Given $z\in C^n$ and $A\in Z^{m\times n}$, we consider the problem of evaluating the counting function $h(y;z):=\sum\{z^x : x \in Z^n; Ax = y, x \geq 0\}$. We provide an explicit expression for $h(y;z)$ as well as an algorithm with possibly numerous but simple computations. In addition, we exhibit finitely many fixed convex cones of … Read more
In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents … Read more
In adversarial environments, disabling the communication capabilities of the enemy is a high priority. We introduce the problem of determining the optimal number and locations for a set of jamming devices in order to neutralize a wireless communication network. This problem is known as the WIRELESS NETWORK JAMMING PROBLEM. We develop several mathematical programming formulations … Read more
In this paper we address the following probabilistic version (PSC) of the set covering problem: $min \{ cx \ |\ {\mathbb P} (Ax\ge \xi) \ge p,\ x_{j}\in \{0,1\}^N\}$ where $A$ is a 0-1 matrix, $\xi$ is a random 0-1 vector and $p\in (0,1]$ is the threshold probability level. We formulate (PSC) as a mixed integer … Read more
We consider revenue management models for pricing a product line with several customer segments, working under the assumption that every customer’s product choice is determined entirely by their reservation price. We model the customer choice behavior by several probabilistic choice models and formulate the problems as mixed-integer programming problems. We study special properties of these … Read more
This paper is a survey of and some minor extensions to the theory of duality for mixed-integer linear programs. The theory of duality for linear programs is well-developed and has been extremely successful in both theory and practice. Much of this broad framework can be extended to MILPs in principle, but this has proven largely … Read more
We construct an integrated multi-period inventory-production-distribution replenishment plan for three-stage supply chains. The supply chain maintains close-relationships with a small group of suppliers, and the nature of the products (bulk, chemical, etc.) makes it more economical to rely upon a direct shipment, full-truck load distribution policy between supply chain nodes. In this paper, we formulate … Read more
The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up … Read more
This paper deals with directed, bidirected, and undirected capacitated network design problems. Using mixed integer rounding (MIR), we generalize flow-cutset inequalities to these three link types and to an arbitrary modular link capacity structure, and propose a generic separation algorithm. In an extensive computational study on 54 instances from the Survivable Network Design Library (SNDlib), … Read more
Due to the high computational complexity of exact methods (e.g., integer programming) for routing and wavelength assigment in optical networks, it is beneficial to decompose the problem into a routing task and a wavelength allocation task. However, by this decomposition it is not necessarily possible to obtain a valid wavelength assignment for a given routing … Read more