We study the predict-then-optimize framework approach, a common application of machine learning, which entails estimating unknown parameters of a linear optimization problem and then solving the optimization task with these estimations. For example, consider an energy allocation problem when the energy cost in different areas is uncertain. Despite the absence of precise energy cost values at the time of problem-solving, machine learning models are employed to predict these costs, and the resulting optimization problem, which consists for example of minimizing energy costs while meeting some minimal requirements, is solved using state-of-the-art optimization algorithms. We focus on the unrealizable setting, i.e. when the used hypothesis set (predictor function class) does not contain the ground truth value. In this case, there is no known algorithm that solves this predict-then-optimize problem. We provide a tractable algorithm which successfully finds an optimal solution in this setting.

We study a logistics network where shippers collaborate and bundle
their shipment requests in order to negotiate better rates with a
common carrier. In this setting, shippers are able to identify
collaborative routes with decreased overall empty truck movements.
After the optimal routes that minimize total cost of covering all
the shippers' demand are determined, this cost is allocated among
the shippers. Our goal is to devise cost allocation mechanisms
that ensure the sustainability of the collaboration. We first
develop cost allocation mechanisms with well-known properties from
the cooperative game theory literature, such as budget balance,
stability and cross monotonicity. Next, we define a set of new
properties, such as a guaranteed discount from the stand alone
cost for each shipper, desirable in our setting and propose
several cost allocation schemes that could lead to implementable
solutions. We also perform a computational study on randomly
generated and real-life data to derive insights on the performance
of the developed allocation schemes.

We consider a two-stage distributionally robust optimization (DRO) model with multimodal uncertainty, where both the mode probabilities and uncertainty distributions could be affected by the first-stage decisions. To address this setting, we propose a generic framework by introducing a $\phi$-divergence based ambiguity set to characterize the decision-dependent mode probabilities and further consider both moment-based and Wasserstein distance-based ambiguity sets to characterize the uncertainty distribution under each mode. We identify two special $\phi$-divergence examples (variation distance and $\chi^2$-distance) and provide specific forms of decision dependence relationships under which we can derive tractable reformulations. Furthermore, we investigate the benefits of considering multimodality in a DRO model compared to a single-modal counterpart through an analytical analysis. We provide a computational study over the facility location problem to illustrate our results, which demonstrate that omission of multimodality and decision-dependent uncertainties within DRO frameworks result in inadequately performing solutions with worse in-sample and out-of-sample performances under various settings.

The public transportation system is experiencing a substantial shift due to the rapid expansion of electromobility infrastructure and operations. This transformation is anticipated to contribute to decarbonizing and promoting environmental sustainability significantly. Among the most pressing planning issues in this area is the optimization of operational and strategic costs associated with electric fleets, which has recently garnered the attention of researchers. This paper investigates the scheduling and procurement problem of electric fleets under travel time and energy consumption uncertainty. A novel mixed-integer linear programming model is proposed, which determines the number of buses required to cover all trips, yields the schedule of the trips, and creates bus charging plans. The robust optimization paradigm is employed to address uncertainty, and a new budget uncertainty set is introduced to control the robustness of the solution. The efficiency of the model is evaluated through an extensive Monte Carlo simulation. Additionally, a case study is conducted on the off-campus college transport network at Binghamton University to demonstrate the real-world applicability of the model. The numerical results have shown that ignoring uncertainty can lead to schedules where up to 48\% of the trips are affected, which are either delayed or missed. The proposed approach can also be applied to other transportation networks with similar characteristics and uncertainties.