Dynamic programming approximation algorithms for the capacitated lot-sizing problem

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 inventor...

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Published in:	Journal of global optimization Vol. 65; no. 2; pp. 231 - 259
Main Authors:	Büyüktahtakın, İ. Esra, Liu, Ning
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.06.2016 Springer Springer Nature B.V
Subjects:	Algorithms Approximation Computation Computer Science Costs Dynamic programming Dynamics Integer programming Inventories Inventory control Mathematical analysis Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Production capacity Production planning Real Functions Stockpiling Studies Supply chain management Approximate dynamic programming Approximation algorithms Production and inventory control Data fitting Mixed-integer programming Capacitated lot-sizing
ISSN:	0925-5001, 1573-2916
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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.
AbstractList	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.
Audience	Academic
Author	Liu, Ning Büyüktahtakın, İ. Esra
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CitedBy_id	crossref_primary_10_1016_j_cie_2020_107051 crossref_primary_10_1016_j_cor_2023_106149 crossref_primary_10_1007_s10479_024_06100_7 crossref_primary_10_1007_s43069_023_00224_5 crossref_primary_10_1016_j_cie_2018_01_018 crossref_primary_10_1016_j_ejor_2021_12_032 crossref_primary_10_1016_j_chaos_2018_09_012 crossref_primary_10_1016_j_cor_2017_11_006 crossref_primary_10_1049_iet_gtd_2018_5754 crossref_primary_10_1080_00207543_2017_1384583
Cites_doi	10.1002/9781118627372 10.1287/mnsc.37.8.909 10.1007/BF01098363 10.1287/opre.34.2.226 10.1287/mnsc.5.1.89 10.1080/0740817X.2010.504683 10.1007/s10107-003-0465-8 10.1007/BF01099265 10.1287/mnsc.37.1.53 10.1111/j.1937-5956.2012.01420.x 10.1002/9780470182963 10.1287/trsc.1030.0041 10.1287/moor.26.2.339.10552 10.1002/nav.20433 10.1287/moor.2013.0607 10.1287/mnsc.26.7.669 10.1111/j.2517-6161.1969.tb00772.x 10.1109/CDC.1995.478953 10.1007/s10479-012-1077-6
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Keywords	Approximate dynamic programming Approximation algorithms Production and inventory control Data fitting Mixed-integer programming Capacitated lot-sizing
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Snippet	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...
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SubjectTerms	Algorithms Approximation Computation Computer Science Costs Dynamic programming Dynamics Integer programming Inventories Inventory control Mathematical analysis Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Production capacity Production planning Real Functions Stockpiling Studies Supply chain management
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Title	Dynamic programming approximation algorithms for the capacitated lot-sizing problem
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