About

Manish Bansal is an Associate Professor in the Grado Department of Industrial and Systems Engineering at Virginia Tech. His main research areas include Operations Research, Game Theory, Machine Learning, Data-Driven Optimization, and Decision Making under Uncertainty. He specializes in methodologies such as Stochastic and Distributionally Robust Integer Programming, Graph Neural Networks, Combinatorial Optimization, and Location Science. His applications span supply chain, logistics, aerospace structures, network designing, and telerobotics. He holds a Ph.D. in Industrial and Systems Engineering from Texas A&M University, along with a Master's degree in the same field from the same institution, and a B.Tech. in Electrical Engineering from the National Institute of Technology, India. Bansal has served as a core faculty member at the Sanghani Center for Artificial Intelligence and Data Analytics and is affiliated with the National Security Institute at Virginia Tech. His professional history includes positions as an Assistant Professor and Associate Professor at Virginia Tech, with prior postdoctoral research at Northwestern University and research assistantship at Texas A&M University. He is actively involved in academic leadership, serving as President of the Engineering Faculty Organization for 2023-2024 and as a faculty senator. His research contributions include numerous publications in the fields of optimization, stochastic programming, and decision-making under uncertainty.

Research topics

• Computer Science
• Mathematical optimization
• Mathematics
• Engineering
• Combinatorics
• Structural engineering
• Reliability engineering
• Algorithm
• Distributed computing
• Telecommunications
• Economics
• Computer network

Selected publications

• Transportation and Inventory Planning in Serial Supply Chain with Heterogeneous Capacitated Vehicles

  Management Science · 2026-02-25

  articleSenior author

  We study serial supply chain problems where a product is transported from a supplier to a warehouse (inbound transportation), and then from the warehouse (outbound transportation) to a retailer such that demand for a given planning horizon is satisfied. We consider heterogeneous vehicles of varying capacities for transportation in each time period, and the objective is to plan inbound and outbound transportation along with inventory in each time period so that overall inventory and transportation costs are minimized. These problems belong to the class of two-echelon lot-sizing (2-ELS) problems with the warehouse and retailer as the first and second echelons, respectively. We address an open question raised in van Hoesel et al. [van Hoesel S, Romeijn HE, Morales DR, Wagelmans APM (2005) Integrated lot sizing in serial supply chains with production capacities. Management Sci. 51(11):1706–1719]: Does there exist a polynomial-time algorithm for 2-ELS with a single capacitated vehicle for each of the inbound and outbound transportation? Specifically, we introduce polynomial-time algorithms for this problem and its three generalizations with multiple capacitated vehicles for inbound and/or outbound transportation, thereby generalizing the results of Kaminsky and Simchi-Levi [Kaminsky P, Simchi-Levi D (2003) Production and distribution lot sizing in a two stage supply chain. IIE Trans. 35(11):1065–1075] and Sargut and Romeijn [Sargut FZ, Romeijn HE (2007) Capacitated production and subcontracting in a serial supply chain. IIE Trans. 39(11):1031–1043] for 2-ELS with a single capacitated vehicle for inbound transportation and uncapacitated outbound transportation. We showcase the practical applications of these approaches in efficiently solving discrete two- and multiechelon lot-sizing problems that arise in freight transportation, the international shipping industry, and the tire manufacturing industry. Based on our computational experiments, we observe that the algorithm for discrete 2-ELS with a capacitated vehicle for inbound and outbound transportation is computationally efficient in comparison with solving the mixed binary formulations of two- and multiechelon lot-sizing problems using an off-the-shelf optimization solver. This paper was accepted by Chung Piaw Teo, optimization and decision analytics. Funding: This work was supported by the Division of Civil, Mechanical and Manufacturing Innovation of National Science Foundation [Grants 1824897 and 2034503]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.04106 .

  PublisherDOI

• Distributionally Risk-Receptive and Robust Multistage Stochastic Integer Programs and Interdiction Models

  Mathematical Programming · 2025-03-20 · 2 citations

  articleOpen accessSenior author

  Abstract In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations of DRR- and DRO-MSIPs by presenting multistage stochastic disjunctive programs and algorithms for solving them. These frameworks are useful for optimization problems under uncertainty where the focus is on analyzing outcomes based on multiple decision-makers’ differing perspectives, such as interdiction problems that are attacker-defender games having non-cooperative players. To assess the performance of the algorithms for DRR- and DRO-MSIPs, we consider instances of distributionally ambiguous multistage maximum flow and facility location interdiction problems that are important in their own right. Based on our computational results, we observe that the cutting plane-based approaches are 2800% and 2410% (on average) faster than the reformulation-based approaches for the foregoing instances with distributional risk-aversion and risk-receptiveness, respectively. Additionally, we conducted out-of-sample tests to showcase the significance of the DRR framework in revealing network vulnerabilities and also in mitigating the impact of data corruption.

  PublisherOA PDFDOI

• k-submodular interdiction problems under distributional risk-receptiveness and robustness: application to machine learning

  Computational Management Science · 2025-08-26

  articleOpen accessSenior author

  Abstract We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg zero-sum games (also referred to as interdiction games) between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender’s objective of maximizing a k -submodular function. We allow uncertainties arising from the success of attacks and inherent data noise, and address challenges due to incomplete knowledge of the probability distribution of random parameters. Specifically, we introduce Distributionally Robust k -Submodular Interdiction Problem (DRO k -SIP) and Distributionally Risk-Receptive k -Submodular Interdiction Problem (DRR k -SIP) along with finitely convergent exact algorithms for solving them. When solving the DRO k -SIP, the attacker optimizes their expected payoff with respect to the worst-case probability distribution within the ambiguity set, and thereby have robust attack strategies despite distributional ambiguity. In contrast, the DRR k -SIP identifies attacker strategies with the best-case probability distribution, and identifies critical vulnerabilities for the defender. The optimal values derived from both DRO k -SIP and DRR k -SIP offer a confidence interval-like range for the expected value of the defender’s objective function, capturing distributional ambiguity. We conduct computational experiments on instances of feature selection and sensor placement problems, using Wisconsin breast cancer data and synthetic data, respectively.

  PublisherOA PDFDOI

• Bi-Parameterized Two-Stage Stochastic Min-Max and Min-Min Mixed Integer Programs

  arXiv (Cornell University) · 2025-01-02

  preprintOpen accessSenior author

  We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve these programs efficiently, we introduce Lagrangian-integrated $L$-shaped ($L^2$) methods, which guarantee exact solutions when the first-stage decisions are pure binary. For mixed-binary first-stage programs, we present a regularization-augmented variant of this method. Our computational results for a stochastic network interdiction problem show that the $L^2$ method outperforms a benchmark method, solving all instances in 23 seconds on average, while the benchmark method failed to solve any instance within 3600 seconds. The $L^2$ method also achieves optimal solutions, on average, 18.4 times faster for a stochastic facility location problem. Furthermore, we show that the $L^2$ method can effectively address distributionally robust optimization problems with decision-dependent ambiguity sets that may be empty for some first-stage decisions, achieving optimal solutions, on average, 5.3 times faster than existing methods.

  PublisherOA PDFDOI

• Distributionally Risk-Receptive and Robust Multistage Stochastic Integer Programs and Interdiction Models

  arXiv (Cornell University) · 2024-06-07

  preprintOpen accessSenior author

  In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations of DRR- and DRO-MSIPs by presenting multistage stochastic disjunctive programs and algorithms for solving them. These frameworks are useful for optimization problems under uncertainty where the focus is on analyzing outcomes based on multiple decision-makers' differing perspectives, such as interdiction problems that are attacker-defender games having non-cooperative players. To assess the performance of the algorithms for DRR- and DRO-MSIPs, we consider instances of distributionally ambiguous multistage maximum flow and facility location interdiction problems that are important in their own right. Based on our computational results, we observe that the cutting plane-based approaches are 2800% and 2410% (on average) faster than the reformulation-based approaches for the foregoing instances with distributional risk-aversion and risk-receptiveness, respectively. Additionally, we conducted out-of-sample tests to showcase the significance of the DRR framework in revealing network vulnerabilities and also in mitigating the impact of data corruption.

  PublisherOA PDFDOI

• $k$-Submodular Interdiction Problems under Distributional Risk-Receptiveness and Robustness: Application to Machine Learning

  arXiv (Cornell University) · 2024-06-18

  preprintOpen accessSenior author

  We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender's objective of maximizing a $k$-submodular function. We allow uncertainties arising from the success of attacks and inherent data noise, and address challenges due to incomplete knowledge of the probability distribution of random parameters. Specifically, we introduce Distributionally Robust $k$-Submodular Interdiction Problem (DRO $k$-SIP) and Distributionally Risk-Receptive $k$-Submodular Interdiction Problem (DRR $k$-SIP) along with finitely convergent exact algorithms for solving them. When solving the DRO $k$-SIP, the attacker optimizes their expected payoff with respect to the worst-case probability distribution within the ambiguity set, and thereby have robust attack strategies despite distributional ambiguity. In contrast, the DRR $k$-SIP identifies attacker strategies with the best-case probability distribution, and identifies critical vulnerabilities for the defender. The optimal values derived from both DRO $k$-SIP and DRR $k$-SIP offer a confidence interval-like range for the expected value of the defender's objective function, capturing distributional ambiguity. We conduct computational experiments on instances of feature selection and sensor placement problems, using Wisconsin breast cancer data and synthetic data, respectively.

  PublisherOA PDFDOI

• Algorithms for Cameras View-Frame Placement Problems in the Presence of an Adversary and Distributional Ambiguity

  IEEE Transactions on Automation Science and Engineering · 2024-01-16 · 1 citations

  articleSenior author

  In this paper, we introduce cameras view-frame placement problem (denoted by CFP) in the presence of an adversary whose objective is to minimize the maximum coverage by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> cameras in response to input provided by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$</tex-math> </inline-formula> autonomous agents in a remote location. We allow uncertainty in the success of attacks, incomplete information of the probability distribution associated with the uncertain data, and varying levels of risk-appetite of the adversary. We present an exact cutting planes based algorithm to solve this problem and provide conditions under which it is finitely convergent. Since this approach solves deterministic CFP in each iteration, we also present improved exact method for CFP with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p=1$</tex-math> </inline-formula> , approximation algorithm and heuristics for Multi-CFP with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p\geq 2$</tex-math> </inline-formula> , and Multi-CFP with fixed tilt of the cameras. To evaluate the effectiveness and performance of the proposed approaches, we conduct computational experiments using randomly generated instances and simulation experiments where these approaches are utilized to find a hidden object in a remote location. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Telerobotic cameras have been widely used for a variety of applications in environment where it is tedious for humans to collect information such as surveillance, natural environment observation, search and rescue, satellite imaging, and many more. Therefore, computationally efficient approaches proposed in this paper for placement of view-frame of camera(s), by adjusting their pan, tilt, and zoom, will improve the effective utilization of a telerobotic cameras system. Additionally, before operating such systems in a military environment, a decision maker needs to analyze vulnerable cameras in the system whose disruption can significantly impact the information acquisition process. The algorithms presented for adversarial camera view-frame placement problem can identify the set of cameras (or vehicles carrying them) that are susceptible to attacks by a reasonable (risk-averse) attacker. Likewise, the proposed algebraic modeling framework and solution approaches are also applicable for planning interdiction actions to minimize the information acquisition by an evader/enemy. These results can be leveraged by autonomy solutions developed by the Army for both logistics (Autonomous Ground Resupply program) and combat missions (Combat Vehicle Robotics program).

  PublisherDOI

• STOCHASTIC PROGRAMMING MODELS FOR AUTONOMOUS GROUND VECHICLES

  SAE technical papers on CD-ROM/SAE technical paper series · 2024-11-15

  article

  &lt;title&gt;ABSTRACT&lt;/title&gt; &lt;p&gt;Significant advances in sensing, robotics, and wireless networks have enabled the collaborative utilization of autonomous aerial, ground and underwater vehicles for various applications. However, to successfully harness the benefits of these unmanned ground vehicles (UGVs) in homeland security operations, it is critical to efficiently solve UGV path planning problem which lies at the heart of these operations. Furthermore, in the real-world applications of UGVs, these operations encounter uncertainties such as incomplete information about the target sites, travel times, and the availability of vehicles, sensors, and fuel. This research paper focuses on developing algebraic-based-modeling framework to enable the successful deployment of a team of vehicles while addressing uncertainties in the distance traveled and the availability of UGVs for the mission.&lt;/p&gt; &lt;p&gt;&lt;bold&gt;Citation:&lt;/bold&gt; S. Venkatachalam, M. Bansal, J. M. Smereka, “Stochastic Programming Models for Autonomous Ground Vehicles”, In &lt;italic&gt;Proceedings of the Ground Vehicle Systems Engineering and Technology Symposium&lt;/italic&gt; (GVSETS), NDIA, Novi, MI, Aug. 13-15, 2019.&lt;/p&gt;

  PublisherDOI

• Optimization of Hybrid Composite Laminates with Distinct Ply Thicknesses Using Integer Programming

  AIAA Journal · 2023-10-24 · 8 citations

  articleSenior author

  Optimization of constant-stiffness composite laminates with discrete values of fiber orientations and ply thicknesses is a nonconvex combinatorial problem. Recent studies show that this problem can be efficiently solved using the mixed integer program (MIP) by reformulating lamination parameters as functions of decision variables that represent fiber orientation and thickness choices. These formulations are limited to analyzing laminates having plies of the same thickness and material. This paper extends the previously employed lamination parameter reformulation to enable laminate designs with plies of different thicknesses and materials, thereby leading to MIP with cubic constraints. The linearization techniques are employed to convert cubic constraints of buckling load factors in terms of binary variables into sets of linear constraints that are efficiently solved with optimization algorithms for MIPs. It is shown that the use of distinct ply thicknesses in the optimization further reduces the mass of single-material laminates made with carbon-fiber-reinforced polymer when compared with previous studies using the same material. Additionally, the combination of plies made of glass-fiber-reinforced polymer and carbon-fiber-reinforced polymer with distinct thicknesses is shown to reduce the weight penalty when optimized for cost minimization in comparison to plies with uniform thickness.

  PublisherDOI

• Discrete multi-module capacitated lot-sizing problems with multiple items

  Operations Research Letters · 2022-01-11 · 7 citations

  articleSenior authorCorresponding
  PublisherDOI

Recent grants

• Modeling and Solution of Planar Facility Location Problems with Uncertainty

  NSF · $413k · 2018–2023

Frequent coauthors

• Kiavash Kianfar

  Texas A&M University

  6 shared

• Sanjay Mehrotra

  4 shared

• Pranav Borwankar

  3 shared

• Rakesh K. Kapania

  Virginia Tech

  3 shared

• Wei Zhao

  Sichuan University

  3 shared

• Kuo-Ling Huang

  2 shared

• Jonathon M. Smereka

  United States Army Combat Capabilities Development Command

  2 shared

• Kartik Kulkarni

  Virginia Tech

  2 shared

Labs

• Manufacturing Systems EngineeringPI

Education

• Ph.D., Industrial and Systems Engineering

  Texas A&M University

  2014

• MS (with Thesis), Industrial and Systems Engineering

  Texas A&M University

  2010

• B.Tech, Electrical Engineering

  National Institute of Technology

  2007