Optimal instant discounts of multiple ride options at a ride-hailing aggregator

Recently, ride-hailing aggregators have emerged to help passengers find the best ride options. It aggregates the results from different service providers, allowing sorting and filtering all in a single app. It is not unusual for an aggregator to offer instant discounts on the prices returned from the service providers to increase its Gross Transaction Value (GTV) or Total Transaction Volume (TTV). In this research, we study this optimal instant discount problem, which can be viewed as a new variant of the classical multi-product price optimization problem. We first use the Nested Logit model to predict the probability a passenger would complete the trip with each ride option. We then formulate the instant discount problem as a nonlinear optimization model with a budget constraint and a group of discount bound constraints. To solve this model, we construct a surrogate relaxation formulation with strong duality. We develop a Lagrangian-dual-based approach to decompose this problem into a series of subproblems, and then design heuristic methods to give feasible solutions. For both cases when the GTV or the TTV is maximized, we quantify the optimality gap, give its asymptotic properties, and establish conditions under which it becomes zero and tight. Finally, we use real data from Meituan, a leading ride-hailing aggregator in China, to validate the proposed approach. Results show that compared to the baseline methods, we can improve the GTV by 1.293%, improve the TTV by 0.475%, and decrease the magnitude of the optimality gap.