Structural Insights and an IP-based Solution Method for Patient-to-room Assignment Under Consideration of Single Room Entitlements

Patient-to-room assignment (PRA) is a scheduling problem in decision support for large hospitals. This work proposes Integer Programming (IP) formulations for dynamic PRA, where either full, limited or uncertain information on incoming patients is available. The applicability is verified through a computational study. Results indicate that large, real world instances can be solved to a … Read more

Branch-and-Bound versus Lift-and-Project Relaxations in Combinatorial Optimization

In this paper, we consider a theoretical framework for comparing branch-and-bound with classical lift-and-project hierarchies. We simplify our analysis of streamlining the definition of branch-and-bound. We introduce “skewed $k$-trees” which give a hierarchy of relaxations that is incomparable to that of Sherali-Adams, and we show that it is much better for some instances. We also … Read more

The Robust Bike Sharing Rebalancing Problem: Formulations and a Branch-and-Cut Algorithm

Bike Sharing Systems (BSSs) offer a sustainable and efficient urban transportation solution, bringing flexible and eco-friendly alternatives to city logistics. During their operation, BSSs may suffer from unbalanced bike distribution among stations, requiring rebalancing operations throughout the system. The inherent uncertain demand at the stations further complicates these rebalancing operations, even when performed during downtime. … Read more

Recycling Valid Inequalities for Robust Combinatorial Optimization with Budget Uncertainty

Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty into optimization problems. The existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is quite poor when … Read more

Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operator

\(\) We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lovász-Schrijver SDP operator \( \text{LS}_+\), with a particular focus on a search for relatively small graphs with high \( \text{LS}_+\)-rank (the least number of iterations of the \( \text{LS}_+\) operator on the fractional stable set polytope to compute … Read more

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

A Combinatorial Flow-based Formulation for Temporal Bin Packing Problems

We consider two neighboring generalizations of the classical bin packing problem: the temporal bin packing problem (TBPP) and the temporal bin packing problem with fire-ups (TBPP-FU). In both cases, the task is to arrange a set of given jobs, characterized by a resource consumption and an activity window, on homogeneous servers of limited capacity. To … Read more

Temporal Bin Packing with Half-Capacity Jobs

Motivated by applications in cloud computing, we study a temporal bin packing problem with jobs that occupy half of a bin’s capacity. An instance is given by a set of jobs, each with a start and end time during which it must be processed, i.e., assigned to a bin. A bin can accommodate two jobs … Read more

On Aligning Non-Order-Associated Binary Decision Diagrams.

Recent studies employ collections of binary decision diagrams (BDDs) to solve combinatorial optimization problems. This paper focuses on the problem of optimally aligning two BDDs, i.e., transforming them to enforce a common order of variables while keeping the total size of the diagrams as small as possible. We address this problem, which is known to … Read more

Dendrograms, Minimum Spanning Trees and Feature Selection

Feature selection is a fundamental process to avoid overfitting and to reduce the size of databases without significant loss of information that applies to hierarchical clustering. Dendrograms are graphical representations of hierarchical clustering algorithms that for single linkage clustering can be interpreted as minimum spanning trees in the complete network defined by the database. In … Read more