This paper formulates a discrete simulation-based optimization (SO) algorithm for a family of large-scale car-sharing service design problems. We focus on the profit-optimal assignment of vehicle fleet across a network of two-way (i.e., round-trip) car-sharing stations. The proposed approach is a metamodel SO approach. A novel metamodel based on a mixed-integer program (MIP) is formulated. The metamodel is embedded within a general-purpose discrete SO algorithm. The proposed algorithm is validated with synthetic toy network experiments. The algorithm is then applied to a high-dimensional Boston case study using reservation data from a major US car-sharing operator. The method is benchmarked versus several algorithms, including stochastic programming. The experiments indicate that the analytical network model information, provided by the MIP to the SO algorithm, is useful both at the first iteration of the algorithm and across subsequent iterations. The solutions derived by the proposed method are benchmarked versus the solution deployed in the field by the car-sharing operator. Via simulation, the proposed solutions improve those deployed with an average improvement of profit of 6% and of vehicle utilization of 3%.

The combination of the problem-specific analytical MIP with a general-purpose SO algorithm enables the discrete SO algorithm to: (i) address high-dimensional problems, (ii) become computationally efficient (i.e., it can identify good quality solutions within few simulation observations), (iii) become robust to the quality of the initial points and of the stochasticity of the simulator. More generally, the information provided by the MIP to the SO algorithm enables it to exploit problem-specific structural information. This leads to an algorithm with both asymptotic convergence guarantees as well as good short term performance (i.e., performance given few simulation observations). We view this general idea of combining analytical MIP formulations with general-purpose SO algorithms, or more broadly with general-purpose sampling strategies of high-resolution data, as an innovative and promising area of future research.

本文针对一系列大规模汽车共享服务设计问题制定了一种基于离散仿真的优化（SO）算法。我们专注于在双向（即往返）汽车共享站网络中对车队进行利润最优分配。所提出的方法是元模型 SO 方法。制定了一种基于混合整数程序（MIP）的新颖元模型。该元模型嵌入到通用离散 SO 算法中。所提出的算法通过合成玩具网络实验进行了验证。然后，使用美国主要汽车共享运营商的预订数据，将该算法应用于高维波士顿案例研究。该方法与多种算法（包括随机规划）进行了基准测试。实验表明，MIP 向 SO 算法提供的分析网络模型信息在算法的第一次迭代和后续迭代中都很有用。通过所提出的方法得出的解决方案与汽车共享运营商在现场部署的解决方案进行了基准比较。通过模拟，所提出的解决方案改进了部署的解决方案，平均利润提高了 6%，车辆利用率提高了 3%。

特定问题的分析 MIP 与通用 SO 算法的结合使离散 SO 算法能够：（i）解决高维问题，（ii）变得计算高效（即，它可以在很少的模拟内识别高质量的解决方案）观察），（iii）对初始点的质量和模拟器的随机性变得稳健。更一般地说，MIP 向 SO 算法提供的信息使其能够利用特定于问题的结构信息。这导致算法既具有渐近收敛保证，又具​​有良好的短期性能（即，在很少的模拟观察下的性能）。我们认为将分析 MIP 公式与通用 SO 算法相结合，或者更广泛地说与高分辨率数据的通用采样策略相结合，是未来研究的一个创新且有前途的领域。