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Vehicle Routing Problem With Fuzzy Time Windows

机译：模糊时间窗的车辆路径问题

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In this paper, a vehicle routing problem with fuzzy time windows (VRPFTW) is proposed and solved. In the transportation business, time windows are not always strictly obeyed and the deviation of service time from the customer-specific time window determines the customer's satisfaction level, which can also be regarded as the supplier's service level. This paper applies fuzzy membership functions to characterize the service level issues associated with time window violation in a vehicle routing problem and proposes VRPFTW. VRPFTW is formulated as a multi-objective model with two goals: (1) to minimize the travel distance and (2) to maximize the service level of the supplier to customers. To solve this multi-objective model, a two-stage algorithm is developed to obtain a Pareto solution for VRPFTW. Using the two-stage algorithm, VRPFTW is decomposed into two subproblems, namely a traditional vehicle routing problem with time windows (VRPTW-α) and a service improvement problem, and each of the objectives is sequentially solved. The service improvement problem is solved under two different scenarios. When the fuzzy membership function is linear, it is shown that the service improvement problem can be solved by the cutting plane algorithm within finite iterations, and when the fuzzy membership function is concave, the service improvement problem can be solved by a subgradient-based algorithm. Moreover, an alternative formulation of VRPFTW is also proposed and analyzed. Experiments are conducted to compare different models of vehicle routing problems with time windows in situations where violation of time windows is allowed, and the results show that the VRPFTW model can achieve considerable cost-savings, while at the same time maintaining an acceptable service level.
机译：提出并解决了带有模糊时间窗的车辆路径问题（VRPFTW）。在运输业务中，并非始终严格遵守时间窗口，服务时间与客户特定时间窗口的偏差决定了客户的满意度，也可以将其视为供应商的服务水平。本文应用模糊隶属度函数对车辆路径问题中与时间窗违规相关的服务水平问题进行特征描述，并提出了VRPFTW。 VRPFTW被制定为具有两个目标的多目标模型：（1）最小化行进距离，（2）最大化供应商对客户的服务水平。为了解决这个多目标模型，开发了一种两阶段算法来获得VRPFTW的Pareto解。使用两阶段算法，将VRPFTW分解为两个子问题，即带有时间窗的传统车辆路径问题（VRPTW-α）和服务改进问题，并依次解决了每个目标。在两种不同的情况下解决了服务改进问题。当模糊隶属度函数是线性的时，表明服务改进问题可以通过切平面算法在有限的迭代内解决；而当模糊隶属度函数是凹面时，可以通过基于次梯度的算法解决服务改进问题。 。此外，还提出并分析了VRPFTW的替代配方。在允许违反时间窗的情况下，通过实验比较了具有时间窗的车辆路径问题的不同模型，结果表明，VRPFTW模型可以节省大量成本，同时保持可接受的服务水平。

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