Strategic Network Planning under Uncertainty with Two-Stage Stochastic Integer Programming.

Abstract

This thesis proposes three risk-averse models applied under demand uncertainty: a chance-constrained approach to network design problems (NDPs), a distributionally robust approach to NDPs, and a carsharing model to maximize profitability. The first stage makes strategic network design decisions, and the second stage utilizes risk-averse approaches to ensure high levels of demand satisfaction while minimizing network design, commodity flow, and potential quality of service (QoS) penalty costs.

The first model optimizes the probabilistic network design problem (PNDP), where we maintain QoS through chance constraints. The chance-constrained models are reformulated as a mixed-integer linear programs (MILPs), and we develop polynomial-time algorithms for special cases. The PNDP is benchmarked against a stochastic programming model that penalizes unmet demand via a linear penalty function. The numerical results suggest cost savings for customized QoS parameters and decreased computational time when using the polynomial-time algorithm over the MILP formulation.

The second model proposes a distributionally robust NDP (DR-NDP) with a marginal moment-based ambiguity set, to obtain arc capacity solutions that optimize the worst-case total cost over all candidate distributions. We estimate the optimal value of DR-NDP with an MILP, optimized via a cutting-plane algorithm that iteratively generates valid cuts for the approximate problem. We benchmark the DR-NDP against a sample average approximation-based model, testing on grid and real-world network instances. Our results show the robustness of DR-NDP solutions and their response to changes in observed demand levels, highlighting potential niche uses of DR-NDP in data-scarce contexts.

The third model maximizes carsharing profits. The first-stage problem determines fleet allocation and the number of parking lots and permits to purchase. The second stage solves a stochastic minimum cost flow problem on a spatial-temporal network to optimize operational profit, given random one-way and round trip rental demand, and ad-hoc relocation. We penalize the expected number or the conditional-value-at-risk of unserved customers to encourage higher QoS and develop a branch-and-cut algorithm with mixed-integer rounding-enhanced Benders cuts to solve both cases. Through testing on real data from Zipcar Boston, we find profitability and QoS decrease as proportion of one-way rental demand increases, and QoS significantly improves by lowering relocation costs.