Developing an Economic Production Quantity Model in Integrated and Non-integrated Three-Layer Supply Chains with an Optimal Inventory Control Policy

Document Type : Research Paper


Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran


This paper develops an economic production quantity model in a three-layer supply chain with two different structures. This chain composes of a supplier, a manufacturer, and multiple retailers. In this chain, the supplier transforms raw material to the semi-finished product, and sends them to the manufacturer. Then, the manufacturer transmutes them to the finished product, and delivers them to the retailers to satisfy market demand. The retailers replenish their inventory at the same time. The demand of each retailer is different due to essence of various demand customers, and according to the decisions of the chain’s members, two structures of non-integrated and integrated supply chains are surveyed. In this paper, we will employ the Stackelberg approach to solve the presented models. The ordering cycle of retailers is the decision variable of the model. The main aim of this study is to develop an inventory and production model in three-layer supply chains to minimize the total cost of chain by utilizing the optimal inventory control policy. At last, numerical examples are presented for each structure of supply chains.


Main Subjects

  1. Laudon, K.C., and Laudon, J.P. (2002). “Management Information Systems: Managing the Digital Firm”, Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, New Jersey.
  2. Ayers, J.B. (2006). “Handbook of Supply chain Management”, Second Edition, Auerbach Publications, Taylor and Francis Group, Boca Raton, New York.
  3. Ganeshan, R., and Harrison, T.P. (1995). “An Introduction to Supply Chain Management”, Department of Management Sciences and Information Systems, 303 Beam Business Building, Penn State University, University Park, PA.
  4. Chopra, S., and Meindl, P. (2001). “Supply Chain Management: Strategy, Planning, and Operations”, Upper Saddle River, NJ: Prentice-Hall, Inc. Chapter1.
  5. Chopra, S., and Meindl, P. (2007). “Supply Chain Management, Strategy, Planning, and Operation”, Prince Hall, Inc., NJ, USA.
  6. Hill, R.M. (1997). “The-single vendor single-buyer integrated production-inventory model with a generalized policy”. European Journal of Operational Research, Vol. 97, No. 3, PP. 493–499.
  7. Goyal, S.K., and Nebebe, F. (2000). “Determination of economic production-shipment policy for a single-vendor single-buyer system”. European Journal of Operational Research, Vol. 121, No. 1, PP.175–178.
  8. Boyaci, T., and Gallego, G. (2002). “Coordinating pricing and inventory replenishment policies for one wholesaler and one or more geographically dispersed retailers”. International Journal of Production Economics, Vol. 77, No. 2, PP. 95–111.
  9. Ben-Tal, A., et al., (2005). “Retailer-supplier flexible commitments contracts: A robust optimization approach”. Manufacturing and Service Operations Management, Vol. 7, No. 3, PP. 248–271.

10. Esmaeili, M., Aryanezhad, M-B, and Zeephongsekul, P. (2009). “A game theory approach in seller–buyer supply chain”. European Journal of Operations Research, Vol. 191, No. 2, PP. 442–448.

11. Cai, G., Chiang, W.C., and Chen. X. (2011). “Game theoretic pricing and ordering decisions with partial lost sales in two-stage supply chains”. International Journal of Production Economics, Vol. 130, No. 2, PP. 175-185.

12. Wang, H. W., Guo, M., and Efstathiou, J. (2004). “A game-theoretical cooperative mechanism design for a two-echelon decentralized supply chain”. European Journal of Operational Research, Vol. 157, No. 2, PP. 372–388.

13. Slikker, M., Fransoo, J., and Wouters, M. (2005). “Cooperation between multiple news-vendors with transshipments”. European Journal of Operational Research, Vol. 167, No. 2, PP. 370–380.

14. Yu, Y., Chu, F., and Chen, H. (2009). “A Stackelberg game and its improvement in a VMI system with a manufacturing vendor”. European Journal of Operational Research, Vol. 192, No. 3, PP. 929–948.

15. Shao, H., Li, Y., and Zhao, D. (2011). “An optimal dicisional model in two-echelon supply chain”. Procedia Engineering, Vol. 15, PP. 4282-4286.

16. Huang, Y., Huang, G.Q., and Newman, S.T. (2011). “Coordinating pricing and inventory decisions a multi-level supply chain: A game-theoretic approach”. Transportation research part E, Vol. 47, No. 2, PP. 115-129.

17. Xiao, T., et al., (2010). “Ordering, wholesale pricing and lead-time decisions in a three-stage supply chain under demand uncertainty”. Computers and Industrial Engineering, Vol. 59, No. 4, PP. 840–852.

18. Sana, S.S. (2011). “A production-inventory model of imperfect quality products in a three-layer supply chain”, Decision Support Systems, Vol. 50, No. 2, PP. 539-547.

19. Pal, B., Sana, S.S., and Chaudhuri, K. (2012). “A three layer multi-item production–inventory model for multiple suppliers and retailers”. Economic Modelling, Vol. 29, No. 6, PP. 2704–2710.

20. Taleizadeh, A.A., et al., (2008). “An economic order quantity under joint replenishment policy to supply expensive imported raw materials with payment in advance”. Journal of Applied Sciences, Vol. 8, No. 23, PP. 4263-4273.

21. Hill, R.M. (1999). “The optimal production and shipment policy for the-single vendor single-buyer integrated production-inventory problem”. International Journal of Production Research, Vol. 37, No. 11, PP. 2463–2475.

22. Abad, P.L. (2003). “Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale”. European Journal of Operational Research, Vol. 144, No. 3, PP. 677–685.

23. Ben-Daya, M., Darwish, and M., Ertogral, K., (2008). “The joint economic lot sizing problem: Review and extensions”. European Journal of Operational Research, Vol. 185, No. 2, PP. 726–742.

24. Sajadieh, M.S., and Akbari Jokar, M.R. (2009). “Optimizing shipment, ordering and pricing policies in a two-stage supply chain with price-sensitive demand”. Transportation Research Part E, Vol. 45, No. 4, PP. 564–571.

25. Zhu, S.X. (2012). “Joint pricing and inventory replenishment decisions with returns and expediting”. Operational Research, Vol. 216, No.1 , PP. 105-112.

26. Hong, K.S., and Lee, C. (2013). “Optimal time-based consolidation policy with price sensitive demand”. International Journal of Production Economics, Vol. 143, No. 2, PP. 275-284.

27. Cárdenas-Barrón, L.E., and Sana, S.S. (2014). “A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams' initiatives”. International Journal of Production Economics, Vol. 155, PP. 249–258.

28. Shu, al., (2015). “On the risk-averse procurement strategy under unreliable supply”. Computers & Industrial Engineering, Vol. 84, PP. 113–121.

29. Zhang, Q., et al., (2016). “Optimal ordering policy in a two-stage supply chain with advance payment for stable supply Capacity”. In Press, doi: