Strategic Pricing and Routing to Maximize Profit in Congested Roads Considering Interactions With Travelers

We introduce an innovative approach for analyzing strategic interactions in transportation networks featuring mobility-on-demand (MoD) services. This study focuses on achieving company–traveler equilibria, whereby a single company optimizes pricing and routing decisions to maximize profitability while considering travelers' mode choices, modeled via a multinomial logit model (MNL). Although profit maximization problems have been extensively studied in the field of revenue management across various domains, their application to transportation networks poses unique challenges, such as the influence of network topology and additional constraints (e.g., flow conservation, rebalancing, etc.). To address the inherent nonlinear relationship arising from endogenous travel demand, we shift our domain space from price to market share. Subsequently, we derive prices using a direct one-to-one correspondence within the MNL. This work is the first effort in leveraging such novel techniques in the context of transportation network analysis. Remarkably, the proposed reformulation results in an equivalent problem exhibiting convexity, offering computational efficiency and interpretability. By solving the Karush–Kuhn–Tucker conditions, we characterize user equilibrium with the generalized route cost, which incorporates the operating cost by rebalancing and travelers' disutility caused by congestion. Our approach is empirically validated through a numerical analysis conducted on the widely recognized Sioux Falls network. The results underscore the effectiveness and practical applicability of our method in analyzing transportation networks featuring MoD services and open the stage for important future investigations.