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Differential evolution to solve the lot size problem in stochastic supply chain management systems

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Abstract

An advanced resource planning model is presented to support optimal lot size decisions for overall performance improvement of real-life supply chain management systems in terms of either total delivery time or total setup costs. Based on a queueing network, a model is developed for a mix of products, which follow a sequence of operations taking place at multiple interdependent supply chain members. At the same time, various sources of uncertainty, both in demand and process characteristics, are taken into account. In addition, the model includes the impact of parallel servers for multiple resources with period dependent time schedules. The corrupting influence of variabilities from rework and breakdown is also explicitly modeled. This integer non-linear problem is solved by standard differential evolution algorithms. They are able to find each product’s lot size that minimizes its total supply chain lead time. We show that this solution approach outperforms the steepest descent method, an approach commonly used in the search for optimal lot sizes. For problems of realistic size, we propose appropriate control parameters for an efficient differential evolutionary search process. Based on these results, we add a major conclusion on the debate concerning the convexity between lot size and lead time in a complex supply chain environment.

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Acknowledgments

The authors would like to thank the Fund for Scientific Research Flanders (FWO) for their support with the Post Doctoral Research project for Kris Lieckens.

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Authors and Affiliations

  1. Faculty of Economics and Business Research Center for Operations Management, KU Leuven, Leuven, Belgium

    Kris Lieckens & Nico Vandaele

  2. Faculty of Economics and Business, KU Leuven Campus Kortrijk, Kortrijk, Belgium

    Nico Vandaele

Authors
  1. Kris Lieckens
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  2. Nico Vandaele
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Corresponding author

Correspondence to Kris Lieckens.

Appendix: Results for Control Parameter Settings in DE

Appendix: Results for Control Parameter Settings in DE

See Tables 5, 6, 7, 8, 9 and 10.

Table 5 Results for DE/rand/1/bin with a small population compared to the base setting with an intermediate population
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Table 6 Results for DE/rand/2/bin with a small population compared to the base setting with an intermediate population
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Table 7 Results for DE/current-to-rand/1 with a small population and \(K=0\) compared to the base setting with an intermediate population
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Table 8 Results for DE/current-to-rand/1 with a small population and \(K=[0,1]\) compared to the base setting with an intermediate population
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Table 9 Results for DE/current-to-rand/1 with a small population and \(K=0.5\) compared to the base setting with an intermediate population
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Table 10 Results for DE/current-to-rand/1 with a small population and \(K=1\) compared to the base setting with an intermediate population
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Lieckens, K., Vandaele, N. Differential evolution to solve the lot size problem in stochastic supply chain management systems. Ann Oper Res 242, 239–263 (2016). https://doi.org/10.1007/s10479-014-1778-0

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  • DOI: https://doi.org/10.1007/s10479-014-1778-0

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