Improving Order Quantity Model with Emergency Safety Stock (ESS)

Authors: Yousef Abu Nahleh, Alhasan Hakami, Arun Kumar, Fugen Daver

Abstract:

This study considers the problem of calculating safety stocks in disaster situations inventory systems that face demand uncertainties. Safety stocks are essential to make the supply chain, which is controlled by forecasts of customer needs, in response to demand uncertainties and to reach predefined goal service levels. To solve the problem of uncertainties due to the disaster situations affecting the industry sector, the concept of Emergency Safety Stock (ESS) was proposed. While there exists a huge body of literature on determining safety stock levels, this literature does not address the problem arising due to the disaster and dealing with the situations. In this paper, the problem of improving the Order Quantity Model to deal with uncertainty of demand due to disasters is managed by incorporating a new idea called ESS which is based on the probability of disaster occurrence and uses probability matrix calculated from the historical data. 

Keywords: Emergency Safety Stocks, Safety stocks, Order Quantity Model, Supply chain.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1089353

References:

[1] D. Whybark and J. Williams, "Material Requirements Planning under uncertainty," Decis Sci, vol. 8, 1976.
[2] J. Wijngaard and J. Wortmann, "MRP and inventories," Eur J Oper Res, vol. 20, pp. 281–293, 1985.
[3] E. Silver, D. Pyke, and R. Peterson, Inventory management and production scheduling. New York: Wiley, 1998.
[4] D. Kemball-Cook and R. Stephenson, "Lessons in logistics from Somalia," Disasters, vol. 8, pp. 57-66, Mar 1984.
[5] S. A. Ardekani and A. G. Hobeika, "Logistics Problems in the Aftermath of the 1985 Mexico City Earthquake," Transportation Quarterly, vol. 42, pp. 107-124, 1988.
[6] B.-T. Aharon, C. Byung Do, M. Supreet Reddy, and Y. Tao, "Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains," Transportation research part B: methodological, vol. 45, pp. 1177-1189, 2011.
[7] M. Dror and P. Trudeau, "Savings by Split Delivery Routing," Transportation Science vol. 23, pp. 141-145 May 1989
[8] M. Gendreau, G. Laporte, and D. Vigo, "Heuristics for the traveling salesman problem with pickup and delivery," Computers & Operations Research, vol. 26, pp. 699-714, 7// 1999.
[9] B. L. Golden, E. K. Baker, J. L. Alfaro, and J. R. Schaffer, "The vehicle routing problem with backhauling: two approaches," Proceedings of the Twenty-First Annual Meeting of the S.E. TIMS, Myrtle Beach, SC, USA, 1985.
[10] Z.-H. Hu, "A container multimodal transportation scheduling approach based on immune affinity model for emergency relief," Expert Systems with Applications, vol. 38, pp. 2632-2639, 3// 2011.
[11] R. Knott, "The logistics of bulk relief supplies," Disasters vol. 11, pp. 113-115 1987.
[12] G. Kontoravdis and J. F. Bard, "A GRASP for the vehicle routing problem with time windows," ORSA Journal on Computing; Winter95, vol. 7, pp. 10-23, 1995.
[13] H. Min, "The multiple vehicle routing problem with simultaneous delivery and pick-up points," Transportation Research Part A: General, vol. 23, pp. 377-386, 9// 1989.
[14] G. Nagy and S. d. Salhi, "Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries," European Journal of Operational Research, vol. 162, pp. 126-141, 4/1/ 2005.
[15] P. Tatham and G. Kovács, "The application of "swift trust” to humanitarian logistics," International Journal of Production Economics, vol. 126, pp. 35-45, 7// 2010.
[16] M.-S. Chang, C.-F. Hsueh, and S.-R. Chen, "Real-time vehicle routing problem with time windows and simultaneous delivery/pickup demands," Journal of the Eastern Asia Society for Transportation Studies, vol. 5, pp. 2273-2286, 2003.
[17] H.-K. Chen, C.-F. Hsueh, and M.-S. Chang, "The real-time time-dependent vehicle routing problem," Transportation Research Part E: Logistics and Transportation Review, vol. 42, pp. 383-408, 9// 2006.
[18] A. Haghani and S.-C. Oh, "Formulation and solution of a multi-commodity, multi-modal network flow model for disaster relief operations," Transportation Research Part A: Policy and Practice, vol. 30, pp. 231-250, 5// 1996.
[19] L. Özdamar, E. Ekinci, and B. Küçükyazici, "Emergency Logistics Planning in Natural Disasters," Annals of Operations Research, vol. 129, pp. 217-245, 2004/07/01 2004.
[20] W. Yi and L. Özdamar, "A dynamic logistics coordination model for evacuation and support in disaster response activities," European Journal of Operational Research, vol. 179, pp. 1177-1193, 6/16/ 2007.
[21] W. Yi and A. Kumar, "Ant colony optimization for disaster relief operations," Transportation Research Part E: Logistics and Transportation Review, vol. 43, pp. 660-672, 11// 2007.
[22] B. Balcik and B. M. Beamon, "{Facility location in humanitarian relief}," International Journal of Logistics Research and Applications, vol. 11, pp. 101-121, // 2008.
[23] M. Jahre, "Researcher project: HUMLOG-NET – Humanitarian Logistics Networks," Norway, 2008.
[24] A. S. Thomas and L. R. Kopczak, "From logistics to supply chain management: The path forward in the humanitarian sector," Fritz Institute, 2005.
[25] B. M. Beamon and S. A. Kotleba, "Inventory modelling for complex emergencies in humanitarian relief operations," International Journal of Logistics: Research and Applications, vol. 9, pp. 1-18, // 2006.
[26] N. Altay and W. G. Green III, "OR/MS research in disaster operations management," European Journal of Operational Research vol. 175 pp. 475-493, 2006.
[27] G. Kovacs and K. M. Spens, "Humanitarian logistics in disaster relief operations. In Jahre, Marianne (ed.): Logistics in the New Valley," CD-ROM Proceedings of the 18th Annual Conference for Nordic Researchers in Logistics, NOFOMA, Oslo, Norway, 2006.
[28] A. Thomas, "Why logistics?" Forced Migration Review, vol. 18, p. 4, 2003.
[29] R. Oloruntoba and R. Gray, Suppl Chain Manage, vol. 11, p. 115, 2006.
[30] L. N. V. Wassenhove, "Humanitarian aid logistics: supply chain management in high gear†," Journal of the Operational Research Society, vol. 57, pp. 475-489, 2005.
[31] B. M. Beamon, "Humanitarian relief chains: issues and challenges," in Proceedings of the 34th International Conference on Computers and Industrial Engineering, 2004, pp. 77-82.
[32] R. Oloruntoba and R. Gray, "Humanitarian aid: an agile supply chain," Supply Chain Management: An International Journal, vol. 11, pp. 115 - 120, 2006.
[33] A. S. Thomas, "Humanitarian Logistics: Enabling Disaster Response," Fritz Institute, 2007.
[34] Y. Ye and N. Liu, "A Bayesian Group-Information-Updated sequential approach for humanitarian logistics planning in natural disasters," Institution of Logistics and Decision Optimization, School of Management, Zhejiang University, China, 2011.
[35] S. Doocy, A. Sirois, J. Anderson, M. Tileva, E. Biermann, J. D. Storey, et al., "Food security and humanitarian assistance among displaced Iraqi populations in Jordan and Syria," Soc Sci Med, vol. 72, pp. 273-82, Jan 2011.
[36] E. J. Lodree and Jr, "Pre-storm emergency supplies inventory planning," Journal of Humanitarian Logistics and Supply Chain Management, vol. 1, pp. 50-77, 2011.
[37] J. Zhang, N. Mou, and M. He, "Research of the Supply Chain System Reliability Based on the Markov Process," in Logistics, ed, 2008, pp. 1276-1281.
[38] J.-m. Cai and X.-m. Li, "The possibility go methodology-analysis of transportation network reliability for emergency logistics under earthquake disasters," in Emergency Management and Management Sciences (ICEMMS), 2011 2nd IEEE International Conference on, 2011, pp. 274-277.
[39] Y. M. Zhang, "Reliability analysis of the emergency logistics supply chain," Applied Mechanics and Materials, vol. 170-173, pp. 101-105, 2012.
[40] J. M. Day, S. A. Melnyk, P. D. Larson, E. W. Davis, and D. C. Whybark, "Humanitarian and Disaster Relief Supply Chains: A Matter of Life and Death," Journal of Supply Chain Management, vol. 48, pp. 21-36, 2012.
[41] G. Kovács and K. Spens, "Identifying challenges in humanitarian logistics," International Journal of Physical Distribution & Logistics Management, vol. 39, pp. 506-528, 2009.
[42] J. Knight and R. Piltz, "Federal Disaster Budgeting:Are We Weather Ready?," Climate Science Watch, August 5 2011.
[43] G. Van Houtum, K. Inderfurth, and W. Zijm, "Materials coordination in stochastic multi-echelon system," Eur J Oper Res, vol. 95, pp. 1–23, 1996.
[44] E. B. Diks, A. G. de Kok, and A. G. Lagodimos, "Multi-echelon systems: A service measure perspective," European Journal of Operational Research, vol. 95, pp. 241-263, 12/6/ 1996.
[45] A. De Kok and J. Fransoo, "Planning supply chain operations: definition and comparison of planning concepts.," in Handbooks in Operations Research and Management Science, 11, Ed., ed North Holland, Amsterdam, 2003, pp. 597–675.
[46] A. Clark and H. Scarf, "Optimal policies for a multi-echelon inventory problem," Manage Sci, vol. 6, pp. 475–490, 1960.
[47] H. Stadtler, "Multi-level lot sizing with setup times and multiple constrained resources: internally rolling schedules with lot-sizing windows," Oper Res vol. 51, pp. 487–502, 2003.
[48] J. Spitter, C. Hurkens, A. De Kok, E. Negenman, and J. Lenstra, "Linear programming models with planned lead times," Eur J Oper Res, vol. 163, pp. 706–720, 2005.
[49] P. Billington, J. McClain, and L. Thomas, "Mathematical programming approaches to capacityconstrained MRP systems," formulation and problem reduction., vol. 29, pp. 1126–1141, 1983.
[50] H. Tempelmeier and M. Derstroff, "A Lagrangean-based heuristic for dynamic multi-level multi-item constrained lotsizing with setup times," Manage Sci vol. 42, pp. 738–757, 1996.
[51] H. Stadtler and C. Kilger, Supply chain management and advanced planning. Berlin: Springer, 2005.
[52] K. Inderfurth and S. Minner, "Safety stocks in multi-stage inventory systems under different service measures," European Journal of Operational Research, vol. 106, pp. 57-73, 4/1/ 1998.
[53] K. Inderfurth, "Safety stock optimization in multi-stage inventory systems," Int J Prod Econ, vol. 24, pp. 103–113, 1991.
[54] S. Minner, "Dynamic programming algorithms for multi-stage safety stock optimization," ORSpektrum, vol. 19, pp. 261–271, 1997.
[55] S. Graves and S. Willems, "Optimizing strategic safety stock placement in supply chains," Manu ServOper Manage, vol. 2, pp. 68-83, 2000.
[56] J. Kleijnen and J. Wan, "Optimization of simulated inventory systems: OpQuest and alternatives," Tilburg University: CentER Discussion Paper, 2006.
[57] S. Eilon and J. Elmaleh, "An evaluation of alternative inventory control policies," Int J Prod Res, vol. 7, pp. 3–14, 1968.
[58] U. Wemmerlöv and D. Whybark, "Lot-sizing under uncertainty in a rolling schedule environment," Int J Prod Res, vol. 22, pp. 467–484, 1984.
[59] T. Callarman and R. Hamrin, "A comparison of dynamic lot sizing rules for use in a single stage MRP system with demand uncertainty," Int J Oper Prod Manage, vol. 4, pp. 39–49, 1984.
[60] T. Callarman and V. Mabert, "Using material requirements planning with demand uncertainty," in Proceedings of the 9th annual midwest AIDS conference, 1978, pp. 151–155.
[61] C. Kohler-Gudum and A. De Kok, "A safety stock adjustment procedure to enable target service levels in simulation of generic inventory systems," Technische Universiteit Eindhoven: BETA Working, 2002.
[62] M. De Bodt and L. VanWassenhove, " Lot sizes and safety stocks in MRP: a case study," Prod Inventory Manage Sci, vol. 24, pp. 1–16, 1983.
[63] R. S. Russell and B. Taylor, Operations Management: Creating Value Along the Supply Chain: Wiley, 2010.