We show that, in any undirected graph, splitting off can be performed while preserving all cuts of value at most 3/4 times the minimum value, and this is best possible. This generalizes a classical splitting-off result of Lovasz.

Parallel machine scheduling problems concern the scheduling of "n" jobs on "m" machines to minimize some function of the job completion time. If preemption is not allowed, then most problems are not only NP-hard, but also very hard from a practical point of view. In this paper, we show that...

We consider the scheduling problem of minimizing the average wighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on time-indexed formulation, the other on a completion-time formulation. We show...

This survey paper prepared for the Handbook of Utility Theory covers the axiomatic foundation of decision making under uncertainty when conditional preferences are allowed to be state dependent, leading to an expected state-dependent utility representation.

We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times.

Given a network, the facility location problem consists of locating a set of sites on the network to serve existing clients so as to minimize its total cost. Special cases include the simple plant location problem (SPLP), bank account location, p-facility location, and p-median problem.

We analyze a model of network formation where the costs of forming links are publicly known but an individual's benefits are not know to the social planner. The objective is to design a mechanism which not only ensures that an efficient network always forms in equilibrium but also ensures that...

We describe an @( n^4 h min{log U, n^2logn}) capacity scaling algorithm for the minimum cost submodular flow problem. Our algorithm modifies and extends the Edmonds-Karp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem. The modification entails...

We study a family of unbounded polyhedra arising in the study of uncapacitated lot-sizing problems with Wagner-Whitin costs. With n the number of periods, we completely characterize the bounded faces of maximal dimension, and derice an O(n^2) alogorithm to express within the polyhedron as a...

The critical role of free entry to correct inherent deviance behavior has been stressed by Vanek (1970), Meade (1972) amongst others. The equivalence theorem (Dreze 1976) defines that labour and entrepreneurial management both lead to the same Pareto optimal equilibrium provided that there is...