This thesis presents new results on a few problems involving maximum flows. The first topic we explore is maximum flow network interdiction. The second topic we explore is reoptimization heuristics for rapidly solving an entire sequence of Maximum Flow Problems. In the Cardinality Maximum Flow Network Interdiction Problem (CMFNIP), an interdictor chooses R arcs to delete from an s-t flow network so as to minimize the maximum flow on the network induced on the undeleted arcs. This is an intensively studied problem that has nontrivial applications in military strategy, intercepting contraband and flood control. CMFNIP is a strongly NP-hard special case of the Maximum Flow Network Interdiction Problem (MFNIP), where each arc has an interdiction cost and the interdictor is constrained by an interdiction budget. Although there are several papers on MFNIP, very few theoretical results have been documented. In this talk, we introduce two exponentially large classes of valid inequalities for CMFNIP and prove that they can be separated in polynomial time. Second, we prove that the integrality gap of the commonly used integer linear programming formulation for CMFNIP is contained in the set Omega(|V| ^(1 e)) where |V| is the number of nodes in the network and e is in the interval (0,1). We prove that this result holds even when the linear programming relaxation is strengthened with our two classes of valid inequalities and we note that this result immediately extends to MFNIP. In the second part of this defense, we explore incremental algorithms for solving an online sequence of Maximum Flow Problems (MFPs). Sequences of MFPs arise in a diverse collection of settings including computational biology, finger biometry, constraint programming and real-time scheduling. To initiate this study, we develop an algorithm for solving a sequence of MFPs when the ith MFP differs from the (i-1)st MFP, for each possible i, in that the underlying networks differ by exactly one arc. Second, we develop maximum flow reoptimization heuristics to rapidly compute a robust minimum capacity s-t cut in light of uncertain arc capacities. Third, we develop heuristics to efficiently compute a maximum expected maximum flow in the context of two-stage stochastic programming. We present computational results illustrating the practical performance of our algorithms.

Agricultural economics report 81. / Cover title. / "This manual supplements 'An iterative linear programming procedure for estimating patterns of agricultural land use,' by the present authors." / 28 p. tables

Optimization methods nowadays play a very important role in financial decisions such as portfolio managements, construction of index funds and pension funds.  This Master Thesis is devoted to the problem of an index fund construction. The problem is represented as a linear optimization problem of re-balancing the portfolio at minimum cost and solved using the Primal-Dual interior point method. The index fund is constructed using ten companies from the Dow Jones Industrial Average Index (DJIA). The Primal-Dual interior point method was first implemented in Matlab and later on in Java.

Bibliography: leaves 238-248 / xxix, 248 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis is concerned with the design and coordination of linear, fixed parameter controllers for the purpose of enhancing the dynamic performance of a multimachine power system. The studies are based on linear control theory and involve state space analysis, modal analysis, eigenanalysis and conventional frequency response techniques. The emphasis is on the small-signal performance of the system / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 1997?

This thesis covers three main issues in content delivery with a focus on placement algorithms of replica servers and replica contents. In a content delivery system, the location of replicas is very important as perceived by a quotation: Closer is better. However, considering the costs incurred by replication, it is a challenge to deploy replicas in a cost-effective manner. The objective of our work is to optimally select the location of replicas which includes sites for replica server deployment, servers for replica contents hosting, and en-route caches for object caching. Our solutions for corresponding applications are presented in three parts of the work, which makes significant contributions for designing scalable, reliable, and efficient systems for Internet content delivery. In the first part, we define the Fault-Tolerant Facility Allocation (FTFA) problem for the placement of replica servers, which relaxes the well known Fault-Tolerant Facility Location (FTFL) problem by allowing an integer (instead of binary) number of facilities per site. We show that the problem is NP-hard even for the metric version, where connection costs satisfy the triangle inequality. We propose two efficient algorithms for the metric FTFA problem with approximation factors 1.81 and 1.61 respectively, where the second algorithm is also shown to be (1.11,1.78)- and (1,2)-approximation through the proposed inverse dual fitting technique. The first bi-factor approximation result is further used to achieve a 1.52-approximation algorithm and the second one a 4-approximation algorithm for the metric Fault-Tolerant k-Facility Allocation problem, where an upper bound of facility number (i. e. k) applies. In the second part, we formulate the problem of QoS-aware content replication for parallel access in terms of combined download speed maximization, where each client has a given degree of parallel connections determined by its QoS requirement. The problem is further converted into the metric FTFL problem and we propose an approximation algorithm which is implemented in a distributed and asynchronous manner of communication. We show theoretically that the cost of our solution is no more than 2F* + RC*, where F* and C* are two components of any optimal solution while R is the maximum number of parallel connections. Numerical experiments show that the cost of our solutions is comparable (within 4% error) to the optimal solutions. In the third part, we establish mathematical formulation for the en-route web caching problem in a multi-server network that takes into account all requests (to any server) passing through the intermediate nodes on a request/response path. The problem is to cache the requested object optimally on the path so that the total system gain is maximized. We consider the unconstrained case and two QoS-constrained cases respectively, using efficient dynamic programming based methods. Simulation experiments show that our methods either yield a steady performance improvement (in the unconstrained case) or provide required QoS guarantees. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1461921 / Thesis (Ph.D.) - University of Adelaide, School of Computer Science, 2009

Lic.-avh. (sammanfattning) Umeå : Sveriges lantbruksuniv. / Härtill 2 uppsatser.

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Systems Science and Industrial Engineering, 2009. / Includes bibliographical references.

Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Earl Barnes; Committee Member: Arkadi Nemirovski; Committee Member: Faiz Al-Khayyal; Committee Member: Guillermo H. Goldsztein; Committee Member: Joel Sokol. Part of the SMARTech Electronic Thesis and Dissertation Collection.

by Dimitri P. Bertsekas, Patrick A. Hossein, Paul Tseng. / "December 1985." / Bibliography: p. 56-57. / National Science Foundation Grant NSF-ECS-8217668

Το πρώτο κεφάλαιο περιλαμβάνει μια ιστορική αναδρομή σχετικά με τη γέννηση και την ανάπτυξη της Επιχειρησιακής Έρευνας και του Γραμμικού Προγραμματισμού. Επίσης παρουσιάζεται το χρονικό των μεγαλυτέρων ανακαλύψεων: ο αλγόριθμος Simplex (Dantzig-1949), ο ελλειψοειδής αλγόριθμος (Khachian-1979) και ο αλγόριθμος εσωτερικών σημείων (Karmarkar-1983). Στη συνέχεια - δεύτερο κεφάλαιο - γίνεται η θεωρητική θεμελίωση της μεθόδου Simplex, συμπεριλαμβάνοντας τόσο την γεωμετρική-εποπτική παρουσίαση της μεθόδου, όσο και την αυστηρή αλγεβρική τεκμηρίωσή της μέσω θεωρημάτων. Το τρίτο κεφάλαιο αφιερώθηκε στον αλγόριθμο των ελλειψοειδών, στη μέθοδο δηλαδή που ουσιαστικά απέδειξε ότι τα προβλήματα του γραμμικού προγραμματισμού μπορούν να λυθούν σε πολυωνυμικό χρόνο. Στο τέταρτο κεφάλαιο παρουσιάζεται η πιο σύγχρονη τάση στον τομέα επίλυσης προβλημάτων γραμμικού προγραμματισμού: οι μέθοδοι εσωτερικού σημείου. Συγκεκριμένα αναπτύσσεται ο αλγόριθμος του Karmakar, η κατηγορία των μεθόδων ομοπαραλληλικής αλλαγής κλίμακας και ο πρωτεύοντας-δυϊκός αλγόριθμος εσωτερικού σημείου. Τέλος, στο πέμπτο κεφάλαιο περιλαμβάνεται η παρουσίαση της έννοιας της υπολογιστικής πολυπλοκότητας αλγορίθμων, η πλήρης ανάλυση της πολυπλοκότητας των αλγορίθμων Simplex και εσωτερικού σημείου του Karmakar, καθώς και η σύγκριση των δύο αλγορίθμων. / The first chapter includes a historical retrospection in respect of the birth and growth of Operational Research and Linear Programming. Furthermore, the chronicle of the biggest discoveries is presented: the Simplex algorithm (Dantzig-1949), the ellipsoid algorithm (Khachian-1979) and the interior point algorithm (Karmarkar-1983). Thereafter -in the second chapter- the theoretical foundation of Simplex method is presented, including both the geometric- supervisory presentation and the strict algebraic documentation of the method via theorems. The third chapter refers to the ellipsoid algorithm, namely the method that proved that the problems of linear programming can be solved in polynomial time. In the fourth chapter, the most contemporary tendency in the field of solving problems of linear programming, is presented: the methods of interior point. Particularly, the algorithm of Karmakar and the primal-dual algorithm of interior point are expounded. Finally, the fifth chapter includes the presentation of the concept of computational complexity of algorithms, the complete analysis of complexity of algorithms Simplex and interior point of Karmakar, as well as the comparison of the two algorithms.