Cross-docking practice plays an important role in improving the efficiency of distribution networks, especially, for optimizing supply chain operations. Moreover, transportation route planning, controlling the Greenhouse Gas (GHG) emissions and customer satisfaction constitute the major parts of the supply chain that need to be taken into account integratedly within a common framework. For this purpose, this paper tries to introduce the reliable Pollution-Routing Problem with Cross-dock Selection (PRP-CDS) where the products are processed and transported through at least one cross-dock. To formulate the problem, a Bi-Objective Mixed-Integer Linear Programming (BOMILP) model is developed, where the first objective is to minimize total cost including pollution and routing costs and the second is to maximize supply reliability. Accordingly, sustainable development of the supply chain is addressed. Due to the high complexity of the problem, two well-known meta-heuristic algorithms including Multi-Objective Simulated-annealing Algorithm (MOSA) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) are designed to provide efficient Pareto solutions. Furthermore, the ε-constraint method is applied to the model to test its applicability in small-sized problems. The efficiency of the suggested solution techniques is evaluated using different measures and a statistical test. To validate the performance of the proposed methodology, a real case study problem is conducted using the sensitivity analysis of demand parameter. Based on the main findings of the study, it is concluded that the solution techniques can yield high-quality solutions and NSGA-II is considered as the most efficient solution tool, the optimal route planning of the case study problem in delivery and pick-up phases is attained using the best-found Pareto solution and the highest change in the objective function occurs for the total cost value by applying a 20% increase in the demand parameter.

跨码头实践在提高分销网络效率方面，尤其是在优化供应链运营方面，起着重要作用。此外，运输路线规划，控制温室气体（GHG）排放和客户满意度构成了供应链的主要部分，需要在一个通用框架内综合考虑。为此，本文尝试介绍可靠的交叉码头选择污染路由问题（PRP-CDS），在该问题中，产品经过至少一个交叉码头进行加工和运输。为了解决这个问题，开发了双目标混合整数线性规划（BOMILP）模型，其中第一个目标是最大程度地降低包括污染和布线成本在内的总成本，第二个目标是最大化供应的可靠性。因此，解决了供应链的可持续发展。由于问题的高度复杂性，设计了两种著名的元启发式算法，包括多目标模拟退火算法（MOSA）和非支配排序遗传算法II（NSGA-II），以提供有效的Pareto解决方案。此外，将ε约束方法应用于模型以测试其在小型问题中的适用性。建议的解决方案技术的效率使用不同的方法和统计测试进行评估。为了验证所提出方法的性能，使用需求参数的敏感性分析进行了实际案例研究问题。根据研究的主要发现，