A Clustering Algorithm for Bi-Criteria Stop Location Design with Elastic Demand

The design of transit networks is a challenging task for transportation planners that span numerous often counter-intuitive considerations. Broadly, the Network Design Problem (NDP) can be approached through cost-benefit models that are capable of representing multiple aspects of system-wide behavior, such as travel demand, transit route location, traffic congestion, or service frequency.

In this study, we address the problem of designing a Light Rapid Transit (LRT) network where budget expenditures modify system efficiency as well as the resulting transit demand in an optimization framework. A key feature of the integrated model is that transit demand and supply are endogenous variables, that is, changing the design of the system affects the demand for the service provided and reciprocally different demand paradigms affect the best design of the system. This mutual interaction requires that a precise demand model be intertwined with a network design model to find efficient transit network designs.

We propose a bi-criteria formulation, which is composed of two competing objective functions seeking to maximize the total ridership and minimize the total budget allocated. Demand is formulated using the random utility maximization method with variables including access time and travel time. The transit station location problem of this study is formulated using mixed integer programming and we propose a heuristic solution algorithm to solve large-scale instances which is inspired by the problem context. The elastic demand is integrated with the optimization problem in an innovative way which facilitates the solution process. The performance of our model is evaluated on two test problems and we carry out its implementation on a real-world instance. Due to the special shape of the Pareto front function, significant practical policy implications, in particular budget allocation, are discussed to emphasize the fact that the trade-off between cost and benefit may result in large investments with little outcomes and vice versa.