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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)

Extended Abstract 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… (More)

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 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)

5 We consider the economic lot-sizing game with general concave ordering cost functions. It is 6 well-known that the core of this game is nonempty when the inventory holding costs are linear. 7 The main contribution of this work is a combinatorial, primal-dual algorithm that computes a cost 8 allocation in the core of these games in polynomial time. We also… (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 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 consider a cooperative game defined by an economic lot sizing problem with concave ordering costs over a finite time horizon, in which each player faces demand for a single product in each period and coalitions can pool orders. We show how to compute a dynamic cost allocation in the strong sequential core of this game, i.e. an allocation over time that… (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)