Title: Column generation approach for solving uncapacitated dynamic lot-sizing problems with time-varying cost

Authors: Warut Boonphakdee; Peerayuth Charnsethikul

Addresses: Department of Industrial Engineering, Faculty of Engineering at Kamphaeng Saen, Kasetsart University, 1 Moo 6, Kamphaeng Saen, Amphoe Kamphaeng Saen, Nakhon Pathom, Thailand ' Department of Industrial Engineering, Faculty of Engineering, Kasetsart University, 50 Ngamwongwan Road, Lat Yao, Chatuchak, Bangkok, Thailand

Abstract: This study proposes the column generation approach for generating the uncapacitated dynamic lot-sizing problem solution under time-varying cost. The dynamic programming approach is also applied to calculate the cost function value. However, this column generation approach generates only an optimal lot size at period 1. Therefore, using the consistent arc method, search the connecting arc from period 1 to period N. Comparing the lot sizes generated by the proposed and the dynamic programming methods, they are the same value. Therefore, they are an optimal solution. Using GUROBI's simplex method can enhance to reduce the running time on dense matrices to be less than the original simplex method, about 25.4% and 26.1% for 12 and 24 periods. The lowest raw material fluctuation price period is selected obviously to order so that the total inventory cost will still be minimal. Therefore, the raw material price significantly influences procurement decision-making.

Keywords: dynamic programming; network inventory; column generation; maximum problem size.

DOI: 10.1504/IJMOR.2022.126051

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.1, pp.55 - 75

Received: 19 May 2021
Accepted: 27 May 2021
Published online: 10 Oct 2022 *

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