In this paper, we investigate a multi-product, three-stage production/distribution system design problem (PDSD) with direct shipment and lateral transshipment capabilities. Our overall goal is to find the most efficient network design to minimize the total fixed facility and transportation costs. Specifically, we locate p capacitated distribution centers in the second stage from a set of candidate locations. At the same time, our design allows for direct shipments between first (suppliers) and third stages (customers) and lateral transshipments among the distribution centers in the second stage. The PDSD problem is known to be NP-hard, and prior studies have explored several heuristic methods including scatter search, tabu search, and genetic algorithms to solve the problem. In this paper, we propose two solution algorithms based on simulated annealing and GRASP heuristics. We apply both long-term and short-term memory lists to maintain an efficient local search, combined with a custom greedy solver that can effectively evaluate the quality of a solution candidate. We conduct a series of computational experiments to validate the proposed algorithms. Compared with the optimal solution, the simulated annealing algorithm presents an average optimality gap of 0.07% and an average time of 25.56% of optimal solution time, while the GRASP algorithm achieves a solution gap of 0.11% with 17.85% of optimal running time. The experimental results also show that the simulated annealing and GRASP algorithms outperform the best-reported heuristic in the literature based on scatter search regarding both solution quality and duration, especially for large-scale problem instances with tighter capacities.

中文翻译：

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直接出货和横向转运的多产品生产/分销系统设计问题

在本文中，我们研究了具有直接装运和横向转运功能的多产品，三阶段生产/分销系统设计问题（PDSD）。我们的总体目标是找到最有效的网络设计，以最大程度地减少固定设施和运输的总成本。具体来说，我们找到p在第二阶段从一组候选位置中选择了功能强大的配送中心。同时，我们的设计允许在第一阶段（供应商）和第三阶段（客户）之间进行直接运输，并在第二阶段进行配送中心之间的横向转运。PDSD问题已知是NP难题，先前的研究已经探索了几种启发式方法，包括散点搜索，禁忌搜索和遗传算法来解决该问题。在本文中，我们提出了两种基于模拟退火和GRASP启发式的求解算法。我们使用长期和短期记忆列表来维持有效的本地搜索，并结合可以有效评估解决方案候选者质量的自定义贪婪求解器。我们进行了一系列计算实验，以验证所提出的算法。与最优解相比，模拟退火算法的平均最优间隙为0.07％，平均时间为最优解时间的25.56％，而GRASP算法的最优解时间为0.11％，最优运行时间为17.85％。实验结果还表明，基于基于散点搜索的解决方案质量和持续时间，模拟退火和GRASP算法的性能优于文献中报告最好的启发式算法，特别是对于容量更小的大型问题实例。