Unit commitment has been at the center of power system operation for well over 50 years. Yet, this problem cannot be considered solved due to its size and complexity. Today, operators rely on off-the-shelf optimization solvers to tackle this challenging problem, and often resort to simplifications to make the problem more tractable and solvable in … Read more
We consider a real-world multimodal freight transportation problem that arises in a food grain organization in India. This problem aims to satisfy the demand for a set of warehouses for different types of food grains from another set of warehouses with surplus quantities over multiple periods of time by rail and road, while minimizing the … Read more
Patient scheduling is a difficult task as it involves dealing with stochastic factors such as an unknown arrival flow of patients. Scheduling radiotherapy treatments for cancer patients faces a similar problem. Curative patients need to start their treatment within the recommended deadlines, i.e., 14 or 28 days after their admission while reserving treatment capacity for … Read more
The Total Matching Polytope generalizes the Stable Set Polytope and the Matching Polytope. In this paper, we give the perfect formulation for Trees and we derive two new families of valid inequalities, the balanced biclique inequalities which are always facet-defining and the non-balanced lifted biclique inequalities obtained by a lifting procedure, which are facet-defining for … Read more
The weighted rectangles partitioning (WRP) problem is defined on a set of active and inactive pixels. The problem is to find a partition of the active pixels into weighted rectangles, such that the sum of their weights is maximal. The problem is formulated as an integer programming problem and instances with an integral relaxation polyhedron … Read more
Nested multi-level structures are frequently encountered in many real-world optimization problems. Decomposition techniques are a commonly applied approach used to handle nested multi-level structures; however, the typical problem-specific focus of such techniques has led to numerous specialized formulations and solution methods. This lack of generalized results for nested multi-level optimization problems is addressed in this … Read more
Full strong-branching (henceforth referred to as strong-branching) is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an analysis of the performance of the strong-branching rule both from a theoretical and a computational perspective. On … Read more
Planning of trajectories, i.e. paths over time, is a challenging task. Thereby, the trajectories for involved commodities often have to be considered jointly as separation constraints have to be respected. This is for example the case in robot motion or air traffic management. Involving these discrete separation constraints in the planning of best possible continuous … Read more
In this paper we study the rank of polytopes contained in the 0-1 cube with respect to $t$-branch split cuts and $t$-dimensional lattice cuts for a fixed positive integer $t$. These inequalities are the same as split cuts when $t=1$ and generalize split cuts when $t > 1$. For polytopes contained in the $n$-dimensional 0-1 … Read more
The continuous-time service network design problem (CTSNDP) occurs widely in practice. It aims to minimize the total operational cost by optimizing the schedules of transportation services and the routes of shipments for dispatching, which can occur at any time point along a continuous planning horizon. In order to be cost effective, shipments often wait to … Read more