Manish Bansal

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

  • Sumin Kang
  • Manish Bansal
    • Categories Integer Programming, Network Optimization, Stochastic Programming Tags , , , ,

    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 … Read more

    Stackelberg Games with k-Submodular Function under Distributional Risk-Receptiveness and Robustness

  • Seonghun Park
  • Manish Bansal
    • Categories Game Theory, Robust Optimization, Stochastic Programming

    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 … Read more

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

  • Sumin Kang
  • Manish Bansal
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , , , ,

    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 … Read more

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

  • Seonghun Park
  • Manish Bansal
    • Categories Combinatorial Optimization, Game Theory, Stochastic Programming Tags , , ,

    In this paper, we introduce cameras view-frame placement problem (denoted by CFP) in the presence an adversary whose objective is to minimize the maximum coverage by p cameras in response to input provided by n autonomous agents in a remote location. We allow uncertainty in the success of attacks, incomplete information of the probability distribution … Read more

    Semi-Infinite Mixed Binary and Disjunctive Programs: Applications to Set-Covering with Infinite Demand Points and Implicit Hitting Set Problems

  • Manish Bansal
    • Categories Combinatorial Optimization, Integer Programming, Semi-infinite Programming

    Sherali and Adams [Discrete Applied Math. 157: 1319-1333, 2009] derived convex hull of semi-infinite mixed binary linear programs (SIMBLPs) using Reformulation-Linearization Technique (RLT). In this paper, we study semi-infinite disjunctive programs (SIDPs — a generalization of SIMBLPs) and present linear programming equivalent and valid inequalities for them. We utilize these results for deriving a hierarchy … Read more

    Semi-Infinite Generalized Disjunctive and Mixed Integer Convex Programs with(out) Uncertainty

  • Manish Bansal
    • Categories 0-1 Programming, Convex Optimization, Semi-infinite Programming

    In this paper, we introduce semi-infinite generalized disjunctive programs that are defined by logical propositions along with disjunctions of sets of logical equations and infinite number of algebraic inequalities. We denote these programs by SIGDPs. For SIGDPs with linear and convex inequalities, we present new reformulations: semi-infinite mixed-binary/disjunctive linear programs and semi-infinite mixed-binary/disjunctive convex programs, … Read more

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

  • Kartik Kulkarni
  • Manish Bansal
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Production and Logistics

    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 the transportation in each time period, and the … Read more

    Distributionally risk-receptive and risk-averse network interdiction problems with general ambiguity set

  • Sumin Kang
  • Manish Bansal
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We introduce generalizations of stochastic network interdiction problem with distributional ambiguity. Specifically, we consider a distributionally risk-averse (or robust) network interdiction problem (DRA-NIP) and a distributionally risk-receptive network interdiction problem (DRR-NIP) where a leader maximizes a follower’s minimal expected objective value for either the worst-case or the best-case, respectively, probability distribution belonging to ambiguity set … Read more

    Planar Maximum Coverage Location Problem with Partial Coverage, Continuous Spatial Demand, and Adjustable Quality of Service

  • Manish Bansal
  • Parshin Shojaee
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization

    We consider a generalization of the classical planar maximum coverage location problem (PMCLP) in which partial coverage is allowed, facilities have adjustable quality of service (QoS) or service range, and demand zones and service zone of each facility are represented by two-dimensional spatial objects such as rectangles, circles, polygons, etc. We denote this generalization by … Read more

    Planar Maximum Coverage Location Problem with Partial Coverage, Continuous Spatial Demand, and Adjustable Quality of Service

  • Manish Bansal
  • Parshin Shojaee
    • Categories Combinatorial Optimization

    We consider a generalization of the classical planar maximum coverage location problem (PMCLP) in which partial coverage is allowed, facilities have adjustable quality of service (QoS) or service range, and demand zones and service zone of each facility are represented by two-dimensional spatial objects such as rectangles, circles, polygons, etc. We denote this generalization by … Read more