Abstract
This paper discusses a basic dynamic lot-sizing model for a single item with rework of defectives. Due to the imperfect production process, some fraction of the generated items is not of sufficient quality. After rework, these goods serve the same demand as the initial perfect quality items; both are called serviceables.The internal processes production and rework are conducted independently from another at different or same periods. The basic model is proven to be NP-hard. We present three main unique characteristics that describe the specific model behavior observed in the optimal solutions: production only, multiple rework, and overproduction of serviceables. Different MIP formulations are derived to analyse the effects of these three characteristics on the optimal solutions that exclude each of these characteristics from the basic model. Afterward, computations for given data sets are conducted, using all different MIP formulations. It can be shown that production only occurs most frequently and has the highest effect on the total cost.
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References
Wagner, H. M., & Whitin, T. M. (1958). Dynamic version of the economic lot size model. Management Science, 5, 89–96.
Brahimi, N., Absi, N., Dauzèré-Pérès, S., & Nordli, A. (2017). Single-item dynamic lot-sizing problems: An updated survey. European Journal of Operational Research, 263(3), 838–863.
Teunter, R. H., Bayindir, Z. P., & van den Heuvel, W. (2006). Dynamic lot sizing with product returns and remanufacturing. International Journal of Production Research, 44(20), 4377–4400.
Helmrich, M. J. R., Jans, R., van den Heuvel, W., & Wagelmans, A. P. (2014). Economic lot-sizing with remanufacturing: Complexity and efficient formulations. IIE Transactions, 46, 67–86.
Cunha, J. O., & Melo, R. A. (2016). A computational comparison of formulations for the economic lot-sizing with remanufacturing. Computers and Industrial Engineering, 92, 72–81.
Kilic, O. A., & van den Heuvel, W. (2019). Economic lot sizing with remanufacturing: Structural properties and polynomial-time heuristics. IISE Transactions, 51(12), 1318–1331.
Goerler, A., & Voß, S. (2016). Dynamic lot-sizing with rework of defective items and minimum lot-size constraints. International Journal of Production Research, 54(8), 1–14.
Goerler, A., Lalla-Ruiz, E., & Voß, S. (2020). Late acceptance hill-climbing matheuristic for the general lot sizing and scheduling problem with rich constraints. Algorithms, 13, 1–26.
van Zyl, A., & Adetunji, O. (2022). A lot sizing model for two items with imperfect manufacturing process, time varying demand and return rates, dependent demand and different quality grades. Journal of Remanufacturing. https://doi.org/10.1007/s13243-022-00110-z
Rudert, S., & Buscher, U. (2022). On the complexity of the economic lot-sizing problem with rework of defectives. Dresdner Beiträge zur Betriebswirtschaftslehre, Nr. 182/22, Dresden: TU Dresden. https://doi.org/10.25368/2022.322
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Rudert, S. (2023). Different MIP Formulations for a Dynamic Lot-Sizing Model with Rework of Defectives. In: Grothe, O., Nickel, S., Rebennack, S., Stein, O. (eds) Operations Research Proceedings 2022. OR 2022. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-24907-5_52
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DOI: https://doi.org/10.1007/978-3-031-24907-5_52
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