# A vendor–purchaser economic lot size problem with remanufacturing

- 385 Downloads
- 2 Citations

## Abstract

In this paper, we study a closed-loop supply chain in which a single purchaser orders a particular product from a single vendor and sells it on the market. A certain fraction of used items return from the market back to the purchaser, who is responsible for collecting and returning them to the vendor. In addition to manufacturing new items, the vendor is able to remanufacture the returns into as-good-as-new items which are subsequently used to serve market demand. Our framework features the conventional joint economic lot size (JELS) model extended to include the return flow of the used items. In line with the assumptions of the JELS model, we assume a deterministic constant demand for the product. The fraction of used items returning from the market is assumed to depend on the purchaser’s collection effort. To stimulate the returns, the vendor may offer the purchaser a transfer payment per item returned. The questions addressed by this study pertain to the optimal centralised control of this closed-loop supply chain, to the individually optimal policies of its members, and to the coordination within this supply chain under a decentralised control. In particular, we show that the transfer payment alone cannot coordinate the supply chain under consideration and may even fail to do so when combined with a two-part tariff—which is otherwise known to coordinate the corresponding forward supply chain. Our numerical study, though, has revealed that the combined contract is capable of substantially reducing the coordination deficit. We also introduce a novel three-part tariff which is shown to enable supply chain coordination in combination with the transfer payment.

## Keywords

EOQ Joint economic lot size Remanufacturing Closed-loop supply chain Coordination## JEL Classification

C61 C71 M10## Notes

### Acknowledgments

The authors would like to thank two anonymous referees and Professor Peter Recht of TU Dortmund University for their many constructive comments on an earlier version of this paper. Imre Dobos gratefully acknowledges the financial support of the OTKA-105888 research programme and the Deutscher Akademischer Austauschdienst (DAAD). Knut Richter acknowledges the support of the Sankt Petersburg University in enabling him to continue his work on the area of closed-loop supply-chain management.

## References

- Affisco JF, Paknejad MJ, Nasri F (2002) Quality improvement and setup reduction in the joint economic lot size model. Eur J Oper Res 142:497–508CrossRefGoogle Scholar
- Akçalı E, Çetinkaya S (2011) Quantitative models for inventory and production planning in closed-loop supply chains. Int J Prod Res 49:2373–2407CrossRefGoogle Scholar
- Atasu A, Çetinkaya S (2006) Lot sizing for optimal collection and use of remanufacturable returns over a finite life-cycle. Prod Oper Manag 15:473–487CrossRefGoogle Scholar
- Atasu A, Guide VDR, Van Wassenhove LN (2008) Product reuse economics in closed-loop supply chain research. Prod Oper Manag 17:483–496CrossRefGoogle Scholar
- Atasu A, Guide VDR, Van Wassenhove LN (2010) So what if remanufacturing cannibalizes my new product sales? Calif Manag Rev 52:56–76CrossRefGoogle Scholar
- Atasu A, Toktay LB, Van Wassenhove LN (2013) How collection cost structure drives a manufacturer’s reverse channel choice. Prod Oper Manag 22:1089–1102Google Scholar
- Banerjee A (1986a) A joint economic lot-size model for purchaser and vendor. Decis Sci 17:292–311CrossRefGoogle Scholar
- Banerjee A (1986b) On “A quantity discount model to increase vendor profits”. Manage Sci 32:1513–1517CrossRefGoogle Scholar
- Ben-Daya M, Darwish M, Ertogral K (2008) The joint economic lot sizing problem: Review and extensions. Eur J Oper Res 185:726–742CrossRefGoogle Scholar
- Cachon GP (2003) Supply chain coordination with contracts. In: de Kok AG, Graves SC (eds) Supply chain management: design, coordination and operation, Elsevier, pp 229–339Google Scholar
- Cai C (2011) Quantity discounts contract coordination model of three-stage closed-loop supply chain under retailer price competition. Proceedings of 2011 International Conference on Transportation, Mechanical, and Electrical Engineering, December 16–18, 2011. Changchun, China, IEEE, pp 195–199Google Scholar
- Corbett CJ, Savaskan RC (2002) Contracting and coordination in closed-loop supply chains. In: Guide VDR, Van Wassenhove LN (eds) Closed-loop supply chains: a business perspective. Carnegie Bosch Institute, Pittsburgh, pp 93–113Google Scholar
- Dobos I, Richter K (2004) An extended production/recycling model with stationary demand and return rates. Int J Prod Econ 90:311–323CrossRefGoogle Scholar
- Dobos I, Gobsch B, Pakhomova N, Pishchulov G, Richter K (2011a) A vendor-purchaser economic lot size problem with remanufacturing and deposit. Discussion Paper 304, Faculty of Economics and Business Administration, European University Viadrina, Frankfurt (Oder), GermanyGoogle Scholar
- Dobos I, Gobsch B, Pakhomova N, Richter K (2011b) Remanufacturing of used products in a closed-loop supply chain. In: Csutora M, Kerekes S (eds) Accounting for climate change – What and how to measure. Proceedings of the EMAN-EU 2011 Conference, 24–25 January 2011, Budapest, Hungary, pp 130–146Google Scholar
- Dobos I, Gobsch B, Pakhomova N, Pishchulov G, Richter K (2013) Design of contract parameters in a closed-loop supply chain. Cent Eur J Oper Res 21:713–727CrossRefGoogle Scholar
- Dolan RJ (1987) Quantity discounts: managerial issues and research opportunities. Marketing Sci 6:1–22CrossRefGoogle Scholar
- Govindan K, Popiuc MN (2013) Reverse supply chain coordination by revenue sharing contract: a case for the personal computers industry. Eur J Oper Res 233:326–336CrossRefGoogle Scholar
- Guide VDR, Van Wassenhove LN (2009) The evolution of closed-loop supply chain research. Oper Res 57:10–18CrossRefGoogle Scholar
- Hong X, Wang Z, Wang D, Zhang H (2013) Decision models of closed-loop supply chain with remanufacturing under hybrid dual-channel collection. Int J Adv Manuf Technol 68:1851–1865CrossRefGoogle Scholar
- Jaber MY, El Saadany AMA (2011) An economic production and remanufacturing model with learning effects. Int J Prod Econ 131:115–127CrossRefGoogle Scholar
- Jonrinaldi, Zhang DZ (2013) An integrated production and inventory model for a whole manufacturing supply chain involving reverse logistics with finite horizon period. Omega 41:598–620CrossRefGoogle Scholar
- Jun Y, Susheng W (2011) Optimal contract design of reverse supply chain considering uncertain recycle price. Proceedings of 2011 International Conference on E -Business and E -Government, May 6–8, 2011. Shanghai, China, IEEE, pp 1419–1423Google Scholar
- Kohli R, Park H (1989) A cooperative game theory model of quantity discounts. Manag Sci 35:693–707CrossRefGoogle Scholar
- Konstantaras I, Skouri K (2010) Lot sizing for a single product recovery system with variable setup numbers. Eur J Oper Res 203:326–335CrossRefGoogle Scholar
- Liu X, Banerjee A, Kim S-L (2009) Models for retail pricing and customer return incentive for remanufacturing a product. In: Proceedings of the POMS 20th Annual Conference, Orlando, Florida, USA, May 1 to 4, 2009Google Scholar
- Liu X, Çetinkaya S (2007) A note on “quality improvement and setup reduction in the joint economic lot size model”. Eur J Oper Res 182:194–204CrossRefGoogle Scholar
- Ma W, Sun J (2012) Research for closed-loop supply chain price models under uncertain demand. Proceedings of 2012 Second International Conference on Business Computing and Global Informatization, 12–14 October 2012. Shanghai, China, IEEE, pp 136–139Google Scholar
- Matsumoto M, Umeda Y (2011) An analysis of remanufacturing practices in Japan. J Remanuf 1:2CrossRefGoogle Scholar
- Minner S, Lindner G (2004) Lot sizing decisions in product recovery management. In: Dekker R, Fleischmann M, Inderfurth K, Van Wassenhove LN (eds) Reverse logistics: quantitative models for closed-loop supply chains. Springer, New York, pp 157–180CrossRefGoogle Scholar
- Monahan JP (1984) A quantity discount pricing model to increase vendor profits. Manag Sci 30:720–726CrossRefGoogle Scholar
- Myerson R (1983) Mechanism design by an informed principal. Econometrica 51:1767–1797CrossRefGoogle Scholar
- Nie J, Huang Z, Zhao Y, Shi Y (2013) Collective recycling responsibility in closed-loop fashion supply chains with a third party: Financial sharing or physical sharing? Math Probl Eng 2013:1–11Google Scholar
- Pibernik R, Zhang Y, Kerschbaum F, Schröpfer A (2011) Secure collaborative supply chain planning and inverse optimization—the JELS model. Eur J Oper Res 208:75–85CrossRefGoogle Scholar
- Pishchulov G, Dobos I, Gobsch B, Pakhomova N, Richter K (2012) Remanufacturing of used products in a closed-loop supply chain with quantity discount. In: Klatte D, Lüthi HJ, Schmedders K (eds) Operations Research Proceedings 2011: Selected Papers of the International Conference on Operations Research (OR 2011), August 30–September 2, 2011. Zurich, Switzerland, Springer, pp 457–462Google Scholar
- Reyniers DJ (2001) The effect of vertical integration on consumer price in the presence of inventory costs. Eur J Oper Res 130:83–89CrossRefGoogle Scholar
- Richter K (1994) An EOQ repair and waste disposal model. In: Proceedings of the Eighth International Working Seminar on Production Economics, Austria, February 1994, vol. 3, pp 83–91Google Scholar
- Richter K (1996a) The variable EOQ repair and waste disposal model with variable setup numbers. Eur J Oper Res 96:313–324CrossRefGoogle Scholar
- Richter K (1996b) The extended EOQ repair and waste disposal model. Int J Prod Econ 45:443–447CrossRefGoogle Scholar
- Ross SA (1973) The economic theory of agency: the principal’s problem. Am Econ Rev 63:134–139Google Scholar
- Rubio S, Chamorro A, Miranda FJ (2008) Characteristics of the research on reverse logistics (1995–2005). Int J Prod Res 46:1099–1120CrossRefGoogle Scholar
- Savaskan RC, Bhattacharya S, Van Wassenhove LN (2004) Closed-loop supply chain models with product remanufacturing. Manag Sci 50:239–252CrossRefGoogle Scholar
- Savaskan RC, Van Wassenhove LN (2006) Reverse channel design: the case of competing retailers. Manag Sci 52:1–14CrossRefGoogle Scholar
- Schrady DA (1967) A deterministic inventory model for reparable items. Nav Res Logist Q 14:391–398CrossRefGoogle Scholar
- Shi C, Bian D, Zhang H (2010) Loss-averse closed-loop supply chain coordination by revenue sharing contract and quantity discount contract. In: Proceedings of 2010 2nd International Conference on Computer Engineering and Technology, Zibo, China, 16–18 April 2010, IEEE, vol. 1, pp 365–369Google Scholar
- Silver EA, Pyke DF, Peterson R (1998) Inventory management and production planning and scheduling, 3rd edn. Wiley, New YorkGoogle Scholar
- Steinhilper R (1998) Remanufacturing: the ultimate form of recycling. Fraunhofer IRB Verlag, StuttgartGoogle Scholar
- Sucky E (2006) A bargaining model with asymmetric information for a single supplier–single buyer problem. Eur J Oper Res 171:516–535CrossRefGoogle Scholar
- Tang O, Teunter RH (2006) Economic lot scheduling problem with returns. Prod Oper Manag 15:488–497CrossRefGoogle Scholar
- Teunter RH (2001) Economic ordering quantities for recoverable item inventory systems. Nav Res Log 48:484–495CrossRefGoogle Scholar
- Teunter R (2004) Lot-sizing for inventory systems with product recovery. Comput Ind Eng 46:431–441CrossRefGoogle Scholar
- Teunter RH, Bayindir ZP, Van Den Heuvel W (2006) Dynamic lot sizing with product returns and remanufacturing. Int J Prod Res 44:4377–4400CrossRefGoogle Scholar
- Teunter R, van der Laan E (2002) On the non-optimality of the average cost approach for inventory models with remanufacturing. Int J Prod Econ 79:67–73CrossRefGoogle Scholar
- Wei J, Zhao J, Li Y (2012) Pricing decisions for a closed-loop supply chain in a fuzzy environment. Asia Pac J Oper Res 29(1):1240003-1–30Google Scholar
- Xu X, Li Y, Cai X (2012) Optimal policies in hybrid manufacturing/remanufacturing systems with random price-sensitive product returns. Int J Prod Res 50:6978–6998CrossRefGoogle Scholar
- Yan N, Sun B (2012) Optimal Stackelberg strategies for closed-loop supply chain with third-party reverse logistics. Asia Pac J Oper Res 29(5):1250026-1–11Google Scholar
- Zeng AZ (2013) Coordination mechanisms for a three-stage reverse supply chain to increase profitable returns. Nav Res Log 60:31–45CrossRefGoogle Scholar
- Zhao X, Zhao X (2011) Pricing decision and performance analysis of closed-loop supply chain with third-party reverse logistics. In: Proceedings of 2011 International Conference on Management and Service Science, Wuhan, China, 12–14 August 2011, IEEE, pp 1–4Google Scholar