Dynamic programming approximation algorithms for the capacitated lot-sizing problem

• 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
• DOI: 10.1007/s10898-015-0349-5

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.