Abstract
In this chapter, we present a bi-level optimization model by considering multiple transportation modes, stochastic passenger travel demand and freight logistics. Passenger travel demand can follow a general probability distribution where its mean and variance are function of the population in the origin and destination areas. The problem is formulated as a bi-level optimization problem. In the lower level, transportation design problem is formulated to minimize traveler costs and in the upper level we consider minimizing carbon monoxide emission and minimizing probability of traffic congestion. The two-stage model is formulated as a single stage model by considering optimality condition of lower level problem as a set of constraints in the upper level model. The formulated single stage model is a Mixed-Integer Non-linear Programming (MINLP) problem. In this chapter, a stochastic multi-modal, bi-level optimization model is presented for passenger and freight transportation problem in urban regions.
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