Abstract This paper addresses the joint optimization of production capacity and safety stocks in supply chains under the guaranteed service approach (GSA). The integrated problem is formulated as a mixed integer nonlinear program (MINLP) and solution procedures are proposed in the cases of general acyclic and spanning tree networks. For general acyclic supply chains, the integrated problem is solved using a Lagrangian decomposition method which iteratively solves capacity planning and safety stock placement subproblems, and adds budget feasibility constraints to strengthen the Lagrangian decomposition lower bound. When the supply chain has a spanning tree structure, an efficient Lagrangian relaxation heuristic dualizes the budget constraint and solves the relaxed problem using a dynamic programming algorithm. Computational experiments on real-world instances show that the Lagrangian decomposition method is able to solve all instances within 0.1% optimality, while a state-of-the-art solver is unable to provide feasible solutions for large instances. In the case of spanning tree networks, the proposed Lagrangian relaxation heuristic finds optimal or near-optimal solutions and greatly improves running time in comparison to the Lagrangian decomposition method. In addition, numerical experiments show that savings can be achieved through joint optimization of capacity and safety stocks.

中文翻译：

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优化一般非循环供应链的产能和安全库存

摘要 本文讨论了在保证服务方法（GSA）下供应链中生产能力和安全库存的联合优化。综合问题被表述为混合整数非线性规划 (MINLP)，并在一般非循环和生成树网络的情况下提出了解决方案。对于一般非循环供应链，综合问题采用拉格朗日分解方法求解，迭代求解产能规划和安全库存放置子问题，并增加预算可行性约束以加强拉格朗日分解下界。当供应链具有生成树结构时，有效的拉格朗日松弛启发式对预算约束进行二元化并使用动态规划算法解决松弛问题。真实世界实例的计算实验表明，拉格朗日分解方法能够在 0.1% 的最优性内解决所有实例，而最先进的求解器无法为大型实例提供可行的解决方案。在生成树网络的情况下，与拉格朗日分解方法相比，所提出的拉格朗日松弛启发式算法可以找到最佳或接近最佳的解决方案，并大大缩短了运行时间。此外，数值实验表明，可以通过容量和安全库存的联合优化来实现节约。与拉格朗日分解方法相比，所提出的拉格朗日松弛试探法可找到最佳或接近最佳的解决方案，并大大缩短了运行时间。此外，数值实验表明，可以通过容量和安全库存的联合优化来实现节约。与拉格朗日分解方法相比，所提出的拉格朗日松弛试探法可找到最佳或接近最佳的解决方案，并大大缩短了运行时间。此外，数值实验表明，可以通过容量和安全库存的联合优化来实现节约。