由于电子商务与先进物流技术的快速发展，消费模式已从单一渠道的线下购买方式转变为线上、线下相结合的多渠道或全渠道模式。因此，研究全渠道背景下企业供应链网络设计问题具有重要的理论与实践意义。本文以全渠道可持续供应链网络为研究对象，分别对确定性和不确定环境下两类可持续供应链网络设计优化问题展开研究。

       首先，针对客户需求量、设施容量等参数已知情况下的可持续供应链网络设计问题，以最小化供应链总成本和碳排放量为优化目标，构建了一个多阶段混合整数线性规划（Mixed integer linear programming，MILP）模型，设计了基于迭代epsilon算法，其通过将双目标问题转化为一系列单目标问题进行求解从而获得原始双目标优化问题得真正帕累托前沿（Pareto frontier）。同时，基于决策者的不同偏好使用模糊决策方法选出供应链网络配置最优决策方案。最后，通过使用C++编程语言编码实现了上述模型与算法，并通过测试算例和105个随机生成算例验证了所构建模型和算法的有效性。

     其次，研究了不确定环境下的可持续供应链网络设计优化问题，综合考虑顾客需求、设施容量的不确定性以及碳排放上限等因素，以供应链总成本最小化为优化目标，首先构建了不确定环境下可持续供应链网络设计模型；使用机会约束规划方法和不确定理论，将所建立的不确定性模型等价转换为确定性的MILP模型。最后，使用C++编程语言编码实现了上述模型并应用CPLEX求解器对基准算例和随机生成算例进行验证与评价。实验结果表明，本研究构建的网络设计模型能够有效求解不确定环境下的可持续供应链网络设计与优化问题。此外，也分析了不同碳上限和不同概率情景下对供应链总成本结构的影响机理，这为相关企业决策者面临不确定环境下的可持续供应链网络规划和运营决策提供一定的理论和技术支持。

Due to the rapid development of e-commerce and advanced logistics technology, the consumption mode has changed from the brick-and-mortar purchase mode (i.e., single offline channel) to the multi-channel or omni-channel modes based on online and offline. Therefore, it has important theoretical and practical significances to study the supply chain network design problems in omnichannel. This paper takes the omni-channel sustainable supply chain network as the research object, and aims to study two types (i.e., deterministic and uncertain) sustainable supply chain network design optimization problems.

First, we consider the deterministic sustainable supply chain network problem with known parameters such as customer demand and facility capacity. The objectives of the considered problem are to simultaneously minimize the total supply chain cost and carbon emissions released by the supply chain activities. We formulate a multi-stage mixed integer linear programming (Mixed Integer linear programming, MILP) model for the problem, and design an epsilon-constraint based iterative algorithm, which converts the studied bi-objective optimization problem into a series of single-objective optimization problems so as to obtain the true Pareto frontier for the original bi-objective problem. Also, the fuzzy decision-making method was designed for helping the decision makers select the optimal or best supply chain network configuration scheme under different preferences. Finally, our model and algorithm were implemented by using C++ programming language, and their effectiveness was verified by benchmark instances and 105 randomly generated examples.

Second, the sustainable supply chain network design problem with parameters uncertainty (such as uncertainty of customer demand, facility capacity, and carbon emission cap) is studied. The objective of the studied problem is to minimize the total supply chain cost. We first formulated an uncertain mathematical model for the studied problem, and then use the chance constrained programming method and uncertainty theory to equivalently transform the formulated uncertainty model into a deterministic MILP model. Finally, both benchmark instances and random testing instances are used to evaluate the efficiency of the above model, which is coded by C++ programming language and solved by the CPLEX MIP solver. The experimental results show that our proposed model is effective and efficient for the considered uncertain SCND problem in omnichannel. Besides, the impact mechanism of different carbon caps and different probability scenarios on the structure of the objective function is also analyzed. The results may support the decision makers to manage and plan their supply chain network effectively, especially under an uncertain environment.

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