Polynomially solvable cases of multifacility distance constraints on cyclic networks

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1993.Thesis (Master's) -- Bilkent University, 1993.Includes bibliographical references leaves 79-81Distance Constraints Problem is to locate one or more new facilities on a network so that the distances between new and existing facilities as well as between pairs of new facilities do not exceed given upper bounds. The problem is AfV-Complete on cyclic networks and polynomially solvable on trees. Although theory for tree networks is well-developed, there is virtually no theory for cyclic networks. In this thesis, we identify a special class of instances for which we develop theory and algorithms that are applicable to any metric space defining the location space. We require that the interaction between new facilities has a tree structure. The method is based on successive applications of EXPANSION and INTERSECTION operations defined on subsets of the location space. Application of this method to general networks yields strongly polynomial algorithms. Finally, we give an algorithm that constructs an e-optimal solution to a related minimax problem.Yeşilkökçen, Naile GülcanM.S

Sensitivity analysis of distance constraints and of multifacility minimax location on tree networks

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ. ,1989.Thesis (Master's) -- Bilkent University, 1989.Includes bibliographical references leaves 77-79.In this thesis, the main concern is to investigate the use of consistency conditions of distance constraints in sensitivity analysis of certain network location problems. The interest is in minimax type of objective functions. A single parametric approach is adopted in the sensitivity analysis for the m-facility minimax location problem on tree networks. Apart from the traditional sensitivity analysis approach, a conceptual framework for imprecision in distance constraints is developed.Doğan, EsraM.S

A review of network location theory and models

Cataloged from PDF version of article.In this study, we review the existing literature on network location problems. The study has a broad scope that includes problems featuring desirable and undesirable facilities, point facilities and extensive facilities, monopolistic and competitive markets, and single or multiple objectives. Deterministic and stochastic models as well as robust models are covered. Demand data aggregation is also discussed. More than 500 papers in this area are reviewed and critical issues, research directions, and problem extensions are emphasized.Erdoğan, Damla SelinM.S

An analysis of minimax facility location problems with area demands /

The unconstrained model, and its solution technique can be easily modified to solve the limiting case where all facilities are fixed points, and also the case when metric constraints are added.Examples are solved to show the impact of assuming area demands, the conflicting nature of the minimax and minisum criteria and to illustrate the solutions techniques developed.A minimax objective function constrained by a bound on the total average cost of servicing all existing facilities (minisum function) is then discussed. Using duality properties, this problem is shown to be equivalent to another model which minimizes the minisum function subject to a bound on the same minimax function. This last problem proves to be easier to solve, and a specialized solution technique is developed. The resulting solutions are nondominated solutions in relation to the two criteria involved. Another way to generate nondominated solutions is by combining the two functions into a weighted sum. The constrained criterion method is shown to be superior both analytically and practically.Most probabilistic facility location problems investigated to date were variations of the generalized Weber formulation. In this research, several single facility minimax location models are analyzed, where both the weights and the locations of the existing facilities are random variables. The demand points are uniformly distributed over rectangular areas, the rectilinear metric is used and the weights are assumed to be independently distributed random variables. Two unconstrained probabilistic models are analyzed and compared to the centroid formulation, it is seen that the probabilistic models are sensitive to deviations from optimal solutions. An expected value criterion formulation is also presented along with lower and upper bound approximating functions

Composite regions of feasibility for certain classes of distance constrained network location problems

Distance constrained network location involves locating m new facilities on a transport network G so as to satisfy upper bounds on distances between pairs of new facilities and pairs of new and existing facilities. The problem is script N sign℘-complete in general, but polynomially solvable for certain classes. While it is possible to give a consistency characterization for these classes, it does not seem possible to give a global description of the feasible set. However, substantial geometrical insights can be obtained on the feasible set by studying its projections onto the network. The j-th projection defines the j-th composite region which is the set of all points in G at which new facility j can be feasibly placed without violating consistency. We give efficient methods to construct these regions for solvable classes without having to know the feasible set and discuss implications on consistency characterization, what if analysis, and recursive solution constructions

Distance constraints on cyclic networks : a new polynomially solvable class

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references leaves 100-101Distance Constraints Problem is to locate new facilities on a network so that the distances between new and existing facilities as well as between pairs of now facilities do not exceed given upper bounds, 'rhc ])roblem is N F-Complele on cyclic networks. The oidy known polynornially solvable class of distance constraints on cyclic networks is the case when the linkage network, which is an auxiliary graph induced by the distance bounds between new facility pairs, is a tree. In this thesis, we identify a new polynornially solvable class where each new facilit}'^ is restricted to an a priori specified feasible region which is confined to a single edge and where the linkage network is cj^clic with the restriction that there exists a node whose deletion breaks all cycles. We then extend the above class to a more general class where the linkage network has a cut vertex whose blocks fulfill the above assumptionsEmir, HülyaM.S

Data-Collection for the Sloan Digital Sky Survey: a Network-Flow Heuristic

The goal of the Sloan Digital Sky Survey is ``to map in detail one-quarter of the entire sky, determining the positions and absolute brightnesses of more than 100 million celestial objects''. The survey will be performed by taking ``snapshots'' through a large telescope. Each snapshot can capture up to 600 objects from a small circle of the sky. This paper describes the design and implementation of the algorithm that is being used to determine the snapshots so as to minimize their number. The problem is NP-hard in general; the algorithm described is a heuristic, based on Lagriangian-relaxation and min-cost network flow. It gets within 5-15% of a naive lower bound, whereas using a ``uniform'' cover only gets within 25-35%.Comment: proceedings version appeared in ACM-SIAM Symposium on Discrete Algorithms (1998

Optimal location of single and multiple obnoxious facilities: Algorithms for the maximin criterion under different norms.

This thesis investigates the computational problem of locating obnoxious (undesirable) facilities in a way that minimizes their effect on a given set of clients (e.g. population centres). Supposing that the undesirable effects of such a facility on a given client are a decreasing function of the distance between them the objective is to locate these facilities as far away as possible from the given set of clients, subject to constraints that prevent location at infinity. Emphasis is given to the MAXIMIN criterion which is to maximize the minimum client-to-facility distance. Distances are measured either in the Euclidean or the rectilinear metric. The properties of the optimal solution to the single facility problem are viewed from different, seemingly unrelated, perspectives ranging from plane geometry to duality theory. In particular, duality results from a mixed integer programming model are used to derive new properties of the optimal solution to the rectilinear problem. A new algorithm is developed for the rectilinear problem where the feasible region is a convex polygon. Unlike previous approaches, this method does not require linear programming at all. In addition to this, an interactive graphical approach is proposed as a site-generation tool used to identify potential locations in realistic problems. Its main advantages are that it requires minimal user intervention and makes no assumptions regarding the feasible region. It has been applied in large scale problems with up to 1000 clients, whereas the largest reported application so far involved 10 clients. Alternative models are presented for the multi-facility problem as well. Each of them is based on different assumptions and is applicable to specific situations. Moreover, an algorithm is established for the two-facility problem based on the properties of the optimal solution. To the best of our knowledge this is the first attempt to address this problem in the plane. Finally, a number of unresolved issues, especially in the multi-facility problem, are outlined and suggested as further research topics