Extremely non-convex optimization problems: the case of the multiple obnoxious facilities location

The multiple facility location problem (MFLP) is to locate certain facilities so as to serve optimally a given set of customers, whose locations and requirements are known. When the facility locations have to be selected from a given set of candidate locations, the corresponding location problem becomes a discrete multiple facility location problem (DMFLP). In this study we consider a special case of DMFLP where multiple facilities that are of different type are to be placed (location decision) and assign customers to these facilities (allocation or assignment). The case will be discussed based on with and without interactions among new facilities. We then propose new heuristic solution methods and branch-and-bound algorithms. Computational results on randomly generated data in comparison with optimal solutions indicate that the new methods are both accurate and efficient.

The facility location problem is a widely studied classical operations research problem. To address this problem we implement an algorithm that calculates the exact solution for a given multiple capacitated facility location problem so long as that exists. Many issues of this problem belong to the NP-hard class of algorithms and as a result the computation time is disappointing for large networks. Therefore, we present a dynamic approximation algorithm for the solution of this problem that is capable to compute an approximation solution in an acceptable time interval. The aforementioned algorithms are integrated in a web-based Decision Support System (DSS). The DSS offers the possibility to create either a random or a custom graph and to evaluate both algorithms by performing alternative scenarios for the future development of the market. Finally, the DSS can export the results of the evaluation to a Microsoft Word document for further use.

In this paper we address the multiple obnoxious facility location problem. In this problem p facilities need to be spread within the unit square in such a way that they are far enough from each other and that their minimal distance from n communities, with known positions within the unit square, is maximized. The problem has a combinatorial component, related to the key observation made in Drezner (Omega 87:105–116, 2019) about the role played by Voronoi points. We propose a new approach, which exploits both the combinatorial component of the problem and, through continuous local optimizations, also its continuous component. We also propose techniques to limit the impact on computation times of the number n of communities. The approach turns out to be quite competitive and is able to return 24 new best known solutions with respect to the best results reported in Kalczynski (Optim Lett 16:1153–1166, 2022).

Locating certain facilities in predetermined sites is named the multiple facility location problems (MFLP). The objective of these kinds of problems is locating facilities to serve a given set of customers so that candidate sites and requirements are known. When the new facility sites have to be selected from a given set of candidate sites, the mentioned location problem becomes a discrete multiple facility location problem (DMFLP). In this paper, a special approach of DMFLP is considered where different multiple facilities have to be placed (location decision) and also customers have to be assigned to these facilities (allocation or assignment). The mathematical model of the proposed problem is developed, and with respect to the complexity of solving the mathematical model, especially in large scale, a new hybrid approach is proposed based on tabu search algorithm to solve the problem at each scale. Computational results on several randomly generated problems in comparison with a new proposed lower bound obtained from Lagrangian relaxation indicate that the proposed hybrid approach is both accurate and efficient.

We address the facility location problem for firms that sell an homogeneous product and compete on delivered prices. If the firms set equilibrium prices at each market, the problem can be seen as a location game for which there exists a Nash equilibrium if demand is inelastic. However, this equilibrium may be Pareto-inefficient and the firms could decide to collude if they can guarantee themselves higher payoffs than those prescribed by the equilibrium. The aim of this paper is to study the joint profit maximization problem to obtain a collusive solution of the location game (Pareto-efficient) and determine if such a solution is also a Nash equilibrium. We develop Integer Linear Programming models to find Pareto-efficient solutions for multiple and single facility location. Nash equilibria are obtained by the best response procedure. An empirical investigation is performed to compare the joint profit of the firms and the profit of each one of the firms, got through the Pareto-efficient locations, with those got through the Nash equilibrium.

There is a number of models that take into account the market competition in the location theory. Aboulian R. et al. formulated the location and design problem (CFLDP), in which the share of the market being served elastically varies depending on the location. The models with elastic demand are considered to be rather complicated and advantageous. We developed this problem and proposed the new one which combines CFLDP and classical p-median problem. In the given formulation a number of new facilities is fixed and is equal to p, so competitive p-median facility location and design problem (CPFLDP) has been derived. Therefore, the task can be considered as a clustering problem. In this paper we develop local search algorithms for CPFLDP. A computational experiment is carried out, the results are discussed.

Multiple voting location problems

Network location problems occur when new facilities are to be located on a network. The network of interest may be a road network, an air transport network, a river network, or a network of shipping lanes. For a given network location problem, the new facilities are often idealized as points, and may be located anywhere on the network; constraints may be imposed upon the problem so that new facilities are not too far from existing facilities. Usually some objective function is to be minimized. For single objective function problems, typically the objective is to minimize either a sum of transport costs proportional to network travel distances between existing facilities and closest new facilities, or a maximum of “losses” proportional to such travel distances, or the total number of new facilities to be located. There is also a growing interest in multiobjective network location problems. Of the approximately 100 references we list, roughly 60 date from 1978 or later; we focus upon work which deals directly with the network of interest, and which exploits the network structure. The principal structure exploited to date is that of a tree, i.e., a connected network without cycles. Tree-like networks may be encountered when having cycles is very expensive, as with portions of interstate highway systems. Further, simple distribution systems with a single distributor at the “hub” can often be modeled as star-like trees. With trees, “reasonable” functions of distance are often convex, whereas for a cyclic network such functions of distance are usually nonconvex. Convexity explains, to some extent, the tractability of tree network location problems.

The multi-period incremental service facility location problem

Solving multiple facilities location problems with separated clusters

Dispersed starting solutions in facility location: The case of the planar [formula omitted]-median problem

Optimization of the supply chain network: Simulation, Taguchi, and Psychoclonal algorithm embedded approach

The hub location problem arises in a variety of domains such as transportation and telecommunication systems. In many real-world situations, hub facilities are subject to disruption. This paper deals with the multiple allocation hub location problem in the presence of facilities failure. To model the problem, a two-stage stochastic formulation is developed. In the proposed model, the number of scenarios grows exponentially with the number of facilities. To alleviate this issue, two approaches are applied simultaneously. The first approach is to apply sample average approximation to approximate the two stochastic problem via sampling. Then, by applying the multiple cuts Benders decomposition approach, computational performance is enhanced. Numerical studies show the effective performance of the SAA in terms of optimality gap for small problem instances with numerous scenarios. Moreover, performance of multi-cut Benders decomposition is assessed through comparison with the classic version and the computational results reveal the superiority of the multi-cut approach regarding the computational time and number of iterations.

This is the first of two papers in which multiple criteria location problems (MCLPs) are discussed. In this paper the main aim is to formalize a discrete MCLP and to develop a generalized network model. A critical overview of various techniques for generating efficient solutions to multiple criteria decision problems is offered. The three most commonly used methods for tackling MCLPs, namely the weighted method, the noninferior set estimation method, and the constraint method, are discussed. The main purpose of the generating techniques is to determine an exact representation of or an approximation to the set of efficient solutions among which one can choose the best or most preferred solution (location plan). To identify the best solution some information about the decisionmaker's preferences or a decision rule is needed. Consequently, in paper 2 we focus on preference-based approaches to multiple criteria decisionmaking and relate them to the concept of interactive decision support. Specifically, optimizing decision rules (utility-function-based approaches) and satisficing decision rules (goal programming methods) are discussed. Advantages and disadvantages of these two approaches to solving the MCLP are highlighted. It is suggested that the utility-maximizing and satisficing decision rules are not mutually exclusive. Accordingly, a quasi-satisficing approach that merges these two decision rules is proposed. Also, a framework for an interactive decision support system (DSS) for tackling MCLPs is presented. The system incorporates the generalized network model into a quasi-satisficing approach. It is argued that the DSS data and analytical components can be effectively integrated by means of the interactive decision support concept which allows for exploring the problem and the alternative solutions both in decision space and in criterion outcome space.

The multiple source location problem is solved for a general array geometry using the principal of least-squares modeling. The incident wavefields may be a mixture of coherent and noncoherent sources that are broadband and/or narrowband. Furthermore, the wavefields may be plane waves and/or spherical waves. An effective algorithmic approach is developed for solving the multiple source location problem in the signal and covariance domains. In each domain, it is necessary to represent a set of vectors as a linear combination of array steering vectors. Using this property, a generic descent algorithmic approach is developed for estimating the wavefield directions of arrival. The success of such iterative approaches is critically dependent on the generation of good estimates to initialize the algorithm. An effective initialization procedure is developed for this purpose. Direction-of-arrival estimates which arise from the proposed procedure are empirically found to be unbiased and low variance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>