基于客户价值和满意度的城市冷链物流时变路径问题

针对车辆保有量日益增加和拥堵情况日趋严重而造成的城市冷链物流时效性不强、客户价值不高、顾客满意度降低等问题，综合考虑客户价值、客户满意度以及成本等因素，提出一种城市冷链物流时变路径优化方法。考虑到冷链配送过程中不同时段的道路拥堵问题，采用分段函数刻画车辆行驶速度，并同时考虑时间窗和车辆载重量等约束，建立了多目标数学模型。使用线性加权法和主要目标法对多目标进行处理，将其转换成单目标数学模型。结合问题NP难特性，设计了单亲遗传算法对小、中、大规模算例进行了求解，结果表明：与未考虑客户价值模型相比，该模型在平均增加3.28%成本的情况下，提高14.96%的客户价值和14.64%的满意度；与未考虑成本模型相比，该模型在减少1.55%的客户价值的前提下，节约17.32%的成本；对比静态路网模型，模型减少0.92%的成本，提高6.27%的客户满意度和16.06%的客户价值。通过对目标函数中成本权重和客户价值权重进行参数分析，表明成本和客户价值之间存在明显的背反关系。

Time-dependent Vehicle Routing of Urban Cold-chain Logistics Based on Customer Value and Satisfaction

The increase in vehicle population and severe congestion causes problems, such as the weak timeliness of urban cold-chain logistics, low customer value, and reduction in customer satisfaction. In this study, customer satisfaction, customer value, and cost were considered, and an optimization algorithm was established to solve the time-dependent vehicle routing problem of urban cold-chain logistics. For road congestion during different periods of the cold-chain distribution process, a piecewise function was used to express the vehicle travelling speed. A multiobjective mathematical model of this problem was established, considering the time window, vehicle capacity, and other constraints. The multiobjective was processed using the linear weighting method and the main objective method, and it was transformed into a single-objective mathematical model. Based on the nondeterministic polynomial-time hardness of the problem, a parthenogenetic algorithm was designed to solve small-, medium-, and large-scale examples. Compared with the model that does not reflect the customer value, the proposed model increases customer value and customer satisfaction by 14.96% and 14.64%, respectively, when the cost decreases by 3.28%. Compared with the model neglecting the cost factor, the proposed model decreases the cost by 17.32% when the customer value decreases by 1.55%. Compared with the static road network model, the model proposed in this study reduces the cost by 0.92% and improves customer satisfaction and customer value by 6.27% and 16.06%, respectively. Through the parameter analysis of the cost and customer-value weights in the objective function, a robust reverse relationship between cost and customer value is observed.