Given a product design and a repair network for capital goods, a level of repair analysis determines for each component in the product (1) whether it should be discarded or repaired upon failure and (2) at which location in the repair network to do this. In this paper, we show how the problem can be modelled as a minimum cost flow problem with side constraints. Advantages are that (1) solving o...

The ongoing transition from the traditional electrical grid to the digitally interconnected smart grid and the increasing deregulation of electricity markets, allow to envision new types of distributed local energy markets. In order to develop such markets, it is important that energy producers and consumers can access a local energy price. In this project, we define an agent-based real-time lo...

Proof: (by induction). We want to show that one SAP doesn’t introduce negative cycles in Gf . Initially there are no negative cost cycles. Feasible prices can be computed by using shortest path distances from s. After finding the shortest s-t path, it has reduced cost 0. Every arc on the path has reduced length 0. This demonstrates that the triangle inequality property is tight on shortest path...

We consider the 1-median problem in R with the Chebyshev-norm: Given n points with nonnegative weights, find a point that minimizes the sum of the weighted distances to the given points. We propose a combinatorial algorithm for this problem by reformulating it as a fractional b-matching problem. This graph-theoretical problem can be solved by a min-cost-flow algorithm. Moreover, we show that th...

We consider a compound problem of the generalized minimum-cost flow problem and the independent-flow problem, which we call the generalized independent-flow problem. The generalized minimumcost flow problem is to find a minimum-cost flow in a capacitated network with gains, where each arc flow is multiplied by a gain factor when going through an arc. On the other hand, the independent-flow prob...

The stability to dislocations of the elastic phase, or “Bragg glass,” of a randomly pinned elastic medium in two dimensions is studied using the minimum-cost-flow algorithm for a disordered fully packed loop model. The elastic phase is found to be unstable to dislocations due to the quenched disorder. The energetics of dislocations are discussed within the framework of renormalization group pre...