Dynamic programming approximation algorithms for the capacitated lot-sizing problem
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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.
KeywordsApproximate dynamic programming Approximation algorithms Data fitting Production and inventory control Mixed-integer programming Capacitated lot-sizing
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.
- 4.Bertsekas, D.P.: Dynamic Programming and Optimal Control, 3rd edition, vol. ii. Athena Scientific, Belmont (2011)Google Scholar
- 5.Bertsekas, D.P., Tsitsiklis, J.N.: Neuro-dynamic programming: an overview. In: Proceedings of the 34th IEEE Conference on, Decision and Control, 1995., volume 1, pp. 560–564, (1995)Google Scholar
- 7.Büyüktahtakın, İ.E.: Dynamic programming via linear programming. In: Cochran Jr, J.J., Cox, L.A., Keskinocak, P., Kharoufeh, J.P., Smith, J.C. (eds.) Wiley Encyclopedia of Operations Research and Management Science. Wiley, Hoboken, NJ (2011)Google Scholar
- 8.Büyüktahtakın, İ.E.: Mixed Integer Programming Approaches to Lot-Sizing and Asset Replacement Problems. PhD thesis, Industrial and Systems Engineering, University of Florida, (2009)Google Scholar
- 17.Küçükyavuz, S.: Mixed-integer optimization approaches for deterministic and stochastic inventory management. In: Geunes, J.P. (ed.) INFORMS TutORials in Operations Research, vol. 8, pp. 90–105. INFORMS, Hanover, MD (2011)Google Scholar
- 19.Muggeo, V.M.: Estimating regression models with unknown break-points. Stat. Med. Wiley Online Libr. 22, 3055–3071 (2003)Google Scholar
- 24.Powell, W.B.: Perspectives of approximate dynamic programming. Ann. Oper. Res. 1–38 (2012)Google Scholar
- 25.Sutton, R., Barto, A.: Reinforcement Learning. MIT Press, Cambridge (1998)Google Scholar