Locating a semi-obnoxious covering facility with repelling polygonal regions

A facility is to be located in the Euclidean plane to serve certain sites by covering them closely. Simultaneously, a set of polygonal areas must be protected from the negative effects from that facility. The problem is formulated as a margin maximization model. Necessary optimality conditions are studied and a finite dominating set of solutions is obtained, leading to a polynomial algorithm. The method is illustrated on some examples.     

Solving the semi-desirable facility location problem using bi-objective particle swarm

In this paper, a new model for the semi-obnoxious facility location problem is introduced. The new model is composed of a weighted minisum function to represent the transportation costs and a distance-based piecewise function to represent the obnoxious effects of the facility. A single-objective particle swarm optimizer (PSO) and a bi-objective PSO are devised to solve the problem. Results are compared on a suite of test problems and show that the bi-objective PSO produces a diverse set of non-dominated solutions more efficiently than the single-objective PSO and is competitive with the best results from the literature. Computational complexity analysis estimates only a linear increase in effort with problem size.     

Location of a semi-obnoxious facility with elliptic maximin and network minisum objectives

This paper considers the problem of locating a single semi-obnoxious facility on a general network, so as to minimize the total transportation cost between the new facility and the demand points (minisum), and at the same time to minimize the undesirable effects of the new facility by maximizing its distance from the closest population center (maximin). The two objectives employ different distance metrics to reflect reality. Since vehicles move on the transportation network, the shortest path distance is suitable for the minisum objective. For the maximin objective, however, the elliptic distance metric is used to reflect the impact of wind in the distribution of pollution. An efficient algorithm is developed to find the nondominated set of the bi-objective model and is implemented on a numerical example. A simulation experiment is provided to find the average computational complexity of the algorithm.     

Low complexity algorithms for optimal consumer push-pull partial covering in the plane

This paper considers a model for locating a consumer within a bounded region in the plane with respect to a set of n existing pull-push suppliers. The objective is to maximize the difference of total profits and costs incurred due to the partial covering of the consumer by the suppliers pull and push influence areas. We develop efficient polynomial time algorithms for the resulting problems in the rectilinear and the Euclidean planes where the bounded region is either a rectangle or a constant size polygon, respectively. Based on these solutions, we develop algorithms for evaluating efficiently the objective function at any possible location of the consumer inside the bounded region. We also employ the algorithms for the Euclidean optimization problem and the rectilinear query computation to solve efficiently their corresponding dynamic versions, where an appearance of a new supplier or an absence of an existing one occurs. Being easy to implement due to the extensive use of simple data structures, such as the balanced and binary segment tree, and the employment of standard mechanisms, such as the sweep line, the Voronoi diagram and the circular ray shooting, our solutions potentially have wide usability.     

A D.C. biobjective location model

In this paper we address the biobjective problem of locating a semiobnoxious facility, that must provide service to a given set of demand points and, at the same time, has some negative effect on given regions in the plane. In the model considered, the location of the new facility is selected in such a way that it gives answer to these contradicting aims: minimize the service cost (given by a quite general function of the distances to the demand points) and maximize the distance to the nearest affected region, in order to reduce the negative impact. Instead of addressing the problem following the traditional trend in the literature (i.e., by aggregation of the two objectives into a single one), we will focus our attention in the construction of a finite -dominating set, that is, a finite feasible subset that approximates the Pareto-optimal outcome for the biobjective problem. This approach involves the resolution of univariate d.c. optimization problems, for each of which we show that a d.c. decomposition of its objective can be obtained, allowing us to use standard d.c. optimization techniques.     

A bi-objective modeling approach applied to an urban semi-desirable facility location problem

This paper introduces a mixed-integer, bi-objective programming approach to identify the locations and capacities of semi-desirable (or semi-obnoxious) facilities. The first objective minimizes the total investment cost; the second one minimizes the dissatisfaction by incorporating together in the same function “pull” and “push” characteristics of the decision problem (individuals do not want to live too close, but they do not want to be too far, from facilities). The model determines the number of facilities to be opened, the respective capacities, their locations, their respective shares of the total demand, and the population that is assigned to each candidate site opened. The proposed approach was tested with a case study for a particular urban planning problem: the location of sorted waste containers. The complete set of (supported or unsupported) non-inferior solutions, consisting of combinations of multi-compartment containers for the disposal of four types of sorted waste in nineteen candidate sites, and population assignments, was generated. The results obtained for part of the historical center of an old European city (Coimbra, Portugal) show that this approach can be applied to a real-world planning scenario.