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Lot Sizing Problem Under Lead-Time Uncertainty

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2024)

Abstract

In the supply chain, lead time uncertainty affects the effectiveness of planning. This paper discusses a lot sizing problem with uncertain lead times modelled by intervals. First, we propose to evaluate the impact of uncertainty on a given production plan by computing a best and a worst production plan over all lead time scenarios. Then, a method based on \(R^*_e\) is proposed for choosing a compromise production plan. Some methods for solving the problems based on mixed integer programming formulations are proposed. Finally, the results are illustrated and discussed using an example.

A. Kasperski and P. Zieliński were supported by the National Science Centre, Poland, grant 2022/45/B/HS4/00355.

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References

  1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: theory, algorithms, and applications. Prentice Hall, Englewood Cliffs, New Jersey (1993)

    Google Scholar 

  2. Altendorfer, K.: Influence of lot size and planned lead time on service level and inventory for a single-stage production system with advance demand information and random required lead times. Int. J. Prod. Econ. 170, 478–488 (2015)

    Article  Google Scholar 

  3. Ammar, O.B., Guillaume, R., Thierry, C.: MRP parameter evaluation under fuzzy lead times. IFAC-PapersOnLine 49(12), 1110–1115 (2016)

    Article  Google Scholar 

  4. Disney, S.M., Maltz, A., Wang, X., Warburton, R.D.: Inventory management for stochastic lead times with order crossovers. Eur. J. Oper. Res. 248(2), 473–486 (2016)

    Article  MathSciNet  Google Scholar 

  5. Fargier, H., Guillaume, R.: Sequential decision making under ordinal uncertainty: A qualitative alternative to the hurwicz criterion. Int. J. Approximate Reasoning 116, 1–18 (2020)

    Article  MathSciNet  Google Scholar 

  6. Giang, P.H.: Decision making under uncertainty comprising complete ignorance and probability. Int. J. Approximate Reasoning 62, 27–45 (2015)

    Article  MathSciNet  Google Scholar 

  7. Goerigk, M., Guillaume, R., Kasperski, A., Zieliński, P.: Robust optimization with belief functions. Int. J. Approximate Reasoning 159, 108941 (2023)

    Article  MathSciNet  Google Scholar 

  8. Graves, S.C.: Uncertainty and production planning. Planning Production and Inventories in the Extended Enterprise: A State of the Art Handbook 1, 83–101 (2011)

    Google Scholar 

  9. Guillaume, R., Thierry, C., Grabot, B.: MRP with imprecise demand and uncertain lead time. In: Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology, pp. 673–679. Atlantis Press (2011)

    Google Scholar 

  10. Hnaien, F., Afsar, H.M.: Robust single-item lot-sizing problems with discrete-scenario lead time. Int. J. Prod. Econ. 185, 223–229 (2017)

    Article  Google Scholar 

  11. Hurwicz, L.: Optimality criteria for decision making under ignorance. Technical report, Cowles Commission discussion paper, statistics (1951)

    Google Scholar 

  12. Krug, Z., Guillaume, R., Battaïa, O.: Decision under ignorance: a comparison of existing criteria. In: Lesot, M.-J., et al. (eds.) IPMU 2020. CCIS, vol. 1237, pp. 158–171. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-50146-4_13

    Chapter  Google Scholar 

  13. Levi, R., Pál, M., Roundy, R.O., Shmoys, D.B.: Approximation algorithms for stochastic inventory control models. Math. Oper. Res. 32(2), 284–302 (2007)

    Article  MathSciNet  Google Scholar 

  14. Milne, R.J., Mahapatra, S., Wang, C.T.: Optimizing planned lead times for enhancing performance of MRP systems. Int. J. Prod. Econ. 167, 220–231 (2015)

    Article  Google Scholar 

  15. Thevenin, S., Ben-Ammar, O., Brahimi, N.: Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty. Eur. J. Oper. Res. 303(3), 1199–1215 (2022)

    Article  MathSciNet  Google Scholar 

  16. Thorsen, A., Yao, T.: Robust inventory control under demand and lead time uncertainty. Ann. Oper. Res. 257, 207–236 (2017)

    Article  MathSciNet  Google Scholar 

  17. Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)

    Article  MathSciNet  Google Scholar 

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Correspondence to Romain Guillaume .

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Guillaume, R., Kasperski, A., Zieliński, P. (2024). Lot Sizing Problem Under Lead-Time Uncertainty. In: Lesot, MJ., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2024. Lecture Notes in Networks and Systems, vol 1174. Springer, Cham. https://doi.org/10.1007/978-3-031-74003-9_12

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