Nelson A. Uhan

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We study minimizing the sum of weighted completion times in a concurrent open shop. We give a primal–dual 2-approximation algorithm for this problem. We also show that several natural linear programming relaxations for this problem have an integrality gap of 2. Finally, we show that this problem is inapproximable within a factor strictly less than 6/5 if P(More)
We study the Maximum Flow Network Interdiction Problem (MFNIP). We present two classes of polynomially separable valid inequalities for Cardinality MFNIP. We also prove the integrality gap of the LP relaxation of Wood’s [19] integer program is not bounded by a constant factor, even when the LP relaxation is strengthened by our valid inequalities. Finally,(More)
We study stochastic linear programming games: a class of stochastic cooperative games whose payoffs under any realization of uncertainty are determined by a specially structured linear program. These games can model a variety of settings, including inventory centralization and cooperative network fortification. We focus on the core of these games under an(More)
We study scheduling as a means to address the increasing energy concerns in manufacturing enterprises. In particular, we consider a flow shop scheduling problem with a restriction on peak power consumption, in addition to the traditional time-based objectives. We investigate both mathematical programming and combinatorial approaches to this scheduling(More)
We study the approximation of the least core value and the least core of supermodular cost cooperative games. We provide a framework for approximation based on oracles that approximately determine maximally violated constraints. This framework yields a 3-approximation algorithm for computing the least core value of supermodular cost cooperative games, and a(More)
We study cooperative games with supermodular costs. We show that supermodular costs arise in a variety of situations; in particular, we show that the problem of minimizing a linear function over a supermodular polyhedron—a problem that often arises in combinatorial optimization—has supermodular optimal costs. In addition, we examine the computational(More)
We consider the problem of scheduling jobs on a single machine to minimize the total electricity cost of processing these jobs under time-of-use electricity tariffs. For the uniform-speed case, in which all jobs have arbitrary power demands and must be processed at a single uniform speed, we prove that the non-preemptive version of this problem is(More)
Consider a situation where a group of agents wishes to share the costs of their joint actions, and needs to determine how to distribute the costs amongst themselves in a fair manner. For example, a set of agents may agree to process their jobs together on a machine, and share the optimal cost of scheduling these jobs. This kind of situation can be modelled(More)
In this work, we introduce decentralized network interdiction games, which model the interactions among multiple interdictors with differing objectives operating on a common network. As a starting point, we focus on decentralized shortest path interdiction (DSPI) games, where multiple interdictors try to increase the shortest path lengths of their own(More)
In this thesis, we study three problems related to various algorithmic and game-theoretic aspects of scheduling. First, we apply ideas from cooperative game theory to study situations in which a set of agents faces supermodular costs. These situations appear in a variety of scheduling contexts, as well as in some settings related to facility location and(More)