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Dynamic programming approximation algorithms for the capacitated lot-sizing problem

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Abstract

This paper provides a new idea for approximating the inventory cost function to be used in a truncated dynamic program for solving the capacitated lot-sizing problem. The proposed method combines dynamic programming with regression, data fitting, and approximation techniques to estimate the inventory cost function at each stage of the dynamic program. The effectiveness of the proposed method is analyzed on various types of the capacitated lot-sizing problem instances with different cost and capacity characteristics. Computational results show that approximation approaches could significantly decrease the computational time required by the dynamic program and the integer program for solving different types of the capacitated lot-sizing problem instances. Furthermore, in most cases, the proposed approximate dynamic programming approaches can accurately capture the optimal solution of the problem with consistent computational performance over different instances.

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Acknowledgments

We gratefully acknowledge the support of the NSF under Grant No. EPS-0903806 and the state of Kansas through the Kansas Board of Regents, and the Strategic Engineering Research Fellowship (SERF) of the College of Engineering at Wichita State University. We also thank anonymous referees and the associate editor, whose remarks helped to clarify our exposition.

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Authors and Affiliations

  1. Industrial and Manufacturing Engineering, Wichita State University, 1845 N Fairmount, Wichita, KS, 67260-0035, USA

    İ. Esra Büyüktahtakın & Ning Liu

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  1. İ. Esra Büyüktahtakın
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  2. Ning Liu
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Correspondence to İ. Esra Büyüktahtakın.

Appendix

Appendix

See Tables 1, 2, 3, 4 and 5.

Table 1 Summary of experiments for \(f=1000\) and \(T=90\)
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Table 2 Summary of experiments for \(f=10,000\) and \(T=90\)
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Table 3 Summary of experiments for \(T=120\)
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Table 4 Summary of experiments for \(T=150\)
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Table 5 Summary of experiments for overall averages over \(T=90\), \(T=120\), and \(T=150\)
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Büyüktahtakın, İ.E., Liu, N. Dynamic programming approximation algorithms for the capacitated lot-sizing problem. J Glob Optim 65, 231–259 (2016). https://doi.org/10.1007/s10898-015-0349-5

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