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Online bipartite matching has attracted much attention due to its importance in various applications such as advertising, ride-sharing, and crowdsourcing. In most online matching problems, the rewards and node arrival probabilities are given in advance and are not controllable. However, many real-world matching services require them to be controllable and the decision-maker faces a non-trivial problem of optimizing them. In this study, we formulate a new optimization problem, Online Matching with Controllable Rewards and Arrival probabilities (OM-CRA), to simultaneously determine not only the matching strategy but also the rewards and arrival probabilities. Even though our problem is more complex than the existing ones, we propose a fast 1/2-approximation algorithm for OM-CRA. The proposed approach transforms OM-CRA to a saddle-point problem by approximating the objective function, and then solves it by the Primal-Dual Hybrid Gradient (PDHG) method with acceleration through the use of the problem structure. In simulations on real data from crowdsourcing and ride-sharing platforms, we show that the proposed algorithm can find solutions with high total rewards in practical times.

The recent development of mobile applications offering ride-hailing services has made large-scale taxi usage data available, and dispatching and pricing technologies based on such data have advanced greatly. While existing methods have achieved some success, they ignore an important perspective: individual priorities in terms of time and money savings. For example, existing methods may dispatch a distant taxi to a customer who prioritizes promptness over cost, and a high-priced taxi to a customer who wants to save money more than time. These mismatches degrade the requester's utility and the service provider's profit. In this paper, we propose a new framework for determining price and time proposals based on the individual's preferences in ride-hailing services. First, we formulate a new optimization problem to yield better price and time proposals for requesters based on their priorities. We model the requester's taxi acceptance probabilities by the generalized cost model and the discrete choice model, both of which are widely used in transportation economics. The price and time proposals yielded by solving our problem achieve high requester satisfaction because price and time proposals are created to suit for each requester. They raise service provider profits because the proposals are less likely to be rejected. Although the discontinuity of the objective function and the difficulty of its evaluation make our problem difficult to solve, we propose a fast approximation algorithm. The proposed algorithm outputs an L-approximate solution in O(n • (n 3 + m 3 )) time, where L is a hyperparameter controlling the relative weighting of requester satisfaction and service provider profit, n is the number of requesters, and m is the number of taxis. Simulations on synthetic and real datasets show that our method increases the requester's satisfaction and the service provider's profit simultaneously with practical computation times.

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