Models and Algorithms for Some Covering Problems on Graphs

2014 - 2015Several real-life problems as well as problems of theoretical importance within the field of Operations Research are combinatorial in nature. Combinatorial Optimization deals with decision-making problems defined on a discrete space. Out of a finite or countably infinite set of feasible solutions, one has to choose the best one according to an objective function. Many of these problems can be modeled on undirected or directed graphs. Some of the most important problems studied in this area include the Minimum Spanning Tree Problem, the Traveling Salesman Problem, the Vehicle Routing Problem, the Matching Problem, the Maximum Flow Problem. Some combinatorial optimization problems have been modeled on colored (labeled) graphs. The colors can be associated to the vertices as well as to the edges of the graph, depending on the problem. The Minimum Labeling Spanning Tree Problem and the Minimum Labeling Hamiltonian Cycle Problem are two examples of problems defined on edge-colored graphs. Combinatorial optimization problems can be divided into two groups, according to their complexity. The problems that are easy to solve, i.e. problems polynomially solvable, and those that are hard, i.e. for which no polynomial time algorithm exists. Many of the well-known combinatorial optimization problems defined on graphs are hard problems in general. However, if we know more about the structure of the graph, the problems can become more tractable. In some cases, they can even be shown to be polynomial-time solvable. This particularly holds for trees...[edited by Author]XIV n.s

Collaborative Prepositioning Network Design for Regional Disaster Response

We present a collaborative prepositioning strategy to strengthen the disaster preparedness of the Caribbean countries, which are frequently hit by hurricanes. Since different subsets of countries are affected in each hurricane season, significant risk pooling benefits can be achieved through horizontal collaboration, which involves joint ownership of prepositioned stocks. We worked with the intergovernmental Caribbean Disaster and Emergency Management Agency to design a collaborative prepositioning network in order to improve regional response capacity. We propose a novel insurance-based method to allocate the costs incurred to establish and operate the proposed collaborative prepositioning network among the partner countries. We present a stochastic programming model, which determines the locations and amounts of relief supplies to store, as well as the investment to be made by each country such that their premium is related to the cost associated with the expected value and the standard deviation of their demand. We develop a realistic data set for the network by processing real-world data. We conduct extensive numerical analyses and present insights that support practical implementation. We show that a significant reduction in total inventory can be achieved by applying collaborative prepositioning as opposed to a decentralized policy. Our results also demonstrate that reducing the replenishment lead time during the hurricane season and improving sea connectivity are essential to increasing the benefits resulting from the network.TÜBİTAK ; Institute for Data Valorisation (IVADO) ; Natural Sciences and Engineering Research Council of Canad

A branch-and-cut algorithm for the minimum branch vertices spanning tree problem

Given a connected undirected graph G=(V,E), the Minimum Branch Vertices Problem (MBVP) asks for a spanning tree of G with the minimum number of vertices having degree greater than two in the tree. These are called branch vertices. This problem, with applications in the context of optical networks, is known to be NP-hard. We model the MBVP as an integer linear program, with undirected variables, we derive valid inequalities and we prove that some of these are facet defining. We then develop a hybrid formulation containing undirected and directed variables. Both models are solved with branch-and-cut. Comparative computational results show the superiority of the hybrid formulation

Laparoscopic repair of right congenital diaphragmatic hernia with intrathoracic kidney \u2013 a video vignette

a case of a right congenital diaphragmatic hernia with thoracic migration of the right kidney is illustrated. Laparoscopic repair was carried out reducing colon and kidney in the abdominal cavity and reinforcing the direct diaphragmatic breech with a nonresorbable PTFE intraperitoneal mesh. Preoperative and postoperative CT scan show the basic feature and the late result. Video shows the surgical technique details