A characterization of irreducible infeasible subsystems in flow networks

Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature by showing a one-to-one correspondence between IISs and Gale-Hoffman-inequalities in which one side of the cut has to be weakly connected. We also show that a single max-flow computation allows one to compute an IIS. Moreover, we prove that finding an IIS of minimal cardinality in this special case of flow networks is strongly NP-hard

A System Dynamics Model of the Air Transport System

In this report, we give a complete algebraic description of a system dynamics model of the air transport system, developed to assess the impact of different policies on the adoption rate of fully electric aircraft until the year 2050. Our model consists of the interaction between three major segments, namely air travel demand, airline industry and aircraft manufacturers. This model was used in the paper “How much can electric aircraft contribute to reaching the Flightpath 2050 CO2 emissions goal? A system dynamics approach for European short haul flights” for the computational results therein

A System Dynamics Model of the Air Transport System

This collection contains a system dynamics model of the air transport system (ATS), developed to assess the impact of different policies on the adoption rate of fully electric aircraft until the year 2050. The model consists of the interaction between three major segments, namely air travel demand, airline industry and aircraft manufacturers. The provided files can be executed using the software Vensim. Furthermore, a data set as an excel file, containing a collection of initial values, parameters, exogenous variables and variables used to calibrate the ATS model is given

Dynamic Shortest Paths Methods for the Time-Dependent TSP

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation

Mixed-Integer Programming Techniques for the Connected Max-k-Cut Problem

We consider an extended version of the classical Max-k-Cut problem in which we additionally require that the parts of the graph partition are connected. For this problem we study two alternative mixed-integer linear formulations and review existing as well as develop new branch-and-cut techniques like cuts, branching rules, propagation, primal heuristics, and symmetry breaking. The main focus of this paper is an extensive numerical study in which we analyze the impact of the different techniques for various test sets. It turns out that the techniques from the existing literature are not sufficient to solve an adequate fraction of the test sets. However, our novel techniques significantly outperform the existing ones both in terms of running times and the overall number of instances that can be solved

Feeder routing for air-to-air refueling operations

With the ever increasing volume of air traffic comes an enormous environmental impact, specifically due to carbon emissions. A promising approach to reduce this impact is the introduction of en route air-to-air refueling, allowing for the design of aircraft with reduced weight and a decreased fuel burn. Aside from the design of aircraft, the key challenge lies in the planning of the refueling operation in order to minimize the fuel burn of the feeder fleet. The air-to-air refueling problem is a variant of a vehicle routing problem in which a fleet of feeders are to perform air-to-air refueling operations for a fixed set of cruisers. In this paper, we devise an IP-based method capable of solving this problem supported by an ODE model of the feeders’ fuel consumption. The algorithmic key to solve the air-to-air refueling problem lies in separating the problem of finding routes serving cruisers and assigning sets of routes to individual feeders. We demonstrate the effectiveness of our methods both on real-world and artificial instances, solving all problems to optimality and significantly outperforming state-of-the-art heuristic methods

GasLib—A Library of Gas Network Instances

The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances that can be used by researchers in the field of gas transport. The advantages are that researchers save time by using these instances and that different models and algorithms can be compared on the same specified test sets. The library instances are encoded in an XML (extensible markup language) format. In this paper, we explain this format and present the instances that are available in the library