We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all arcs, and the location of sources and sinks. The concave cost over each arc is assumed to be evaluated … Read more
This paper points out the impact of opportunity cost of time (high discount rate or high rate of time preference, time-dependent profits, etc.) in designing real-world Steiner trees like electricity, gas, water, or telecommunications networks. We present the Steiner Tree Scheduling Problem which consists of finding a Steiner tree in an activity-on-arc graph that spans … Read more
Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR based Branch and Bound (DSATUR) is an effective exact algorithm for the … Read more
In this paper we consider a particular method of clustering for graphs, namely the modularity density maximization. We propose a hierarchical divisive heuristic which works by splitting recursively a cluster into two new clusters by maximizing the modularity density, and we derive four reformulations for the mathematical programming model used to obtain the optimal splitting. … Read more
In this paper we establish conditions under which uniqueness of market equilibrium is obtained in a setup where prior to trading of electricity, transmission capacities between different market regions are fixed. In our setup, firms facing fluctuating demand decide on the size and location of production facilities. They make production decisions constrained by the invested … Read more
In this work, we introduce multi-interdictor games, which model interactions among multiple interdictors with differing objectives operating on a common network. As a starting point, we focus on shortest path multi-interdictor (SPMI) games, where multiple interdictors try to increase the shortest path lengths of their own adversaries attempting to traverse a common network. We first … Read more
The “sequential ordering problem” (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hernández & Salazar introduced a “multi-commodity flow” (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formulation by fixing variables … Read more
We consider distributed optimization where $N$ nodes in a connected network minimize the sum of their local costs subject to a common constraint set. We propose a distributed projected gradient method where each node, at each iteration $k$, performs an update (is active) with probability $p_k$, and stays idle (is inactive) with probability $1-p_k$. Whenever … Read more
For an infeasible network flow system with supplies and demands, we consider the problem of finding a minimum irreducible infeasible subsystem cover, i.e., a smallest set of constraints that must be dropped to obtain a feasible system. The special cases of covers which only contain flow balance constraints (node cover) or only flow bounds (arc … Read more
We propose an equilibrium model that allows to analyze the long-run impact of the regulatory environment on transmission line expansion by the regulator and investment in generation capacity by private firms in liberalized electricity markets. The model incorporates investment decisions of the transmission operator and private firms in expectation of an energy-only market and cost-based … Read more