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This paper reconsiders the ODMTS Design with Adoptions problem (ODMTS-DA) tocapture the latent demand in on-demand multimodal transit systems. The ODMTS-DAis a bilevel optimization problem, for which Basciftci and Van Hentenryck(2022) proposed an exact combinatorial Benders decomposition. Unfortunately,their proposed algorithm only finds high-quality solutions for medium-sizedcities and is not practical for large metropolitan areas. The main contributionof this paper is to propose a new path-based optimization model, called P-Path,to address these computational difficulties. The key idea underlying P-Path isto enumerate two specific sets of paths which capture the essence of the choicemodel associated with the adoption behavior of riders. With the help of thesepath sets, the ODMTS-DA can be formulated as a single-level mixed-integerprogramming model. In addition, the paper presents preprocessing techniquesthat can reduce the size of the model significantly. P-Path is evaluated on twocomprehensive case studies: the mid-size transit system of the Ann ArborYpsilanti region in Michigan (which was studied by Basciftci and Van Hentenryck(2022)) and the large-scale transit system for the city of Atlanta. Theexperimental results show that P-Path solves the Michigan ODMTS-DA instances ina few minutes, bringing more than two orders of magnitude improvements comparedto the existing approach. For Atlanta, the results show that P-Path can solvelarge-scale ODMTS-DA instances (about 17 millions of variables and 37 millionsof constraints) optimally in a few hours or in a few days. These results showthe tremendous computational benefits of P-Path which provides a scalableapproach to the design of on-demand multimodal transit systems with latentdemand.

Path-Based Formulations for the Design of On-demand Multimodal Transit Systems with Adoption Awareness