We consider a bilevel network interdiction problem where the follower aims to maximize the amount of flow from the source node to the sink node, and the leader aims to minimize the number of arcs from a critical set that have positive flow on them, that is, active arcs, in the maximum flow solution obtained by the follower. This problem is motivated by an application in human trafficking disruption. We consider both the optimistic and pessimistic variants of this bilevel optimization problem and develop their respective single-level reformulations. We present a tailored solution method to the pessimistic problem, which solves the problem to optimality for one practically important class of networks. Through computational experiments on randomly generated layered network instances, we show the effectiveness of the proposed methods and demonstrate that the tailored method is orders of magnitude faster than existing approaches in the literature. We also conduct computational experiments on randomly generated test instances inspired by domestic human trafficking networks and draw domain-specific insights. History: Accepted by Russell Bent, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the National Science Foundation [Grant 2039584]. The computational experiments discussed in this paper were performed on the Palmetto Computing Cluster. The Palmetto Computing Cluster is supported by the National Science Foundation [Grants MRI# 2024205, MRI# 1725573, and CRI# 2010270]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0423 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0423 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Abstract In this article, we study the integrated hurricane relief logistics and evacuation planning (IHRLEP) problem, integrating hurricane evacuation and relief item pre‐positioning operations that are typically treated separately. We propose a fully adaptive multistage stochastic programming (MSSP) model and solution approaches based on two‐stage stochastic programming (2SSP). Utilizing historical forecast errors modeled using the auto‐regressive model of order one, we generate hurricane scenarios and approximate the hurricane process as a Markov chain, and each Markovian state is characterized by the hurricane's location and intensity attributes. We conduct a comprehensive numerical experiment based on case studies motivated by Hurricane Florence and Hurricane Ian. Through the computational results, we demonstrate the value of fully adaptive policies given by the MSSP model over static ones given by the 2SSP model in terms of the out‐of‐sample performance. By conducting an extensive sensitivity analysis, we offer insights into how the value of fully adaptive policies varies in comparison to static ones with key problem parameters.

Abstract We study a network interdiction problem involving two agents: a defender and an evader. The evader seeks to traverse a path from a source node to a terminus node in a directed network without being detected. The game takes place in two stages. In the first stage, the defender removes a set of arcs in the network. In the second stage, the defender and evader play a simultaneous game. The defender monitors a set of arcs, thus increasing the probability that the evader will be detected on that arc (if the evader uses the arc). The evader selects a source‐terminus path. Because the second stage is played simultaneously, both agents use mixed‐strategy solutions. We approach the solution of the second‐stage problem by proposing a constraint‐and‐column generation algorithm. We show that both the constraint‐generation and column‐generation problems are NP‐hard. Accordingly, we prescribe approximate versions of these problems that can be solved more efficiently. Our algorithm relies on solving the approximate versions until it is necessary to obtain an exact solution of the constraint‐generation and column‐generation problems. Then, to link the first‐ and second‐stage problems, we model the original problem using an epigraph reformulation, which we solve using a Benders‐decomposition based approach. The efficacy of our approach is demonstrated on a set of randomly generated test instances.

In this work, we study the optimal design of two-armed clinical trials to maximize the accuracy of parameter estimation in a statistical model, where the interaction between patient covariates and treatment are explicitly incorporated to enable precision medication decisions. Such a modeling extension leads to significant complexities for the produced optimization problems because they include optimization over design and covariates concurrently. We take a min-max optimization model and minimize (over design) the maximum (over population) variance of the estimated interaction effect between treatment and patient covariates. This results in a min-max bilevel mixed integer nonlinear programming problem, which is notably challenging to solve. To address this challenge, we introduce a surrogate optimization model by approximating the objective function, for which we propose two solution approaches. The first approach provides an exact solution based on reformulation and decomposition techniques. In the second approach, we provide a lower bound for the inner optimization problem and solve the outer optimization problem over the lower bound. We test our proposed algorithms with synthetic and real-world data sets and compare them with standard (re)randomization methods. Our numerical analysis suggests that the proposed approaches provide higher-quality solutions in terms of the variance of estimators and probability of correct selection. We also show the value of covariate information in precision medicine clinical trials by comparing our proposed approaches to an alternative optimal design approach that does not consider the interaction terms between covariates and treatment. Summary of Contribution: Precision medicine is the future of healthcare where treatment is prescribed based on each patient information. Designing precision medicine clinical trials, which are the cornerstone of precision medicine, is extremely challenging because sample size is limited and patient information may be multidimensional. This work proposes a novel approach to optimally estimate the treatment effect for each patient type in a two-armed clinical trial by reducing the largest variance of personalized treatment effect. We use several statistical and optimization techniques to produce efficient solution methodologies. Results have the potential to save countless lives by transforming the design and implementation of future clinical trials to ensure the right treatments for the right patients. Doing so will reduce patient risks and reduce costs in the healthcare system.

Abstract In the multi‐vehicle covering tour problem with speed optimization, we aim to construct a set of maximal coverage routes for a fleet of vehicles that serve (observe) a set of secondary sites, given a fixed time schedule and coverage requirements. We develop an exact solution approach using a branch‐and‐price framework with a label‐correcting algorithm and a set of innovative dominance rules to solve the resulting pricing problem. We also develop a two‐stage heuristic capable of finding effective initial solutions. In addition, we consider practical extensions to the model by incorporating risk thresholds, energy capacities, and time windows. To validate our proposed solution approaches, we perform an extensive set of numerical experiments. Numerical results show the computational advantage of our proposed solution approaches compared with a state‐of‐the‐art commercial solver.

Despite many existing research on data forwarding in low-duty-cycle wireless sensor networks (WSNs), relatively little work has been done on energy-efficient data forwarding with probabilistic delay bounds. Probabilistic delay guarantees (i.e., delay bounded data delivery with reliability constraints) are of increasing importance for many delay-constrained applications, since deterministic delay bounds are prohibitively expensive to guarantee in WSNs. However, radio duty-cycling and unreliable wireless links pose challenges for achieving the probabilistic delay guarantee in WSNs. In this paper, we propose EEAF, a novel energy-efficient adaptive forwarding technique tailored for low-duty-cycle WSNs with unreliable wireless links. We show the existence of path diversity in low-duty-cycle WSNs, where delay-optimal routing and energy-optimal routing are likely following different paths. The key idea of EEAF is to exploit the intrinsic path diversity to provide probabilistic delay guarantees while minimizing transmission cost. In EEAF, an early arriving packet will be adaptively switched to the energy-optimal path for energy conservation. Delay quantiles are derived at each node in a distributed manner and are used as the guidelines in the adaptive forwarding decision making. Extensive testbed experiment and large-scale simulation show that EEAF effectively reduces the transmission cost by 12%~25% with probabilistic delay guarantees under various network settings. In addition, we extend the EEAF technique with data aggregation for event-based traffic scenarios. Evaluation using publicly available WSN event traffic traces yields very encouraging results with up to 40% energy saving in probabilistic delay bounded data delivery.

Abstract We study a class of stochastic network interdiction problems where the defender has incomplete (ambiguous) preferences. Specifically, we focus on the shortest path network interdiction modeled as a Stackelberg game, where the defender (leader) makes an interdiction decision first, and then the attacker (follower) selects a shortest path after the observation of random arc costs and interdiction effects in the network. We assume that the defender's risk preferences over exogenously given probabilities can be summarized by the expected utility theory. Although the exact form of the utility function is ambiguous to the defender, we assume that a set of pairwise gamble comparisons made by the defender is available, which can be used to restrict the shape of the utility function. We present two approaches to tackle this problem. The first approach conducts utility estimation and optimization separately, by first finding the best fit for a piecewise linear concave utility function according to the available data, and then optimizing the expected utility. The second approach integrates utility estimation and optimization, by modeling the utility ambiguity under a robust optimization framework following Armbruster and Delage [B. Armbruster and E. Delage, Manag. Sci., 61 (2015), 111‐128] and Hu and Mehrotra [J. Hu and S. Mehrotra, IIE Trans., 47 (2015), 358‐372]. We conduct extensive computational experiments to evaluate the performances of these approaches.

Surgery scheduling is of critical importance, because an operating room (OR) is the major cost generating unit in the hospital. However, schedulers face tremendous challenges brought by case cancellation, which have been observed in most departments. On the other hand, the randomness of surgery duration also has a significant impact on an OR schedule. In this paper, we develop a stochastic integer programming model for multiple ORs that simultaneously considers the uncertainties of case cancellation and surgery duration. We aim at minimizing the costs from the perspectives of both health care providers and patients. The Benders decomposition is used to address the computational complexity. A series of experiments is conducted to show the effectiveness of the proposed model and solution approaches. A case study based on two departments at West China Hospital is carried out, where the total cost can be reduced by approximately 27%. A sensitivity analysis is conducted in the case study, from which we gain managerial insights.

We present a computational study of several strategies to solve two-stage stochastic linear programs by integrating the adaptive partition-based approach with level decomposition. A partition-based formulation is a relaxation of the original stochastic program, obtained by aggregating variables and constraints according to a scenario partition. Partition refinements are guided by the optimal second-stage dual vectors computed at certain first-stage solutions. The proposed approaches rely on the level decomposition with on-demand accuracy to dynamically adjust partitions until an optimal solution is found. Numerical experiments on a large set of test problems including instances with up to one hundred thousand scenarios show the effectiveness of the proposed approaches. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0765 .

Classic vehicle routing models usually treat fuel cost as input data, but fuel consumption heavily depends on the travel speed, which leads to the study of optimizing speeds over a route to improve fuel efficiency. In this paper, we propose a joint vehicle routing and speed optimization problem to minimize the total operating cost including fuel cost. The only assumption made on the dependence between fuel cost and travel speed is that it is a strictly convex differentiable function. This problem is very challenging, with medium-sized instances already difficult for a general mixed-integer convex optimization solver. We propose a novel set-partitioning formulation and a branch-cut-and-price algorithm to solve this problem. We introduce new dominance rules for the labeling algorithm so that the pricing problem can be solved efficiently. Our algorithm clearly outperforms the off-the-shelf optimization solver, and is able to solve some benchmark instances to optimality for the first time. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0810 .

We consider a Stackelberg game in a network where a leader minimizes the cost of interdicting arcs and a follower seeks the shortest distance between given origin and destination nodes under uncertain arc traveling cost. In particular, we consider a risk-averse leader, who aims to keep high probability that the follower’s traveling distance is longer than a given threshold, interpreted by a chance constraint. Under the assumption of a wait-and-see follower—i.e., the follower selects a shortest path after seeing realizations of the random arc cost—we propose a branch-and-cut algorithm and apply lifting techniques to exploit the combinatorial structure of the risk-averse leader’s interdiction problem. We demonstrate the computational efficacy of our approaches, risk-averse interdiction solution patterns, and result sensitivity, by testing instances of randomly generated grid networks and real-world transportation networks.

We consider a class of packing problems with uncertain data, which we refer to as the chance-constrained binary packing problem. In this problem, a subset of items is selected that maximizes the total profit so that a generic packing constraint is satisfied with high probability. Interesting special cases of our problem include chance-constrained knapsack and set packing problems with random coefficients. We propose a problem formulation in its original space based on the so-called probabilistic covers. We focus our solution approaches on the special case in which the uncertainty is represented by a finite number of scenarios. In this case, the problem can be formulated as an integer program by introducing a binary decision variable to represent feasibility of each scenario. We derive a computationally efficient coefficient strengthening procedure for this formulation, and demonstrate how the scenario variables can be efficiently projected out of the linear programming relaxation. We also study how methods for lifting deterministic cover inequalities can be leveraged to perform approximate lifting of probabilistic cover inequalities. We conduct an extensive computational study to illustrate the potential benefits of our proposed techniques on various problem classes.