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

Local search and swapping strategies.Challenging the greedy maximization of a polymatroid subject to a cardinality constraint

This paper studies the maximization of a polymatroid subject to a cardinality constraint. In particular, we consider the problem of improving the value of the greedy set by swapping one of its members with an element that does not belong to it. To achieve this goal, we first define a (set-based) post-greedy measure of curvature … Read more

Model-Free Assortment Pricing with Transaction Data

We study a problem in which a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers’ valuations and only assumes, instead, that purchase … Read more

Matching Algorithms and Complexity Results for Constrained Mixed-Integer Optimal Control with Switching Costs

We extend recent work on the performance of the combinatorial integral approximation decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs) in the presence of combinatorial constraints or switching costs on an equidistant grid. For the time discretized problem, we reformulate the emerging rounding problem in the decomposition approach as a matching problem on a bipartite … Read more