Minimizing Net Present Value of Costs in Lot-Sizing in a Two-Echelon Inventory System

Document Type: Research Paper

Authors

Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran

Abstract

In this paper, a two-echelon supplier-manufacturer system has been studied through net present value (NPV) approach. The production rate is finite and constant in both echelons. Also it is assumed that there is a lead-time between the first echelon and it is getting to the second echelon. It is also assumed that the lot-size of manufacturer (second echelon) is m times larger than the supplier’s factors (first echelon), and the supplier can receive wares (the raw material) from the manufacturer in a cycle through several shipments, due to the point that shortage is not allowed. So, it is supposed that the supplier’s production rate is greater than manufacturer’s. The aim is to determine the optimal lot-size of each echelon such that the NPV of the total cost of system is minimized. After approximating the NPV objective function via Maclaurin expansion in both zero and non-zero lead-time cases, an exact algorithm is presented to find optimal solution of the presented model. Based on the results, the two approaches of average cost and NPV do not lead to a same result, and non-equivalency is occurred in this case.

Keywords

Main Subjects


  1. Muller, H. E. (2009). “Supplier integration: an international comparison of supplier and automaker experiences”, International Journal of Automotive Technology and Management, Vol. 9, No.1, PP. 18-39.
  2. Clark, A. J. (1958). “A dynamic, single-item, multi-echelon inventory model”, RM-2297, Rand Corporation, Santa monica, California
  3. Clark, A. J. and Scarf, H. (1960). “Optimal policies for a multi-echelon inventory problem”, Management Science, Vol. 6, No. 4, PP. 475–490.
  4. Goyal, S. (1976). “An integrated inventory model for a single supplier-single customer problem”, International Journal of Production Research, Vol. 15, No. 1, PP. 107–111.
  5. Banerjee, A. (1986). “A joint economic-lot-size model for purchaser and vendor”, Decision Sciences, Vol. 17, No. 3, PP. 292–311.
  6. Goyal, S. (1988). “A joint economic‐lot‐size model for purchaser and vendor”, Management Science, Vol. 19, No. 1, PP. 236–241.
  7. Monahan, J. (1984). “A quantity discount pricing model to increase vendor profits”, Management Science, Vol. 30, No. 6, PP. 720–726.
  8. Lee, H. L. and Rosenblatt, M. J. (1986). “A generalized quantity discount pricing model to increase supplier's profits”, Management Science, Vol. 32, No. 9, PP. 1177–1185.
  9. Hwang, H. and Kim, K.H. (1986). “Supplier's discount policy with a single price break point”, Production Economics Supply, Vol. 10, No. 1, PP. 279–286.
  10. Kim, K. H. and Hwang, H. (1989). “Simultaneous improvement of supplier's profit and buyer's cost by utilizing quantity discount”, J Oper Res Soc, Vol. 40, No. 3, PP. 255–265.
  11. Joglekar, P. N. (1988). Note—Comments on “A quantity discount pricing model to increase vendor profits”, Management Science, Vol. 34, No. 11, PP. 1391–1398.
  12. Beullens, P. and Janssens, G. K. (2014). “Adapting inventory models for handling various payment structures using net present value equivalence analysis”, International Journal of Production Economics, Vol. 157, No. 1, PP. 190–200.
  13. Silver, E. A., Peterson, R. and Pyke, D. F. (1998). Inventory Management and Production Planning and Scheduling, Wiley, New York.
  14. Hillier, F. S. and Lieberman, G. J. (2005). Introduction to operations research, McGraw-Hill, New York, London.
  15. Beullens, P. (2014). “Revisiting foundations in lot sizing-connections between Harris, Crowther, Monahan, and Clark”, International Journal of Production Economics, Vol. 155, No. 1, PP. 68–81.
  16. Lu, L. (1995). “A one-vendor multi-buyer integrated inventory model”, European Journal of Operational Research, Vol. 81, No. 2, PP. 312–323.
  17. Goyal, S. K. (1995). “A one-vendor multi-buyer integrated inventory model: A comment”, European Journal of Operational Research, Vol. 82, No. 1, PP. 209–210.
  18. 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.
  19. Hill, R. and Omar, M. (2006). “Another look at the single-vendor single-buyer integrated production-inventory problem”, International Journal of Production Research, Vol. 44, No. 4, PP. 791–800.
  20. Munson, C. and Rosenblatt, M. (2001). “Coordinating a three-level supply chain with quantity discounts”, IIE Transactions, 33, No. 5, 371–384.
  21. Van der Laan, E., and Teunter, R. (2002). “Average costs versus net present value: a comparison for multi-source inventory models”, Quantitative Approaches to Distribution Logistics and Supply Chain Management, PP. 359–378, Springer, Berlin Heidelberg
  22. Beullens, P. and Janssens, G. K. (2011). “Holding costs under push or pull conditions – the impact of the anchor point”, European Journal of Operational Research, Vol. 215, No. 1, PP. 115–125.
  23. Ben-Daya, M. and Al-Nassar, A. (2008). “An integrated inventory production system in a three-layer supply chain”, Production Planning and Control, Vol. 19, No. 2, PP. 97–104.
  24. Giri, B. and Bardhan, S. (2011). “Coordinating a two-echelon supply chain under inflation and time value of money”, International Journal of Industrial Engineering Computations, Vol. 2, No. 4, PP. 811–818.
  25. Gloc, C., and Kim., T. (2014). “Shipment consolidation in a multiple-vendor single-byer integrated inventory model”, Computers and Industrial Engineering, Vol. 70, No. 1, PP. 31–24.
  26. Sadjadi, S., Zokaee, S. and Dabiri, N. (2014). “A single-vendor single-buyer joint economic lot size model subject to budget constraints”, The International Journal of Advanced Manufacturing Technology, Vol. 70, No. 9-12, PP. 1699–1707.
  27. Malekian, Y. and Mirmohammadi S. H. (2015). “Determination of joint economic lot-size in a two-echelon production system with finite rate considering lead-time”, International Journal of Optimization in Civil Engineering, Vol. 5, No. 3, PP. 375–389.
  28. Glock, C. H. (2012). “The joint economic lot size problem: a review”, International Journal of Production Economics, Vol. 135, No. 2, PP. 671–686.
  29. Grubbström, R. W. (1967). “On The Application of the laplace transform to certain economic problems”, Management Science, Vol. 13, No. 7, PP. 558–567.