This paper focuses on developing effective algorithms for solving a bilevel program. The most popular approach is to replace the lower-level problem with its Karush-Kuhn-Tucker conditions to generate a mathematical program with complementarity constraints (MPCC). However, MPCC does not satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. In this paper, inspired by a recent work using the lower-level Wolfe duality (WDP), we apply the lower-level Mond-Weir duality to present a new reformulation, called MDP, for bilevel program. It is shown that, under mild assumptions, they are equivalent in globally or locally optimal sense. An example is given to show that, different from MPCC, MDP may satisfy the MFCQ at its feasible points. Relations among MDP, WDP, and MPCC are investigated. On this basis, we extend the MDP reformulation to present another new reformulation (called eMDP), which has similar properties to MDP. Furthermore, to compare two new reformulations with the MPCC and WDP approaches, we design a procedure to generate 150 tested problems randomly and comprehensive numerical experiments show that MDP has quite evident advantages over MPCC and WDP in terms of feasibility to the original bilevel programs, success efficiency, and average CPU time, whereas eMDP is far superior to all other three reformulations. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12071280 and 11901380]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0108 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0108 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

This paper proposes a pricing strategy based on the variable-ratio charging-compensation scheme for a ride-hailing platform with combined travel modes (Express or Carpool) of riders in a general network composed of multiple corridors. We establish a Stackelberg game model with the platform as a leader and the riders as followers to capture the decision-making process of stakeholders, in which the pricing decision is determined by the platform in the upper level taking each rider’s optimal response into account and travel modes are selected by riders independently in the lower level. The built model is a mixed-integer bilevel programming problem, which is difficult to solve due to its inherent hierarchical structure and discrete variables. By means of some mathematical techniques, we transform the bilevel model equivalently into a single-level mixed-integer nonlinear programming problem. Based on the numerical examples and results analysis, we bring some interesting managerial insights into the pricing of ride-hailing platforms, one of which is that booking fees of Express, unit time and distance fees of Express, compensations for Express riders and Express drivers are the core pricing factors to affect travel mode choices of riders.