Mean-variance model for the build-operate-transfer scheme under demand uncertainty

A mean-variance model was developed for determining the optimal toll and capacity in a build-operate-transfer (BOT) roadway project subject to traffic demand uncertainty. This mean-variance model involves two objectives: maximizing mean profit and minimizing the variance (or standard deviation) of profit. The variance associated with profit is considered as a risk. Because maximizing expected profit and minimizing risk are often conflicting, there may not be a single best solution that can simultaneously optimize both objectives. Hence, it is necessary to explicitly consider this as a multiobjective problem so that a set of nondominated solutions can be generated. In this study, the optimal toll and capacity selection for the BOT problem under demand uncertainty is formulated as a special case of the stochastic network design problem. A simulation-based multiobjective genetic algorithm was developed to solve this stochastic bilevel mathematical programming formulation. Numerical results are also presented as a case study.