Competitive facility location problem is a typical facility locating optimization problem but in a competitive environment. The main characteristic of this problem is the competitive nature of the market. In essence, the problem involves two competitors, i.e., a leader and a follower, who seek to attract customers by establishing new facilities to maximize their own … Read more
We study the single allocation hub location problem with heterogeneous economies of scale (SAHLP-h). The SAHLP-h is a generalization of the classical single allocation hub location problem (SAHLP), in which the hub-hub connection costs are piecewise linear functions of the amounts of flow. We model the problem as an integer non-linear program, which we then … Read more
We study a class of single-objective nonlinear optimization problems, the so-called Integer Linear Generalized Maximum Multiplicative Programs (IL-GMMP). This class of optimization problems has a significant number of applications in different fields of study including but not limited to game theory, systems reliability, and conservative planning. An IL-GMMP can be reformulated as a mixed integer … Read more
We explore the benefits of multi-variable branching strategies for linear programming based branch and bound algorithms for the 0-1 knapsack problem, i.e., of branching on sets of variables rather than on a single variable (the current default in integer programming solvers). We present examples where multi-variable branching shows advantage over single-variable branching, and partially characterize … Read more
The paper overviews stochastic optimization models of insurance mathematics and methods for their solution from the point of view of stochastic programming and stochastic optimal control methodology, with vector optimality criteria. The evolution of an insurance company’s capital is considered in discrete time. The main random variables, which influence this evolution, are levels of payments, … Read more
Recently, Guan, Pan, and Zohu presented a MIP model for the thermal single- unit commitment claiming that provides an integer feasible solution for any convex cost function. In this note we provide a counterexample to this statement and we produce evidence that the perspective function is needed for this aim. CitationResearch Report 19-03, Istituto di … Read more
The Unit Commitment (UC) problem in electrical power production requires to optimally operate a set of power generation units over a short time horizon (one day to a week). Operational constraints of each unit depend on its type (e.g., thermal, hydro, nuclear, …), and can be rather complex. For thermal units, typical ones concern minimum … Read more
We study uncertain linear complementarity problems (LCPs), i.e., problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Gamma-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon [16]. There, we studied Gamma-robustified LCPs for … Read more
In 2013, Orlin proved that the max flow problem could be solved in $O(nm)$ time. His algorithm ran in $O(nm + m^{1.94})$ time, which was the fastest for graphs with fewer than $n^{1.06}$ arcs. If the graph was not sufficiently sparse, the fastest running time was an algorithm due to King, Rao, and Tarjan. We … Read more
With wind and solar becoming major contributors to electricity production in many systems, wholesale market operators have become increasingly aware of the need to address uncertainty when forming prices. While implementing theoretically ideal stochastic market clearing to address uncertainty may be impossible, the use of operating reserve demand curves allows market designers to inject an … Read more