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Optimization of multi-period supply planning under stochastic lead times and a dynamic demand

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  • Ben-Ammar, Oussama
  • Bettayeb, Belgacem
  • Dolgui, Alexandre

Abstract

Supply planning and inventory control are vital in Supply Chain (SC) optimization processes for companies that aim to produce highest-quality finished product at lowest cost and right on time. Optimization means planners’ need to reduce average stock levels and determine the optimal safety lead-times. This study deals with a multi-period production planning problem with a known dynamic demand. Order lead-times are independent, discrete random variables with known and bounded probability distributions. A general probabilistic model, including a recursive procedure to calculate the expected total cost (ETC), is derived. A genetic algorithm (GA) is developed for this model to determine planned lead-times and safety stock level while minimizing the ETC, where ETC is the sum of expected backlogging cost (ETBC) and expected inventory holding cost (ETHC). This approach is then compared to three other classical models to test its efficiency. The results prove that, under certain assumptions, it could be better to optimize planned lead-times rather than implement safety stocks. To understand the effect of lead-time dispersion on solution robustness, different levels of variance and different shapes of lead-time distributions are studied. Analysis proves that the lead-time variability has little effect on ETC when unit inventory holding cost is close to unit backlogging cost.

Suggested Citation

  • Ben-Ammar, Oussama & Bettayeb, Belgacem & Dolgui, Alexandre, 2019. "Optimization of multi-period supply planning under stochastic lead times and a dynamic demand," International Journal of Production Economics, Elsevier, vol. 218(C), pages 106-117.
    • Handle: RePEc:eee:proeco:v:218:y:2019:i:c:p:106-117
    DOI: 10.1016/j.ijpe.2019.05.003
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    1. Robert S. Kaplan, 1970. "A Dynamic Inventory Model with Stochastic Lead Times," Management Science, INFORMS, vol. 16(7), pages 491-507, March.
    2. Stephen C. Graves & Sean P. Willems, 2000. "Optimizing Strategic Safety Stock Placement in Supply Chains," Manufacturing & Service Operations Management, INFORMS, vol. 2(1), pages 68-83, June.
    3. Bandaly, Dia & Satir, Ahmet & Shanker, Latha, 2016. "Impact of lead time variability in supply chain risk management," International Journal of Production Economics, Elsevier, vol. 180(C), pages 88-100.
    4. Tang, Ou & Grubbstrom, Robert W., 2005. "Considering stochastic lead times in a manufacturing/remanufacturing system with deterministic demands and returns," International Journal of Production Economics, Elsevier, vol. 93(1), pages 285-300, January.
    5. Jula, Payman & Leachman, Robert C., 2011. "Long- and Short-Run supply-chain optimization models for the allocation and congestion management of containerized imports from Asia to the United States," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(5), pages 593-608, September.
    6. Petrovic, Dobrila & Roy, Rajat & Petrovic, Radivoj, 1998. "Modelling and simulation of a supply chain in an uncertain environment," European Journal of Operational Research, Elsevier, vol. 109(2), pages 299-309, September.
    7. Jing-Sheng Song & Paul H. Zipkin, 1996. "Inventory Control with Information About Supply Conditions," Management Science, INFORMS, vol. 42(10), pages 1409-1419, October.
    8. Roberto Rossi & S. Armagan Tarim & Ramesh Bollapragada, 2012. "Constraint-Based Local Search for Inventory Control Under Stochastic Demand and Lead Time," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 66-80, February.
    9. Leachman, Robert C. & Jula, Payman, 2012. "Estimating flow times for containerized imports from Asia to the United States through the Western rail network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 296-309.
    10. James R. Bradley & Lawrence W. Robinson, 2005. "Improved Base-Stock Approximations for Independent Stochastic Lead Times with Order Crossover," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 319-329, November.
    11. Disney, Stephen M. & Maltz, Arnold & Wang, Xun & Warburton, Roger D.H., 2016. "Inventory management for stochastic lead times with order crossovers," European Journal of Operational Research, Elsevier, vol. 248(2), pages 473-486.
    12. He, Xin James & Kim, Jeon G. & Hayya, Jack C., 2005. "The cost of lead-time variability: The case of the exponential distribution," International Journal of Production Economics, Elsevier, vol. 97(2), pages 130-142, August.
    13. Lawrence W. Robinson & James R. Bradley, 2008. "Note--Further Improvements on Base-Stock Approximations for Independent Stochastic Lead Times with Order Crossover," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 325-327, December.
    14. Bookbinder, James H. & Cakanyildirim, Metin, 1999. "Random lead times and expedited orders in (Q,r) inventory systems," European Journal of Operational Research, Elsevier, vol. 115(2), pages 300-313, June.
    15. Minner, Stefan, 2003. "Multiple-supplier inventory models in supply chain management: A review," International Journal of Production Economics, Elsevier, vol. 81(1), pages 265-279, January.
    16. Heckmann, Iris & Comes, Tina & Nickel, Stefan, 2015. "A critical review on supply chain risk – Definition, measure and modeling," Omega, Elsevier, vol. 52(C), pages 119-132.
    17. Riezebos, Jan, 2006. "Inventory order crossovers," International Journal of Production Economics, Elsevier, vol. 104(2), pages 666-675, December.
    18. Heng Kuang & S. Jack Hu & Jeonghan Ko, 2016. "A dynamic programming approach to integrated assembly planning and supplier assignment with lead time constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 54(9), pages 2691-2708, May.
    19. Dolgui, Alexandre & Ould-Louly, Mohamed-Aly, 2002. "A model for supply planning under lead time uncertainty," International Journal of Production Economics, Elsevier, vol. 78(2), pages 145-152, July.
    20. Richard Ehrhardt, 1984. "( s , S ) Policies for a Dynamic Inventory Model with Stochastic Lead Times," Operations Research, INFORMS, vol. 32(1), pages 121-132, February.
    21. Steven Nahmias, 1979. "Simple Approximations for a Variety of Dynamic Leadtime Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 27(5), pages 904-924, October.
    22. Ben-Ammar, Oussama & Dolgui, Alexandre & Wu, Desheng Dash, 2018. "Planned lead times optimization for multi-level assembly systems under uncertainties," Omega, Elsevier, vol. 78(C), pages 39-56.
    23. David Simchi-Levi & Yao Zhao, 2005. "Safety Stock Positioning in Supply Chains with Stochastic Lead Times," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 295-318, December.
    24. Alp Muharremoglu & Nan Yang, 2010. "Inventory Management with an Exogenous Supply Process," Operations Research, INFORMS, vol. 58(1), pages 111-129, February.
    25. Tang, Ou & Nurmaya Musa, S., 2011. "Identifying risk issues and research advancements in supply chain risk management," International Journal of Production Economics, Elsevier, vol. 133(1), pages 25-34, September.
    26. Barbara B. Flynn & Xenophon Koufteros & Guanyi Lu, 2016. "On Theory in Supply Chain Uncertainty and its Implications for Supply Chain Integration," Journal of Supply Chain Management, Institute for Supply Management, vol. 52(3), pages 3-27, July.
    27. May, Benjamin Isaac & Atkinson, Michael P. & Ferrer, Geraldo, 2017. "Applying inventory classification to a large inventory management system," Journal of Operations and Supply Chain Management (JOSCM), Fundação Getulio Vargas, Escola de Administração de Empresas de São Paulo (FGV EAESP), vol. 10(1), June.
    28. Louly, Mohamed-Aly & Dolgui, Alexandre, 2013. "Optimal MRP parameters for a single item inventory with random replenishment lead time, POQ policy and service level constraint," International Journal of Production Economics, Elsevier, vol. 143(1), pages 35-40.
    29. Hayya, Jack C. & Bagchi, Uttarayan & Kim, Jeon G. & Sun, Daewon, 2008. "On static stochastic order crossover," International Journal of Production Economics, Elsevier, vol. 114(1), pages 404-413, July.
    30. Chengbin Chu & Jean‐Marie Proth & Xiaolan Xie, 1993. "Supply management in assembly systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(7), pages 933-949, December.
    31. Tang, Ou & Grubbstrom, Robert W., 2003. "The detailed coordination problem in a two-level assembly system with stochastic lead times," International Journal of Production Economics, Elsevier, vol. 81(1), pages 415-429, January.
    32. Arıkan, Emel & Fichtinger, Johannes & Ries, Jörg M., 2014. "Impact of transportation lead-time variability on the economic and environmental performance of inventory systems," International Journal of Production Economics, Elsevier, vol. 157(C), pages 279-288.
    33. Lawrence V. Snyder & Zümbül Atan & Peng Peng & Ying Rong & Amanda J. Schmitt & Burcu Sinsoysal, 2016. "OR/MS models for supply chain disruptions: a review," IISE Transactions, Taylor & Francis Journals, vol. 48(2), pages 89-109, February.
    34. Begen, Mehmet A. & Pun, Hubert & Yan, Xinghao, 2016. "Supply and demand uncertainty reduction efforts and cost comparison," International Journal of Production Economics, Elsevier, vol. 180(C), pages 125-134.
    35. Arikan, E. & Fichtinger, J. & Ries, J. M., 2014. "Impact of transportation lead-time variability on the economic and environmental performance of inventory systems," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 63386, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    36. SteadieSeifi, M. & Dellaert, N.P. & Nuijten, W. & Van Woensel, T. & Raoufi, R., 2014. "Multimodal freight transportation planning: A literature review," European Journal of Operational Research, Elsevier, vol. 233(1), pages 1-15.
    37. Lawrence W. Robinson & James R. Bradley & L. Joseph Thomas, 2001. "Consequences of Order Crossover Under Order-Up-To Inventory Policies," Manufacturing & Service Operations Management, INFORMS, vol. 3(3), pages 175-188, September.
    38. Georghios P. Sphicas, 1982. "Technical Note—On the Solution of an Inventory Model with Variable Lead Times," Operations Research, INFORMS, vol. 30(2), pages 404-410, April.
    39. Matthew J. Liberatore, 1979. "Technical Note—The EOQ Model under Stochastic Lead Time," Operations Research, INFORMS, vol. 27(2), pages 391-396, April.
    40. Paul Zipkin, 1986. "Stochastic leadtimes in continuous‐time inventory models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 763-774, November.
    41. Ryu, Si Wook & Lee, Kyung Keun, 2003. "A stochastic inventory model of dual sourced supply chain with lead-time reduction," International Journal of Production Economics, Elsevier, vol. 81(1), pages 513-524, January.
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