Reliable network design considering endogenous customers’ choices under probabilistic arc failures

We consider a reliable network design where the facility location and road ban decisions are jointly optimized to minimize the total expected costs and risks against uncertain exogenous arc-dependent failures and customers’ endogenous interactions. We formulate endogenous customers’ choices by incorporating an expressive measure, Cumulative prospect theory, into the widely used multinomial logit model. Additionally, we use a well-known downside measure, Conditional value-at-risk, for the designer to control integrated risks from exogenous arc failures and endogenous customers’ choices. Accordingly, a mixed-integer trilinear program is developed. To solve the model, we first transform it into a class of mixed-integer linear programs based on the separable structure. Then, a customized branch-and-Benders-cut algorithm is proposed to solve these mixed-integer linear programs. We devise a set of novel valid inequalities based on the endogenous transition of choice probability to strengthen the weak relaxation of the master problem. Moreover, by aggregating the grouping and dual iterations shrinking techniques for solving sub-problems, the branch-and-Benders-cut algorithm can converge within 30 seconds and the whole problem can be solved within 15 minutes for a network with 90 nodes and 149 road segments. Some managerial insights for balancing risk and cost are finally extracted.