In the field of robust optimization uncertain data is modeled by uncertainty sets, i.e. sets which contain all relevant outcomes of the uncertain parameters. The complexity of the related robust problem depends strongly on the shape of the uncertainty set. Two popular classes of uncertainty are budgeted uncertainty and ellipsoidal uncertainty. In this paper we … Read more
The multiple Checkpoint Ordering Problem (mCOP) aims to find an optimal arrangement of n one-dimensional departments with given lengths such that the total weighted sum of their distances to m given checkpoints is minimized. In this paper we suggest an integer linear programming (ILP) approach and a dynamic programming (DP) algorithm, which is only exact … Read more
We study disruptions at a major airport. Disruptions could be caused by bad weather, for example. Our study is from the perspective of the airport, the air services provider (such as air traffic control) and the travelling public, rather than from the perspective of a single airline. Disruptions cause flights to be subjected to ground … Read more
In the literature, packing and partitioning orbitopes were discussed to handle symmetries that act on variable matrices in certain binary programs. In this paper, we extend this concept by restrictions on the number of 1-entries in each column. We develop extended formulations of the resulting polytopes and present numerical results that show their effect on … Read more
In this paper we consider energy management optimization problems in a future wherein an interaction with micro-grids has to be accounted for. We will model this interaction through a set of contracts between the generation companies owning centralized assets and the micro-grids. We will formulate a general stylized model that can, in principle, account for … Read more
In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering inequalities. To handle symmetries as well as set packing, partitioning, or covering constraints simultaneously, we introduce constrained symresacks which are the convex hull of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and … Read more
There is often a significant trade-off between formulation strength and size in mixed integer programming (MIP). When modeling convex disjunctive constraints (e.g. unions of convex sets), adding auxiliary continuous variables can sometimes help resolve this trade-off. However, standard formulations that use such auxiliary continuous variables can have a worse-than-expected computational effectiveness, which is often attributed … Read more
Range anxiety, the persistent worry about not having enough battery power to complete a trip, remains one of the major obstacles to widespread electric-vehicle adoption. As cities look to attract more users to adopt electric vehicles, the emergence of wireless in-motion car charging technology presents itself as a solution to range anxiety. For a limited … Read more
In automated valet parking system, a central computer controls a number of robots which have the capability to move in two directions, under cars, lift a car up, carry it to another parking slot, and drop it. We study the theoretical throughput limitations of these systems: Given a car park layout, an initial configuration of … Read more
We consider the 0-1 Penalized Knapsack Problem (PKP). Each item has a profit, a weight and a penalty and the goal is to maximize the sum of the profits minus the greatest penalty value of the items included in a solution. We propose an exact approach relying on a procedure which narrows the relevant range … Read more