## The Hamiltonian p-median Problem: Polyhedral Results and Branch-and-Cut Algorithm

 In this paper we study the Hamiltonian $$p$$-median problem, in which a weighted graph on $$n$$ vertices is to be partitioned into $$p$$ simple cycles of minimum total weight. We introduce two new families of valid inequalities for a formulation of the problem in the space of natural edge variables. Each one of the … Read more

## On optimally solving sub-tree scheduling for wireless sensor networks with partial coverage

Energy efficiency and balancing are very important issues from the perspective of increasing the lifetime of a wireless sensor network (WSN). In this study, we concentrate on energy balancing. Given a WSN, we consider the problem to minimize its total power consumption over consecutive time slots with respect to communication activities. Disjoint subsets of nodes … Read more

## Models and Algorithms for the Weighted Safe Set Problem

Given a connected graph G = (V, E), a Safe Set S is a subset of the vertex set V such that the cardinality of each connected component in the subgraph induced by V \ S does not exceed the cardinality of any neighbor connected component in the subgraph induced by S. When the vertices … Read more

## Adaptive robust optimization with discrete uncertainty

In this paper, we study adaptive robust optimization problems with discrete uncertainty. We first show that an adaptive robust counterpart of the multiple knapsack problem includes $\Sigma_2^P$-hard problems. Then, we theoretically prove the validity of a non-trivial reformulation of this class of problems which can be solved by an enumerative algorithm akin to a Branch-and-Benders-cut … Read more

## Robust Multi-product Newsvendor Model with Substitution under Cardinality-constrained Uncertainty Set

This work studies a Robust Multi-product Newsvendor Model with Substitution (R-MNMS), where the demand and the substitution rates are stochastic and are subject to cardinality-constrained uncertainty sets. The goal of this work is to determine the optimal order quantities of multiple products to maximize the worst-case total profit. To achieve this, we first show that … Read more

## A Branch-and-Cut Algorithm for Solving Mixed-integer Semidefinite Optimization Problems

This paper is concerned with a cutting-plane algorithm for solving mixed-integer semidefinite optimization (MISDO) problems. In this algorithm, the positive semidefinite constraint is relaxed, and the resultant mixed-integer linear optimization problem is repeatedly solved with valid inequalities for the relaxed constraint. We prove convergence properties of the algorithm. Moreover, to speed up the computation, we … Read more

## A multi-stage stochastic integer programming approach for a multi-echelon lot-sizing problem with returns and lost sales

We consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We consider a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We propose a … Read more

## A Branch-and-Cut Algorithm for Mixed Integer Bilevel Linear Optimization Problems and Its Implementation

In this paper, we describe an algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) by a generalized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MIBLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range … Read more

## Stochastic binary problems with simple penalties for capacity constraints violations

This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly \NP-hard in general. We provide pseudo-polynomial algorithms for three special cases … Read more