected joint total cost of the system. The results show that the CLSC is more profitable than the forward supply chain when the remanufacturing cost of the returned product is significantly low compared to the manufacturing cost of the new product, the demand variation at the retailer is low, and the fraction of demand returned is close to 1.


Two-echelon production-inventory model Random demand and return rate Closed-loop supply chain Remanufacturing Inventory control 


  1. Atasu A, Guide VDR Jr, Van Wassenhove LN (2008) Product reuse economics in closed-loop supply chain research. Prod Oper Manag 17(5):483–496CrossRefGoogle Scholar
  2. Chung SL, Wee HM, Yang PC (2008) Optimal policy for a closed-loop supply chain inventory system with remanufacturing. Math Comput Model 48(5–6):867–881CrossRefGoogle Scholar
  3. Dobos I, Richter K (2004) An extended production/recycling model with stationary demand and return rates. Int J Prod Econ 90(3):311–323CrossRefGoogle Scholar
  4. Dobos I, Richter K (2006) A production/recycling model with quality consideration. Int J Prod Econ 104(2):571–579CrossRefGoogle Scholar
  5. El Saadany AMA, Jaber MY (2008) The EOQ repair and waste disposal model with switching costs. Comput Ind Eng 55(1):219–233CrossRefGoogle Scholar
  6. El Saadany AMA, Jaber MY (2010) A production/remanufacturing inventory model with price and quality dependant return rate. Comput Ind Eng 58(3):352–362CrossRefGoogle Scholar
  7. Giri BC, Sharma S (2015) Optimizing a closed-loop supply chain with manufacturing defects and quality dependent return rate. J Manuf Syst 35:92–111CrossRefGoogle Scholar
  8. Giri BC, Sharma S (2016) Optimal production policy for a closed-loop hybrid system with uncertain demand and return under supply disruption. J Clean Prod 112:2015–2028CrossRefGoogle Scholar
  9. Guide VDR Jr, Van Wassenhove LN (2009) The evolution of closed-loop supply chain research. Oper Res 57(1):10–18CrossRefGoogle Scholar
  10. Guide VDR Jr, Teunter RH, Van Wassenhove LN (2003) Matching demand and supply to maximize products from remanufacturing. Manuf Serv Oper Manag 5(4):303–316CrossRefGoogle Scholar
  11. Hariga M, As’ad R, Khan Z (2017) Manufacturing-remanufacturing policies for a centralized two stage supply chain under consignment stock partnership. Int J Prod Econ 183(1):362–374CrossRefGoogle Scholar
  12. Hasanov P, Jaber MY, Zolfaghari S (2012) Production, remanufacturing and waste disposal models for the cases of pure and partial backordering. Appl Math Model 36(11):5249–5261CrossRefGoogle Scholar
  13. Jaber MY, El Saadany AMA (2009) The production, remanufacture and waste disposal model with lost sales. Int J Prod Econ 120(1):115–124CrossRefGoogle Scholar
  14. Jaber MY, El Saadany AMA (2011) An economic production and remanufacturing model with learning effects. Int J Prod Econ 131(1):115–127CrossRefGoogle Scholar
  15. Jaber MY, Zanoni S, Zavanella LE (2014) A consignment stock coordination scheme for the production, remanufacturing and waste disposal problem. Int J Prod Res 52(1):50–65CrossRefGoogle Scholar
  16. Jorjani S, Leu J, Scott C (2004) Model for the allocation of electronics components to reuse options. Int J Prod Res 42(6):1131–1145CrossRefGoogle Scholar
  17. Koh SG, Hwang H, Sohn KI, Ko CS (2002) An optimal ordering and recovery policy for reusable items. Comput Ind Eng 43(1–2):59–73CrossRefGoogle Scholar
  18. Konstantaras I, Skouri K (2010) Lot sizing for a single product recovery system with variable setup numbers. Eur J Oper Res 203(2):326–335CrossRefGoogle Scholar
  19. Konstantaras I, Skouri K, Jaber MY (2010) Lot sizing for a recoverable product with inspection and sorting. Comput Ind Eng 58(3):452–462CrossRefGoogle Scholar
  20. Korugan A, Gupta S (1998) A multi-echelon inventory system with returns. Comput Ind Eng 35(98):145–148CrossRefGoogle Scholar
  21. Lee W (2005) A joint economic lot size model for raw material ordering, manufacturing setup, and finished goods delivering. Omega 33(2):163–174CrossRefGoogle Scholar
  22. Lin HC (2015) Two-echelon stochastic inventory system with returns and partial backlogging. Int J Syst Sci 46(6):966–975CrossRefGoogle Scholar
  23. Lund RT (1996) The remanufacturing industry: hidden giant. Boston University. Accessed 25 June 2013
  24. Mabini M, Pintelon L, Gelders L (1992) EOQ type formulations for controlling repairable inventories. Int J Prod Econ 28(1):21–33CrossRefGoogle Scholar
  25. Maiti T, Giri BC (2017) Two-way product recovery in a closed-loop supply chain with variable markup under price and quality dependent demand. Int J Prod Econ 183(1):259–272CrossRefGoogle Scholar
  26. Mawandiya BK, Jha JK, Thakkar J (2016) Two-echelon closed-loop supply chain deterministic inventory models in a batch production environment. Int J Sustain Eng 9(5):315–328Google Scholar
  27. Mawandiya BK, Jha JK, Thakkar J (2017) Production-inventory model for two-echelon closed-loop supply chain with finite manufacturing and remanufacturing rates. Int J Syst Sci Oper Logist 4(3):199–218Google Scholar
  28. Mitra S (2009) Analysis of a two-echelon inventory system with returns. Omega 37(1):106–115CrossRefGoogle Scholar
  29. Mitra S (2012) Inventory management in a two-echelon closed-loop supply chain with correlated demands and returns. Comput Ind Eng 62(4):870–879CrossRefGoogle Scholar
  30. Muckstadt JA, Isaac MH (1981) An analysis of single item inventory systems with returns. Nav Res Logist Q 28(2):237–254CrossRefGoogle Scholar
  31. Nahmias S, Rivera H (1979) A deterministic model for a repairable item inventory system with a finite repair rate. Int J Prod Res 17(3):215–221CrossRefGoogle Scholar
  32. Priyan S, Uthayakumar R (2015) Two-echelon multi-product multi-constraint product returns inventory model with permissible delay in payments and variable lead time. J Manuf Syst 36:244–262CrossRefGoogle Scholar
  33. Ravindran A, Phillips DT, Solberg JJ (2010) Oper Res Princ Pract. Wiley, IndiaGoogle Scholar
  34. Richter K (1996a) The EOQ repair and waste disposal model with variable setup numbers. Eur J Oper Res 95(2):313–324CrossRefGoogle Scholar
  35. Richter K (1996b) The extended EOQ repair and waste disposal model. Int J Prod Econ 45(1–3):443–447CrossRefGoogle Scholar
  36. Richter K (1997) Pure and mixed strategies for the EOQ repair and waste disposal problem. OR Spektrum 19(2):123–129CrossRefGoogle Scholar
  37. Richter K, Dobos I (1999) Analysis of the EOQ repair and waste disposal problem with integer setup numbers. Int J Prod Econ 59(1–3):463–467CrossRefGoogle Scholar
  38. Savaskan RC, Van Wassenhove LN (2006) Reverse channel design: the case of competing retailers. Manag Sci 52(1):1–14CrossRefGoogle Scholar
  39. Schrady DA (1967) A deterministic inventory model for reparable items. Nav Res Logist 14(3):391–398CrossRefGoogle Scholar
  40. Schulz T, Voigt G (2014) A flexibly structured lot sizing heuristic for a static remanufacturing system. Omega 44(1):21–31CrossRefGoogle Scholar
  41. Shi J, Zhang G, Sha J (2011) Optimal production planning for a multi-product closed loop system with uncertain demand and return. Comput Oper Res 38(3):641–650CrossRefGoogle Scholar
  42. Tai AH, Ching WK (2014) Optimal inventory policy for a Markovian two echelon system with returns and lateral transhipment. Int J Prod Econ 151:48–55CrossRefGoogle Scholar
  43. Teng HM, Hsu PH, Chiu Y, Wee HM (2011) Optimal ordering decisions with returns and excess inventory. Appl Math Comput 217(22):9009–9018Google Scholar
  44. Teunter RH (2001) Economic ordering quantities for recoverable item inventory systems. Nav Res Logist 48(6):484–495CrossRefGoogle Scholar
  45. Teunter R (2004) Lot-sizing for inventory systems with product recovery. Comput Ind Eng 46(3):431–441CrossRefGoogle Scholar
  46. Tsai DM (2012) Optimal ordering and production policy for a recoverable item inventory system with learning effect. Int J Syst Sci 43(2):349–367CrossRefGoogle Scholar
  47. Waters D (2003) Inventory control and management. Wiley, UKGoogle Scholar
  48. Yang PC, Wee HM, Chung SL, Ho PC (2010) Sequential and global optimization for a closed-loop deteriorating inventory supply chain. Math Comput Model 52(1–2):161–176CrossRefGoogle Scholar
  49. Yuan KF, Gao Y (2010) Inventory decision-making models for a closed-loop supply chain system. Int J Prod Res 48(20):6155–6187CrossRefGoogle Scholar
  50. Yuan KF, Ma SH, He B, Gao Y (2015) Inventory decision-making models for a closed-loop supply chain system with different decision-making structures. Int J Prod Res 53(1):183–219CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Institute of TechnologyNirma UniversityAhmedabadIndia
  2. 2.Department of Industrial and Systems EngineeringIndian Institute of Technology KharagpurKharagpurIndia

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