Abstract
A version of the dynamic lot-sizing (DLS) problem involving durable products with end-of-use constraints is analyzed in this paper. First, we mathematically formulate this problem, then certain properties are derived to construct the structure of the optimal solution. Next, based on these properties, a recursive optimization algorithm is proposed for a single-item problem. Moreover, an approximate algorithm is designed on the basis of the optimization algorithm, with linear computational complexity. A heuristic approach is proposed for solving the two-item DLS problem. The difficulty in solving this problem lies in its decomposition into item-level subproblems while ensuring the feasibility of the solution. The proposed technique aims to resolve this issue by combining the capabilities of Lagrangian relaxation to decompose the problem into smaller subproblems, and a genetic algorithm (GA) is used to update the Lagrangian multipliers. Further, the computational results obtained using the proposed approach are enumerated to demonstrate its effectiveness. Finally, the conclusion and remarks are given to discuss the possible future works.
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Acknowledgements
We gratefully acknowledge the support of (i) The Major Program of the National Social Science Fund of China (Grant No. 13 & ZD147), and National Natural Science Foundation of China, Nos. 91024002, and 71372100, for Y.J. Li; (ii) Research Grants Council of Hong Kong, General Research Fund Nos.�410211 and�410213, and NSFC Key Program Grant No. 70932005, for X.Q. Cai; and (iii) NSFC Research Fund Nos.�71302005 and 71371186 for L. Xu.
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Li, Y., Cai, X., Xu, L. et al. Heuristic approach on dynamic lot-sizing model for durable products with end-of-use constraints. Ann Oper Res 242, 265–283 (2016). https://doi.org/10.1007/s10479-013-1526-x
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DOI: https://doi.org/10.1007/s10479-013-1526-x