Cost function and optimal boundaries for a two-level inventory system with information sharing and two identical retailers

Document Type : Article

Authors

1 Department of Information Science, University of Otago, Dunedin 9054, P.O. Box 56, New Zealand

2 Department of Industrial Engineering, Sharif University of Technology, Tehran, P.O. Box 11365, Iran

3 Department of Industrial Engineering, University of Science and Culture, Tehran, P.O. Box 13145/871, Iran

Abstract

In this paper, we consider a two-echelon inventory system with a central warehouse and two identical retailers employing information sharing. Transportation times to each retailer and the warehouse are constant. Retailers face independent Poisson demand and apply continuous review policy, -policy. The warehouse initiates with m batches (of given size ) and places an order to an outside supplier when a retailer’s inventory position reaches , where  is the inventory position considered by central warehouse and  is a non-negative constant. So far, an approximate cost function as well as exact analysis of system for only one retailer has been proposed. However, the derivation of the exact value of the expected total cost of this system for more than one retailer, is still an open question. This paper attempts to meet this challenge and derive the exact cost function for two retailers. To achieve this purpose, we resort to conditional probability to split the problem into two simpler problems then we obtain the exact expected total cost of the system.

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References

References:
1. Forrester, J.W. "Industrial dynamics: a major breakthrough for decision makers", Harvard Business Review, 36(4), pp. 37-66 (1958).
2. Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E., Designing and Managing the Supply Chain: Concepts, Strategies, and Case Studies, The McGraw-Hill/Irwin Series in Operations and Decision Sciences, McGraw- Hill, Illinois (2003).
3. Lee, H.L., So, K.C., and Tang, C.S. "The value of information sharing in a two-level supply chain", Management Science, 46(5), pp. 626-643 (2000).
4. Raghunathan, S. and Yeh, A.B. "Beyond EDI: impact of continuous replenishment program (CRP) between a manufacturer and its retailers", Information Systems Research, 12(4), pp. 406-419 (2001).
5. Yao, Y. and Dresner, M. "The inventory value of information sharing, continuous replenishment, and vendor-managed inventory", Transportation Research Part E: Logistics and Transportation Review, 44(3), pp. 361-378 (2008).
6. Dong, Y., Dresner, M., and Yao, Y. "Beyond information sharing: An empirical analysis of vendor-managed inventory", Production and Operations Management, 23(5), pp. 817-828 (2014).
7. Cui, R., Allon, G., Bassamboo, A., and Van Mieghem, J.A. "Information sharing in supply chains: An empirical and theoretical valuation", Management Science, 61(11), pp. 2803-2824 (2015).
8. Chen, M.-C., Yang, T., and Yen, C.-T. "Investigating the value of information sharing in multi-echelon supply chains", Quality & Quantity, 41(3), pp. 497-511 (2007).
9. Razmi, J., Rad, R.H., and Sangari, M.S. "Developing a two-echelon mathematical model for a vendormanaged inventory (VMI) system", The International Journal of Advanced Manufacturing Technology, 48(5- 8), pp. 773-783 (2010).
10. Li, C. "Controlling the bullwhip effect in a supply chain system with constrained information flows", Applied Mathematical Modelling, 37(4), pp. 1897-1909 (2013).
11. Cannella, S., Dominguez, R., Framinan, J.M., and Bruccoleri, M. "Insights on partial information sharing in supply chain dynamics", International Conference on Industrial Engineering and Systems Management (IESM), Seville, Spain, pp. 344-350 (2015).
12. Cannella, S., Framinan, J.M., and Barbosa-Povoa, A. "An IT-enabled supply chain model: a simulation study", International Journal of Systems Science, 45(11), pp. 2327-2341 (2014).
13. Cannella, S., and Ciancimino, E. "Up-to-date supply chain management: The coordinated (S, R) orderup- to", In Advanced Manufacturing and Sustainable Logistics, Dangelmaier, W., Blecken, A., Delius, A., and S. Klopfer, Eds., pp. 175-185, Springer, Berlin, Germany (2010).
14. Cannella, S. "Order-up-to policies in information exchange supply chains", Applied Mathematical Modelling, 38(23), pp. 5553-5561 (2014).
15. Prajogo, D. and Olhager, J. "Supply chain integration and performance: The effects of long-term relationships, information technology and sharing, and logistics integration", International Journal of Production Economics, 135(1), pp. 514-522 (2012).
16. Ganesh, M., Raghunathan, S., and Rajendran, C. "The value of information sharing in a multi-product, multi-level supply chain: Impact of product substitution, demand correlation, and partial information sharing", Decision Support Systems, 58, pp. 79-94 (2014).
17. Sabitha, D., Rajendran, C., Kalpakam, S., and Ziegler, H. "The value of information sharing in a serial supply chain with AR (1) demand and non-zero replenishment lead times", European Journal of Operational Research, 255(3), pp. 758-777 (2016).
18. Ali, M.M., Boylan, J.E., and Syntetos, A.A. "Forecast errors and inventory performance under forecast information sharing", International Journal of Forecasting, 28(4), pp. 830-841 (2012).
19. Babai, M.Z., Boylan, J.E., Syntetos, A.A., and Ali, M.M. "Reduction of the value of information sharing as demand becomes strongly auto-correlated", International Journal of Production Economics, 181, pp. 130-135 (2016).
20. Trapero, J.R., Kourentzes, N., and Fildes, R. "Impact of information exchange on supplier forecasting performance", Omega, 40(6), pp. 738-747 (2012).
21. Cannella, S., Lopez-Campos, M., Dominguez, R., Ashayeri, J., and Miranda, P.A. "A simulation model of a coordinated decentralized supply chain", International Transactions in Operational Research, 22(4), pp. 735-756 (2015).
22. Li, X. andWang, Q. "Coordination mechanisms of supply chain systems", European Journal of Operational Research, 179(1), pp. 1-16 (2007).
23. Axsater, S. "Simple solution procedures for a class of two-echelon inventory problems", Operations Research, 38(1), pp. 64-69 (1990).
24. Axsater, S. "Exact and approximate evaluation of batch-ordering policies for two-level inventory systems", Operations Research, 41(4), pp. 777-785 (1993).
25. Forsberg, R. "Optimization of order-up-to-S policies for two-level inventory systems with compound Poisson demand", European Journal of Operational Research, 81(1), pp. 143-153 (1995).
26. Forsberg, R. "Exact evaluation of (R, Q)-policies for two-level inventory systems with Poisson demand", European Journal of Operational Research, 96(1), pp. 130-138 (1997).
27. Axsater, S. "Exact analysis of continuous review (R,Q)policies in two-echelon inventory systems with compound Poisson demand", Operations Research, 48(5), pp. 686-696 (2000).
28. Simchi-Levi, D. and Zhao, Y. "Three generic methods for evaluating stochastic multi-echelon inventory systems", Working Paper, Massachusetts Institute of Technology, Cambridge (2007).
29. Simchi-Levi, D. and Zhao, Y. "Performance evaluation of stochastic multi-echelon inventory systems: a survey", Advances in Operations Research, 2012, Article ID: 126254, 34 pages (2012).https://doi.org/10.1155/2012/126254.
30. Chen, F. and Zheng, Y.-S. "Evaluating echelon stock (R, nQ) policies in serial production/inventory systems with stochastic demand", Management Science, 40(10), pp. 1262-1275 (1994).
31. Chen, F. and Zheng, Y.-S. "Near-optimal echelonstock (R, nQ) policies in multistage serial systems", Operations Research, 46(4), pp. 592-602 (1998).
32. Axsater, S. and Rosling, K. "Notes: Installation vs. echelon stock policies for multilevel inventory control", Management Science, 39(10), pp. 1274-1280 (1993).
33. Moinzadeh, K. "A multi-echelon inventory system with information exchange", Management Science, 48(3), pp. 414-426 (2002).
34. Haji, R. and Sajadifar, S.M. "Deriving the exact cost function for a two-level inventory system with information sharing", Journal of Industrial and Systems Engineering, 2(1), pp. 41-50 (2008).
35. Sajadifar, S.M. and Haji, R. "Optimal solution for a two-level inventory system with information exchange leading to a more computationally efficient search", Applied Mathematics and Computation, 189(2), pp. 1341-1349 (2007).
36. Axsater, S. and Marklund, J. "Optimal position-based warehouse ordering in divergent two-echelon inventory systems", Operations Research, 56(4), pp. 976-991 (2008).
37. Svoronos, A. and Zipkin, P. "Estimating the performance of multi-level inventory systems", Operations Research, 36(1), pp. 57-72 (1988).
38. Deuermeyer, B.L., and Schwarz, L.B., A Model for the Analysis of System Service Level in Warehouse- Retailer Distribution Systems: the Identical Retailer Case, Purdue University (1981).
39. Cachon, G.P. and Fisher, M. "Supply chain inventory management and the value of shared information", Management Science, 46(8), pp. 1032-1048 (2000).
40. Gurbuz, M.C ., Moinzadeh, K., and Zhou, Y.P. "Coordinated replenishment strategies in inventory/ distribution systems", Management Science, 53(2), pp. 293-307 (2007).
41. Wang, Q., Chay, Y., and Wu, Z. "A simple coordination strategy for a decentralized supply chain", Working Paper, Nanyang Business School, Nanyang Technological University, Singapore (2006).
42. Klastorin, T.D., Moinzadeh, K., and Son, J. "Coordinating orders in supply chains through price discounts", IIE Transactions, 34(8), pp. 679-689 (2002).
43. Haji, R. and Haji, A. "One-for-one period policy and its optimal solution", Journal of Industrial and Systems Engineering, 1(2), pp. 200-217 (2007).
44. Kurt Salmon Associates, Inc., Efficient Consumer Response: Enhancing Consumer Value in the Grocery Industry, Research Department Food Marketing Institute, Washington, Dc (1993).
45. Kurt Salmon Associates, Inc., Quick Response: Meeting Customer Need, Kurt Salmon Associates, Atlanta, GA (1997).
46. Stalk, G., Evans, P., and Shulman, L.E. "Competing on capabilities: The new rules of corporate strategy", Harvard Business Review, 70(2), pp. 57-69 (1991).
47. Hadley, G. and Whitin, T.M., Analysis of Inventory Systems, Prentice Hall, Englewood, Cliffs, NJ (1963).
Scientia Iranica
Volume 26, Issue 1
Transactions on Industrial Engineering (E)
January and February 2019
Pages 472-485

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