We study an optimal investment problem that arises in the context of the vehicle-sharing system. Given a set of locations to build stations, we need to determine i) the sequence of stations to be built and the number of vehicles to acquire in order to obtain the target state where all stations are built, and ii) the number of vehicles to acquire and their allocation in order to maximize the total profit returned by operating the system when some or all stations are open. The profitability associated with operating open stations, measured over a specific time period, is represented as a linear optimization problem applied to a collection of open stations. With operating capital, the owner of the system can open new stations. This property introduces a set-dependent aspect to the duration required for opening a new station, and the optimal investment problem can be viewed as a variant of the Traveling Salesman Problem (TSP) with set-dependent cost. We propose an A* search algorithm to address this particular variant of the TSP. Computational experiments highlight the benefits of the proposed algorithm in comparison to the widely recognized Dijkstra algorithm and propose future research to explore new possibilities and applications for both exact and approximate A* algorithms.

翻译：我们研究了共享车辆系统背景下产生的一个最优投资问题。给定一组建设站点的位置，我们需要确定：i) 站点建设的顺序以及在达到所有站点都建成的目标状态时所需购置的车辆数量；ii) 在部分或全部站点运营时，为了最大化系统运营总利润所需购置的车辆数量及其分配方案。在特定时间段内，运营已开放站点的盈利能力被建模为一个应用于已开放站点集合的线性优化问题。利用运营资本，系统所有者可以开设新站点。这一特性使得开设新站点所需的时间具有集合依赖性，而该最优投资问题可被视为旅行商问题（TSP）的一个变种，其中成本具有集合依赖性。我们提出了一种A*搜索算法来解决这个特殊的TSP变种。计算实验凸显了该算法相较于广泛认可的Dijkstra算法的优势，并提出了未来研究方向，以探索精确型和近似型A*算法的新可能性与应用。