# American Institute of Mathematical Sciences

October  2014, 10(4): 1147-1168. doi: 10.3934/jimo.2014.10.1147

## Optimal ordering policies and sourcing strategies with supply disruption

 1 School of Software, Dongguan University of Technology, Dongguan 523808, Guangdong 2 Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190 3 School of Economics and Business Administration, Chongqing University, 400044, Chongqing, China

Received  August 2011 Revised  September 2013 Published  February 2014

Successful supply chain management has to find an effective sourcing strategy to cope with uncertainty in both supply and demand. Most of existing literature deals with the problems related to the uncertain demand, however, in this paper, we discuss a model in which a firm is in the face of demand uncertainty and supplier reliability uncertainty at the same time prior to a single selling season. The firm has two instants to order from two suppliers (one supplier is completely reliable and the other is unreliable), while the unreliable supplier's reliability is uncertain at instant 1 and is completely observed at instant 2. To determine the cost-minimizing ordering strategies at both instants, the firm has to evaluate the trade-off between a more accurate forecast and a potentially higher unit cost at instant 2. We present the optimal supplementary order quantities with the realized reliability and give the optimal ordering policies and sourcing strategies at instant 1 under certain conditions. We find conditions under which the order quantity from the unreliable supplier at instant 1 is decreasing in the reorder costs at instant 2.
Citation: Xiaoming Yan, Minghui Zhang, Ke Liu, Yong Wang. Optimal ordering policies and sourcing strategies with supply disruption. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1147-1168. doi: 10.3934/jimo.2014.10.1147
##### References:
 [1] N. Agrawal and S. Nahmmias, Rationalization of the supplier base in the presence of yield uncertainty,, Production and Operations Management, 6 (1997), 291. doi: 10.1111/j.1937-5956.1997.tb00432.x. [2] R. Anupindi and R. Akella, Diversification under supply uncertainty,, Management Science, 39 (1993), 944. doi: 10.1287/mnsc.39.8.944. [3] A. Arreola-Risa and G. A. De Croix, Inventory management under random disruptions and partial back-orders,, Naval Research Logistics, 45 (1998), 687. doi: 10.1002/(SICI)1520-6750(199810)45:7<687::AID-NAV3>3.0.CO;2-7. [4] V. Babich, A. N. Burnetas and P. H. Ritchken, Competition and diversification effects in supply chains with supplier default risk,, Manufacturing & Service Operations Management, 9 (2007), 123. doi: 10.1287/msom.1060.0122. [5] C-Y. Chiu, M-F. Yang, C-J. Tang and Y. Lin, Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity,, Journal of Industrial and Management Optimization, 9 (2013), 945. doi: 10.3934/jimo.2013.9.945. [6] M. Dada, N. C. Petruzzi and L. B. Schwarz, A newsvendor's procurement problem when suppliers are unreliable,, Manufacturing & Service Operations Management, 9 (2007), 9. doi: 10.1287/msom.1060.0128. [7] M. M. Fadiloglu, E. Berk and M. C. Gurbuz, Supplier diversification under binomial yield,, Operations Research Letters, 36 (2008), 539. doi: 10.1016/j.orl.2008.05.008. [8] A. Hsu and Y. Bassok, Random yield and random demand in a production system with downward substitution,, Operations Research, 47 (1999), 277. doi: 10.1287/opre.47.2.277. [9] T. Li, S. P. Sethi and J. Zhang, Supplier diversification with responsive pricing,, Production and Operations Management, 22 (2013), 447. [10] J. Li, S. Wang and T. C. E. Cheng, Competition and cooperation in a single-retailer two-supplier supply chain with supply disruption,, International Journal of Production Economics, 124 (2010), 137. doi: 10.1016/j.ijpe.2009.10.017. [11] S. Liu, K. C. So and F. Zhang, Effect of supply reliability in a retail setting with joint marketing and inventory secisions,, Manufacturing & Service Operations Management, 12 (2010), 19. [12] S. Minner, Multiplt-supplier inventory models in supply chain management: A review,, International Journal of Production Economics, 81 (2002), 265. doi: 10.1016/S0925-5273(02)00288-8. [13] M. Parlar, Continuous review inventory problem with random supply interruptions,, European Journal of Operational Research, 99 (1997), 366. doi: 10.1016/S0377-2217(96)00165-8. [14] M. Parlar and D. Perry, Analysis of a (Q, r, T) inventory policy with deterministic and random yields when future demand is uncertain,, European Journal of Operational Research, 84 (1995), 431. [15] J.-S. Song and P. H. Zipkin, Inventory control with information about supply conditions,, Management Science, 42 (1996), 1411. doi: 10.1287/mnsc.42.10.1409. [16] S. Y. Tang and P. Kouvelis, Supplier diversification strategies in the presence of yield uncertainty and buyer competition,, Manufacturing & Service Operations Management, 13 (2011), 439. doi: 10.1287/msom.1110.0337. [17] B. Tomlin, Disruption-management strategies for short life-cycle products,, Naval Research Logistics, 56 (2009), 318. doi: 10.1002/nav.20344. [18] B. Tomlin, The impact of supply learning when suppliers are unreliable,, Manufacturing & Service Operations Management, 11 (2009), 192. doi: 10.1287/msom.1070.0206. [19] X. Yan and K. Liu, An inventory system with two suppliers and default risk,, Operations Research Letters, 37 (2009), 322. doi: 10.1016/j.orl.2009.04.007. [20] S. T. Yang, J. Yang and L. A. Malek, Sourcing with random yields and stochastic demand: A newvendor apporach,, Computers & Operations Research, 34 (2007), 3682. [21] Q. Yang, S. Song and C. Wu, Inventory policies for a partially observed supply capacity model,, Journal of Industrial and Management Optimization, 9 (2013), 13. doi: 10.3934/jimo.2013.9.13. [22] C. A. Yano and H. L. Lee, Lot sizing with random yield: A review,, Operations Research, 43 (1995), 311. doi: 10.1287/opre.43.2.311. [23] Y. Sheffi, The Resilient Enterprise: Overcoming Vulnerability for Competitive Advantage,, The MIT Press, (2007).

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##### References:
 [1] N. Agrawal and S. Nahmmias, Rationalization of the supplier base in the presence of yield uncertainty,, Production and Operations Management, 6 (1997), 291. doi: 10.1111/j.1937-5956.1997.tb00432.x. [2] R. Anupindi and R. Akella, Diversification under supply uncertainty,, Management Science, 39 (1993), 944. doi: 10.1287/mnsc.39.8.944. [3] A. Arreola-Risa and G. A. De Croix, Inventory management under random disruptions and partial back-orders,, Naval Research Logistics, 45 (1998), 687. doi: 10.1002/(SICI)1520-6750(199810)45:7<687::AID-NAV3>3.0.CO;2-7. [4] V. Babich, A. N. Burnetas and P. H. Ritchken, Competition and diversification effects in supply chains with supplier default risk,, Manufacturing & Service Operations Management, 9 (2007), 123. doi: 10.1287/msom.1060.0122. [5] C-Y. Chiu, M-F. Yang, C-J. Tang and Y. Lin, Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity,, Journal of Industrial and Management Optimization, 9 (2013), 945. doi: 10.3934/jimo.2013.9.945. [6] M. Dada, N. C. Petruzzi and L. B. Schwarz, A newsvendor's procurement problem when suppliers are unreliable,, Manufacturing & Service Operations Management, 9 (2007), 9. doi: 10.1287/msom.1060.0128. [7] M. M. Fadiloglu, E. Berk and M. C. Gurbuz, Supplier diversification under binomial yield,, Operations Research Letters, 36 (2008), 539. doi: 10.1016/j.orl.2008.05.008. [8] A. Hsu and Y. Bassok, Random yield and random demand in a production system with downward substitution,, Operations Research, 47 (1999), 277. doi: 10.1287/opre.47.2.277. [9] T. Li, S. P. Sethi and J. Zhang, Supplier diversification with responsive pricing,, Production and Operations Management, 22 (2013), 447. [10] J. Li, S. Wang and T. C. E. Cheng, Competition and cooperation in a single-retailer two-supplier supply chain with supply disruption,, International Journal of Production Economics, 124 (2010), 137. doi: 10.1016/j.ijpe.2009.10.017. [11] S. Liu, K. C. So and F. Zhang, Effect of supply reliability in a retail setting with joint marketing and inventory secisions,, Manufacturing & Service Operations Management, 12 (2010), 19. [12] S. Minner, Multiplt-supplier inventory models in supply chain management: A review,, International Journal of Production Economics, 81 (2002), 265. doi: 10.1016/S0925-5273(02)00288-8. [13] M. Parlar, Continuous review inventory problem with random supply interruptions,, European Journal of Operational Research, 99 (1997), 366. doi: 10.1016/S0377-2217(96)00165-8. [14] M. Parlar and D. Perry, Analysis of a (Q, r, T) inventory policy with deterministic and random yields when future demand is uncertain,, European Journal of Operational Research, 84 (1995), 431. [15] J.-S. Song and P. H. Zipkin, Inventory control with information about supply conditions,, Management Science, 42 (1996), 1411. doi: 10.1287/mnsc.42.10.1409. [16] S. Y. Tang and P. Kouvelis, Supplier diversification strategies in the presence of yield uncertainty and buyer competition,, Manufacturing & Service Operations Management, 13 (2011), 439. doi: 10.1287/msom.1110.0337. [17] B. Tomlin, Disruption-management strategies for short life-cycle products,, Naval Research Logistics, 56 (2009), 318. doi: 10.1002/nav.20344. [18] B. Tomlin, The impact of supply learning when suppliers are unreliable,, Manufacturing & Service Operations Management, 11 (2009), 192. doi: 10.1287/msom.1070.0206. [19] X. Yan and K. Liu, An inventory system with two suppliers and default risk,, Operations Research Letters, 37 (2009), 322. doi: 10.1016/j.orl.2009.04.007. [20] S. T. Yang, J. Yang and L. A. Malek, Sourcing with random yields and stochastic demand: A newvendor apporach,, Computers & Operations Research, 34 (2007), 3682. [21] Q. Yang, S. Song and C. Wu, Inventory policies for a partially observed supply capacity model,, Journal of Industrial and Management Optimization, 9 (2013), 13. doi: 10.3934/jimo.2013.9.13. [22] C. A. Yano and H. L. Lee, Lot sizing with random yield: A review,, Operations Research, 43 (1995), 311. doi: 10.1287/opre.43.2.311. [23] Y. Sheffi, The Resilient Enterprise: Overcoming Vulnerability for Competitive Advantage,, The MIT Press, (2007).
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