The well-known Dijkstra's algorithm uses weights to determine the shortest path. The focus here is instead on the opposite problem, does there exist weights for a certain set of shortest paths? OSPF (Open Shortest Path First) is one of several possible protocols that determines how routers will send data in a network like the internet. Network operators would however like to have some control of how the traffic is routed, and being able to determine the weights, which would lead to the desired shortest paths to be used, would be a help in this task.The first part of this thesis is a mathematical explanation of the problem with a lot of examples to make it easier to understand. The focus here is on trying to combine several routing patterns into one, so that the result will be fewer, but more fully spanned, routing patterns, and it can e.g. be shown that there can't exist a common set of weights if two routing patterns can't be combined.The second part is a program that can be used to make several tests and changes to a set of routing patterns. It has a polynomial implementation of a function that can combine routing patterns. The examples that I used to combine routing patterns, showed that this will increase the likelihood of finding and significantly speed up the computation of a “valid cycle”. / Egentligen 30p/45hp, men det fanns inte som alternativ.

<p>The well-known Dijkstra's algorithm uses weights to determine the shortest path. The focus here is instead on the opposite problem, does there exist weights for a certain set of shortest paths? OSPF (Open Shortest Path First) is one of several possible protocols that determines how routers will send data in a network like the internet. Network operators would however like to have some control of how the traffic is routed, and being able to determine the weights, which would lead to the desired shortest paths to be used, would be a help in this task.The first part of this thesis is a mathematical explanation of the problem with a lot of examples to make it easier to understand. The focus here is on trying to combine several routing patterns into one, so that the result will be fewer, but more fully spanned, routing patterns, and it can e.g. be shown that there can't exist a common set of weights if two routing patterns can't be combined.The second part is a program that can be used to make several tests and changes to a set of routing patterns. It has a polynomial implementation of a function that can combine routing patterns. The examples that I used to combine routing patterns, showed that this will increase the likelihood of finding and significantly speed up the computation of a “valid cycle”.</p> / Egentligen 30p/45hp, men det fanns inte som alternativ.

Στην εργασία αυτή αντιμετωπίζεται το πρόβλημα της χωροθέτησης εγκαταστάσεων και της κατανομής της ζήτησης σε περιφερειακό επίπεδο μέσω της παρουσίασης σχετικών μαθηματικών υποδειγμάτων μικτού ακέραιου προγραμματισμού, τα οποία στη συνέχεια εφαρμόζονται σε περιπτωσιολογική μελέτη. Η εργασία αφορά την χωροθέτηση δημοσίων εγκαταστάσεων. Ειδικότερα, αναφέρεται στην κατηγορία των προβλημάτων χωροθέτησης που χρησιμοποιούν την τυπική συνάρτηση αποδοτικότητας minsum. Σε αυτές τις περιπτώσεις οι εγκαταστάσεις τοποθετούνται έτσι ώστε να ελαχιστοποιούν το άθροισμα του συνολικού κόστους μεταφοράς. Η εργασία επικεντρώνεται στην χωροθέτηση οχληρών εγκαταστάσεων και συγκεκριμένα στη χωροθέτηση εγκαταστάσεων διαχείρισης αστικών απορριμμάτων. Αυτές οι εγκαταστάσεις ασκούν επιδράσεις όχι μόνο στον χώρο που καταλαμβάνουν, αλλά και σε μεγάλες εκτάσεις γύρω τους. Το πρόβλημα χωροθέτησης σε αυτές τις περιπτώσεις γίνεται ακόμα πιο πολύπλοκο λόγω της αναγκαίας συνεκτίμησης πολλαπλών κριτηρίων. Για τον σκοπό αυτό αναπτύσσεται ένα εξειδικευμένο πλαίσιο παραγωγής μαθηματικών υποδειγμάτων. Ειδικότερα,. στην παρούσα διδακτορική εργασία, δημιουργήθηκαν μαθηματικά υποδείγματα βελτιστοποίησης μικτού ακέραιου προγραμματισμού, τα οποία στη συνέχεια αναλύονται με μεθόδους πολυκριτηριακής ανάλυσης. Τα υποδείγματα αυτά εφαρμόζονται σε περιπτωσιολογική μελέτη με θέμα το χωροθετικό σχεδιασμό ενός περιφερειακού συστήματος διαχείρισης των αστικών απορριμμάτων για τον νομό Αχαΐας. / This study considers a facility location problem with demand allocation in regional level through mixed integer programming models that have been developed for these propose. Afterwards, these models applied in a case study. The present research concerns mostly the public facility location problems. In particular, the PhD dissertation deals with models using the typical mathematical function of efficiency minsum. Therese models locate the facilities in order to minimize the sum of costs for opening facilities and variable transportation costs. The problem becomes more complicated if, in addition it is necessary to locate undesirable facilities. The selection of proper sites for the facilities with obnoxious characteristics is a sensitive issue that has often cause social and political tension. The multiobjective nature of the problem implies that a number of environmental social and political criteria have to be considered. The study presents a model generating framework for formulating location allocation models that applied in municipal solid waste management systems. These models analyzed via multicriteria methodology in order to select the locations of different types of facilities at the regional level. Finally, we apply these concepts in a case study for the development of a solid waste management system for a specific region in Greece.

In this study, we consider the General Lot Sizing and Scheduling Problem in single level capacitated environments with sequence dependent item changeovers. Process industries may be regarded as suitable application areas of the problem. The focus on capacity utilization and intensively time consuming changeovers necessitate the integration of lot sizing and sequencing decisions in the production plan. We present a mathematical model which captures the essence of cases in the most generic and realistic setting of the problem. We discuss the impact and validity of some of the assumptions commonly encountered in the related literature. We also represent the problem using an alternative formulation and attempt to enhance the formulations with the use of some additional inequalities. Finally, we develop a heuristic by restricting the number of possible changeovers. Computational results are discussed.

In this thesis, we use integer programming techniques to solve the resource constrained shortest path problem (RCSPP) which seeks a minimum cost path between two nodes in a directed graph subject to a finite set of resource constraints. Although NP-hard, the RCSPP is extremely useful in practice and often appears as a subproblem in many decomposition schemes for difficult optimization problems. We begin with a study of the RCSPP polytope for the single resource case and obtain several new valid inequality classes. Separation routines are provided, along with a polynomial time algorithm for constructing an auxiliary conflict graph which can be used to separate well known valid inequalities for the node packing polytope. We establish some facet defining conditions when the underlying graph is acyclic and develop a polynomial time sequential lifting algorithm which can be used to strengthen one of the inequality classes. Next, we outline a branch-and-cut algorithm for the RCSPP. We present preprocessing techniques and branching schemes which lead to strengthened linear programming relaxations and balanced search trees, and the majority of the new inequality classes are generalized to consider multiple resources. We describe a primal heuristic scheme that uses fractional solutions, along with the current incumbent, to search for new feasible solutions throughout the branch-and-bound tree. A computational study is conducted to evaluate several implementation choices, and the results demonstrate that our algorithm outperforms the default branch-and-cut algorithm of a leading integer programming software package. Finally, we consider the dial-a-flight problem (DAFP), a new vehicle routing problem that arises in the context of on-demand air transportation and is concerned with the scheduling of a set of travel requests for a single day of operations. The DAFP can be formulated as an integer multicommodity network flow model consisting of several RCSPPs linked together by set partitioning constraints which guarantee that all travel requests are satisfied. Therefore, we extend our branch-and-cut algorithm for the RCSPP to solve the DAFP. Computational experiments with practical instances provided by the DayJet Corporation verify that the extended algorithm also outperforms the default branch-and-cut algorithm of a leading integer programming software package.

abstract: Carbon Capture and Storage (CCS) is a climate stabilization strategy that prevents CO2 emissions from entering the atmosphere. Despite its benefits, impactful CCS projects require large investments in infrastructure, which could deter governments from implementing this strategy. In this sense, the development of innovative tools to support large-scale cost-efficient CCS deployment decisions is critical for climate change mitigation. This thesis proposes an improved mathematical formulation for the scalable infrastructure model for CCS (SimCCS), whose main objective is to design a minimum-cost pipe network to capture, transport, and store a target amount of CO2. Model decisions include source, reservoir, and pipe selection, as well as CO2 amounts to capture, store, and transport. By studying the SimCCS optimal solution and the subjacent network topology, new valid inequalities (VI) are proposed to strengthen the existing mathematical formulation. These constraints seek to improve the quality of the linear relaxation solutions in the branch and bound algorithm used to solve SimCCS. Each VI is explained with its intuitive description, mathematical structure and examples of resulting improvements. Further, all VIs are validated by assessing the impact of their elimination from the new formulation. The validated new formulation solves the 72-nodes Alberta problem up to 7 times faster than the original model. The upgraded model reduces the computation time required to solve SimCCS in 72% of randomly generated test instances, solving SimCCS up to 200 times faster. These formulations can be tested and then applied to enhance variants of the SimCCS and general fixed-charge network flow problems. Finally, an experience from testing a Benders decomposition approach for SimCCS is discussed and future scope of probable efficient solution-methods is outlined. / Dissertation/Thesis / Masters Thesis Industrial Engineering 2017

This thesis is focused on PostgreSQL database system. You can find here introducing to temporal databases, database system PostgreSQL, proposal of temporal extension for PostgreSQL and implementation chapter with examples of using this extension. In this thesis is also using temporal database systems and use temporal databases in practise.

We study the facial structure of the independent set polytope using the concept of conflict hypergraphs. A conflict hypergraph is a hypergraph whose vertices correspond to the binary variables, and edges correspond to covers in the constraint matrix of the independent set polytope. Various structures such as cliques, odd holes, odd anti-holes, webs and anti-webs are identified on the conflict hypergraph. These hypergraph structures are shown to be generalization of traditional graph structures. Valid inequalities are derived from these hypergraph structures, and the facet defining conditions are studied. Chvatal-Gomory ranks are derived for odd hole and clique inequalities. To test the hypergraph cuts, we conduct computational experiments on market-share (also referred to as market-split) problems. These instances consist of 100% dense multiple-knapsack constraints. They are small in size but are extremely hard to solve by traditional means. Their difficult nature is attributed mainly to the dense and symmetrical structure. We employ a special branching strategy in combination with the hypergraph inequalities to solve many of the particularly difficult instances. Results are reported for serial as well as parallel implementations.

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The paper considers Nils Christie’s theory of the ideal victim with its output in different cases of child abduction. Two parts illuminate the similarities and differencies between family and stereotypical abductions and between different cases based on Christie’s theory. The purpose of the paper is to investigate if the theory appears to explain why one kind seems to receive more attention than the other, even though it is basically the same crime. The thesis also examines which of Christie’s criteria that seems to be of most importance to give the victim attention.   The study categorizes the different criteria under three different titles: ideal victim, ideal perpetrator and ideal circumstances, illustrated by a model which defines the concept with the denomination, a true ideal victim. The investigation is carried out through an internet search of the number of hits at the Google search engine, as well as through close up studies of a few cases. The possibilities for abducted children and their families to claim a valid status as a victim is highlighted as of very great, if not of the most, significance for generating attention. The differences between the two types according to Christie’s theory is shown, as is the difference in hits between the two which indicates that ideal victims of abduction get more attention.