The value of multi-stage stochastic programming in capacity planning under uncertainty

This paper addresses a general class of capacity planning problems under uncertainty, which arises, for example, in semiconductor tool purchase planning. Using a scenario tree to model the evolution of the uncertainties, we develop a multi-stage stochastic integer programming formulation for the problem. In contrast to earlier two-stage approaches, the multi-stage model allows for revision … Read more

Preemptive scheduling with position costs

This paper is devoted to basic scheduling problems in which the scheduling cost of a job is not a function of its completion time. Instead, the cost is derived from the integration of a cost function over the time intervals on which the job is processed. This criterion is specially meaningful when job preemption is … Read more

Constraint Reduction for Linear Programs with Many Inequality Constraints

Consider solving a linear program in standard form, where the constraint matrix $A$ is $m \times n$, with $n \gg m \gg 1$. Such problems arise, for example, as the result of finely discretizing a semi-infinite program. The cost per iteration of typical primal-dual interior-point methods on such problems is $O(m^2n)$. We propose to reduce … Read more

Generalization of the primal and dual affine scaling algorithms

We obtain a class of primal ane scaling algorithms which generalize some known algorithms. This class, depending on a r-parameter, is constructed through a family of metrics generated by ��r power, r  1, of the diagonal iterate vector matrix. We prove the so-called weak convergence of the primal class for nondegenerate linearly constrained convex … Read more

Solving Multi-Leader-Follower Games

Multi-leader-follower games arise when modeling competition between two or more dominant firms and lead in a natural way to equilibrium problems with equilibrium constraints (EPECs). We examine a variety of nonlinear optimization and nonlinear complementarity formulations of EPECs. We distinguish two broad cases: problems where the leaders can cost-differentiate and problems with price-consistent followers. We … Read more

Robust DWDM Routing and Provisioning under Polyhedral Demand Uncertainty

We present mixed integer linear programming models that are robust in the face of uncertain traffic demands known to lie in a certain polyhedron for the problem of dense wavelength division multiplexing network routing and provisioning at minimal cost. We investigate the solution of the problem in a set of numerical experiments for two models … Read more

Approximating K-means-type clustering via semidefinite programming

One of the fundamental clustering problems is to assign $n$ points into $k$ clusters based on the minimal sum-of-squares(MSSC), which is known to be NP-hard. In this paper, by using matrix arguments, we first model MSSC as a so-called 0-1 semidefinite programming (SDP). We show that our 0-1 SDP model provides an unified framework for … Read more

In Situ Column Generation for a Cutting-Stock Problem

Working with an integer bilinear programming formulation of a one-dimensional cutting-stock problem, we develop an ILP-based local-search heuristic. The ILPs holistically integrate the master and subproblem of the usual price driven pattern-generation paradigm, resulting in a unified model that generates new patterns in situ. We work harder to generate new columns, but we are guaranteed … Read more

A semidefinite programming based heuristic for graph coloring

The Lovasz theta function is a well-known polynomial lower bound on the chromatic number. . Any near optimal solution of its semidefinite programming formulation carries valuable information on how to color the graph. A self-contained presentation of the role of this formulation in obtaining heuristics for the graph coloring problem is presented. Citation Submitted to … Read more

Elastic-Mode Algorithms for Mathematical Programs with Equilibrium Constraints: Global Convergence and Stationarity Properties

The elastic-mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions satisfying first- and second-order necessary optimality conditions for the original problem are also first- and second-order points of the elastic-mode formulation. Here we study … Read more