## Approximation Guarantees for Min-max-min Robust Optimization and K-Adaptability under Objective Uncertainty

In this work we investigate the min-max-min robust optimization problem for binary problems with uncertain cost-vectors. The idea of the approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It is known that the min-max-min robust problem … Read more

## General Polyhedral Approximation of Two-Stage Robust Linear Programming

 We consider two-stage robust linear programs with a budget of uncertainty for the righthand side. In this scenario set, which is frequently used in robust optimization, the uncertain righthand side for each row lies in an interval and the relative increases summed over all rows are less than a budget $$\Gamma$$. We develop a … Read more

## Finding Groups with Maximum Betweenness Centrality via Integer Programming with Random Path Sampling

One popular approach to access the importance/influence of a group of nodes in a network is based on the notion of centrality. For a given group, its group betweenness centrality is computed, first, by evaluating a ratio of shortest paths between each node pair in a network that are “covered” by at least one node … Read more

## Worst-Case Analysis of Heuristic Approaches for the Temporal Bin Packing Problem with Fire-Ups

We consider the temporal bin packing problem with fire-ups (TBPP-FU), a branch of operations research recently introduced in multi-objective cloud computing. In this scenario, any item is equipped with a resource demand and a lifespan meaning that it requires the bin capacity only during that time interval. We then aim at finding a schedule minimizing … Read more

## Ordering integers under different permutations

 The question of finding the largest integer contained between two given lists of integers is trivial when integer ordering is interpreted in its usual way. We propose a nontrivial variant wherein each ordering comparison is performed after integers have been mapped under some bijection, and analyze the computational complexity of our combinatorial problem under … Read more

## Submodular Dispatching

Motivated by applications in e-commerce logistics where orders or items arrive at different times and must be dispatched or processed in batches, we propose the submodular dispatching problem (SMD), a strongly NP-hard model defined by a set of orders with release times and a non-decreasing submodular dispatch time function. A single uncapacitated vehicle must dispatch … Read more

## A $\sqrt{5}/2$-approximation algorithm for optimal piecewise linear approximations of bounded variable products

We investigate the optimal piecewise linear approximation of the bivariate product $xy$ over rectangular domains. More precisely, our aim is to minimize the number of simplices in the triangulation underlying the approximation, while respecting a prescribed approximation error. First, we show how to construct optimal triangulations consisting of up to five simplices. Using … Read more

## Approximation algorithm for the two-stage stochastic set multicover problem with simple resource

We study a two-stage, finite-scenarios stochastic version of the set multicover problem, where there is uncertainty about a demand for each element to be covered and the penalty cost is imposed linearly on the shortfall in each demand. This problem is NP-hard and has an application in shift scheduling in crowdsourced delivery services. For this … Read more

## Exactness of Parrilo’s conic approximations for copositive matrices and associated low order bounds for the stability number of a graph

De Klerk and Pasechnik (2002) introduced the bounds $\vartheta^{(r)}(G)$ ($r\in \mathbb{N}$) for the stability number $\alpha(G)$ of a graph $G$ and conjectured exactness at order $\alpha(G)-1$: $\vartheta^{(\alpha(G)-1)}(G)=\alpha(G)$. These bounds rely on the conic approximations $\mathcal{K}_n^{(r)}$ by Parrilo (2000) for the copositive cone $\text{COP}_n$. A difficulty in the convergence analysis of $\vartheta^{(r)}$ is the bad behaviour … Read more

## Boole-Bonferroni Inequalities to Approximately Determine Optimal Arrangements

We consider the problem of laying out several objects in an equal number of pre-defined positions. Objects are allowed finitely many orientations, can overlap each other, and must be arranged contiguously. We are particularly interested in the case when the evaluation of the dimensions of the objects requires computational or physical effort. We develop a … Read more