A stochastic programming model with endogenous and exogenous uncertainty for reliable network design under random disruption

Designing and maintaining a reliable and efficient transportation network is an important industrial problem. Integrating infrastructure protection with the network design model is efficient as these models provide strategic decisions to make a transportation network simultaneously efficient and reliable. We studied a combined network design and infrastructure protection problem subject to random disruptions where the protection is imperfect and multi-level and the effect of disruption is imperfect. In this research, we modeled a resource-constrained decision maker seeking to optimally allocate protection resources to the facilities, and construct links in the network to minimize the expected post-disruption transportation cost (PDTC). We modeled the problem as a two-stage stochastic program with both endogenous and exogenous uncertainty: a facility’s post-disruption capacity depends probabilistically on the protection decision, making the uncertainty endogenous, while the link construction decision directly affects the transportation decision. We implemented an accelerated L-shaped algorithm to solve the model and predictive modeling techniques to estimate the probability of a facility’s post-disruption capacity for a given protection and disruption intensity. Numerical results show that solution quality is sensitive to the number of protection levels modeled; average reduction in the expected PDTC is 18.7% as the number of protection levels increases from 2 to 5. Results demonstrate that the mean value model performs very poorly as the uncertainty increases. Results also indicate that the stochastic programming model is sensitive to the estimation error of the predictive modeling techniques; on average the expected PDTC becomes 6.38% higher for using the least accurate prediction model.