An allocation based modeling and solution framework for location problems with dense demand /

In this thesis we present a unified framework for planar location-allocation problems with dense demand. Emergence of such information technologies as Geographical Information Systems (GIS) has enabled access to detailed demand information. This proliferation of demand data brings about serious computational challenges for traditional approaches which are based on discrete demand representation. Furthermore, traditional approaches model the problem in location variable space and decide on the allocation decisions optimally given the locations. This is equivalent to prioritizing location decisions. However, when allocation decisions are more decisive or choice of exact locations is a later stage decision, then we need to prioritize allocation decisions. Motivated by these trends and challenges, we herein adopt a modeling and solution approach in the allocation variable space.Our approach has two fundamental characteristics: Demand representation in the form of continuous density functions and allocation decisions in the form of service regions. Accordingly, our framework is based on continuous optimization models and solution methods. On a plane, service regions (allocation decisions) assume different shapes depending on the metric chosen. Hence, this thesis presents separate approaches for two-dimensional Euclidean-metric and Manhattan-metric based distance measures. Further, we can classify the solution approaches of this thesis as constructive and improvement-based procedures. We show that constructive solution approach, namely the shooting algorithm, is an efficient procedure for solving both the single dimensional n-facility and planar 2-facility problems. While constructive solution approach is analogous for both metric cases, improvement approach differs due to the shapes of the service regions. In the Euclidean-metric case, a pair of service regions is separated by a straight line, however, in the Manhattan metric, separation takes place in the shape of three (at most) line segments. For planar 2-facility Euclidean-metric problems, we show that shape preserving transformations (rotation and translation) of a line allows us to design improvement-based solution approaches. Furthermore, we extend this shape preserving transformation concept to n-facility case via vertex-iteration based improvement approach and design first-order and second-order solution methods. In the case of planar 2-facility Manhattan-metric problems, we adopt translation as the shape-preserving transformation for each line segment and develop an improvement-based solution approach. For n-facility case, we provide a hybrid algorithm. Lastly, we provide results of a computational study and complexity results of our vertex-based algorithm

Feedback algorithm for switch location : analysis of complexity and application to network design

An accelerated feedback algorithm to solve the single-facility minisum problem is studied with application to designing networks with the star topology. The algorithm, in which the acceleration with respect to the Weiszfeld procedure is achieved by multiplying the current Weiszfeld iterate by an accelerating feedback factor, is shown to converge faster than the accelerating procedures available in the literature. Singularities encountered in the algorithm are discussed in detail. A simple practical exception handling subroutine is developed. Several applications of the algorithm to designing computer networks with the star topology are demonstrated. Applications of the algorithm as a subroutine for multi-switch location problems are considered. Various engineering aspects involved in acquiring and processing coordinates for geographic locations are discussed. A complete algorithm in pseudocode along with the source code listing in Mathematica 4.1 is presented

"Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians

The "effet Condorcet" refers to the fact that the application of the pair-wise majority rule to individual preference orderings can generate a collective preference containing cycles. Condorcet's solution to deal with this disturbing fact has been recognized as the search for a median in a certain metric space. We describe the many areas of "applied" or "pure" mathematics where the notion of (metric) median has appeared. If it were actually necessary to give examples proving that "social mathematics" is mathematics, the median case would provide a convincing example.Condorcet's effect ; Fermat's point ; majority rule ; "Mathématique sociale" ; median algebra ; metric space ; permutohedron

A Heuristic Simulation and Optimization Algorithm for Large Scale Natural Gas Storage Valuation under Uncertainty

Natural gas storage valuation is an optimal scheduling of natural gas storage facilities. It is a complex predictive decision making research problem since it involves the financial decisions and the physical storage facility characteristics. The challenge arises from large scale stochastic input data sets and complex mathematical models. Research in the literature has been heavily focused on the financial facet of the valuation with little emphasis on the physical storage facility characteristics. The mathematical models and the solution approaches provided in the literature so far are also either overly simplified or are only relevant for very small scale problems. The contribution of this research is on the physical storage facility characteristics in combination with the financial aspect of the natural gas storage valuation. A large scale stochastic non-linear natural gas storage valuation problem that includes underground and aboveground storage facilities is formulated and solved efficiently. A new heuristic simulation and optimization natural gas storage valuation algorithm that handles a very complex and large size problems is proposed. The algorithm (i) decreases significantly the computation time from hundreds of days to fractions of a second, (ii) provides a reasonable solution quality, and (iii) incorporates all the possible underground and aboveground physical gas storage facility complexities. The research has both practical applications and mathematical significance. Practically, natural gas storage facility managers can use the models developed in this research as decision support tools to make a predictive storage decision under uncertainty within a reasonable time. Mathematically, a novel perspective to solving a non-linear natural gas storage facilities valuation problem is provided. Such approach can be used in a variety of applications; for instance, the algorithm can be applied to a high penetration of renewables to electric power grid and fluid flow network optimization among others

Public Facility Location: Issues and Approaches

The papers collected in this issue were presented at the Task Force Meeting on Public Facility Location, held at IIASA in June 1980. The meeting was an important occasion for scientists with different backgrounds and nationalities to compare and discuss differences and similarities among their approaches to location problems. Unification and reconciliation of existing theories and methods was one of the leading themes of the meeting, and the papers collected here are part of the raw material to be used as a starting point towards this aim. The papers themselves provide a wide spectrum of approaches to both technical and substantive problems, for example, the way space is treated (continuously in Beckmann, in Mayhew, and in Thisse et al, discretely in all the others), the way customers are assigned to facilities (by behavioral models in Ermoliev and Leonardi, in Sheppard, and in Wilson, by normative rules in many others), the way the objective function is defined (ranging from total cost, to total profit, total expected utility for customers, accessibility, minimax distance, maximum covering, to a multi-objective treatment of all of them as in Revelle et al. There is indeed room for discussion, in order to find both similarities and weaknesses in different approaches. A general weakness of the current state of the art of location modeling may also be recognized: its general lack of realism relative to the political and institutional issues implied by locational decisions. This criticism, developed by Lea, might be used both as a concluding remark and as a proposal for new challenging research themes to scholars working in the field of location theory