Flow shop scheduling with peak power consumption constraints

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 problem, and test our approaches with … Read more

A Primal-Dual Algorithm for Computing a Cost Allocation in the Core of Economic Lot-Sizing Games

We consider the economic lot-sizing game with general concave ordering cost functions. It is well-known that the core of this game is nonempty when the inventory holding costs are linear. The main contribution of this work is a combinatorial, primal-dual algorithm that computes a cost allocation in the core of these games in polynomial time. … Read more

The Complexity of Egalitarian Mechanisms for Linear Programming Games

We show that the most cost-efficient subset problem for linear programming games is NP-hard, and in fact inapproximable within a constant factor in polynomial time, unless P = NP. This in turn implies that computing the prices output by an egalitarian mechanism and computing a cost allocation in the equal split-off set for linear programming … Read more

Cost-sharing mechanisms for scheduling under general demand settings

We investigate cost-sharing mechanisms for scheduling cost-sharing games. We assume that the demand is general—that is, each player can be allocated one of several levels of service. We show how to design mechanisms for these games that are weakly group strategyproof, approximately budget-balanced, and approximately efficient, using approximation algorithms for the underlying scheduling problems. We … Read more

Approximating the Least Core Value and Least Core of Cooperative Games with Supermodular Costs

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 + \epsilon)-approximation algorithm for computing the least core value of supermodular cost cooperative games, and a polynomial-time … Read more

Minimizing the sum of weighted completion times in a concurrent open shop

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 … Read more

Near-Optimal Solutions and Integrality Gaps for Almost All Instances of Single-Machine Precedence-Constrained Scheduling

We consider the problem of minimizing the weighted sum of completion times on a single machine subject to bipartite precedence constraints where all minimal jobs have unit processing time and zero weight, and all maximal jobs have zero processing time and unit weight. For various probability distributions over these instances–including the uniform distribution–we show several … Read more

The Maximum Flow Network Interdiction Problem: Valid Inequalities, Integrality Gaps, and Approximability

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 (1993) integer program is not bounded by a constant factor, even when the LP relaxation is strengthened by our valid inequalities. Finally, … Read more

Sharing Supermodular Costs

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 complexity of the least core … Read more