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In this work, a bi-objective multi-facility location-allocation problem is investigated, in which the locations of the customers and their arrivals are stochastic. We first formulate the problem as a continuous location-allocation model with no constraints on the capacity of the facilities. Then, we develop an approximated discrete model in which the facilities with limited capacities can be located on a set of candidate points. The proposed model has two objective functions that are evaluated using discrete event system simulation. The first objective is to minimize the expected total time the customers spend in the system until their services begin. The time that each customer spends in... 

Abstract In a recent work, Alizadeh et al. (2013) studied a capacitated multi-facility location-allocation problem in which customers had stochastic demands based on the Bernoulli distribution function. Authors considered capacitated sub-sources of facilities to satisfy customer demands. In this discrete stochastic problem, the goal was to find optimal locations of facilities among candidate locations and optimal allocations of existing customers to operating facilities so that the total sum of fixed costs of operating facilities, allocation costs of customers and expected values of servicing and outsourcing costs was minimized. The model was formulated as a mixed-integer nonlinear... 

This article studies a multi-product and multi-period location-routing-inventory problem in which location-allocation, inventory and routing decisions are to be taken in a three-level supply chain including suppliers, depots and customers. Products are distributed from depots to customers by a homogeneous fleet of vehicles. Backlogging is allowable on condition that the backlog quantity of each customer does not exceed a predefined fraction of his demand. A mixed-integer programming formulation is presented to describe the problem then a new hybrid heuristic algorithm based on the simulated annealing and imperialist competitive algorithm is designed to solve the model. Comprehensive... 

Many research works in mathematical modeling of the facility location problem have been carried out in discrete and continuous optimization area to obtain the optimum number of required facilities along with the relevant allocation processes. This paper proposes a new multi-objective facility-location problem within the batch arrival queuing framework. Three objective functions are considered: (I) minimizing the weighted sum of the waiting and the traveling times, (II) minimizing the maximum idle time pertinent to each facility, and (III) minimizing the total cost associated with the opened facilities. In this way, the best combination of the facilities is determined in the sense of... 

The k-level Uncapacitated Facility Location (UFL) problem is a generalization of the UFL and the k-median problems. A significant shortcoming of the classical UFL problem is that often a few very distant customers, known as outliers, can leave an undesirable effect on the final solution. This deficiency is considered in a new variant called UFL with outliers, in which, in contrast to the other problems that need all of the customers to be serviced, there is no need to service the entire set of customers. UFL with Penalties (UFLWP) is a variant of the UFL with outliers problem in which we will decide on whether to provide service for each customer and pay the connection cost, or to reject it... 

This paper introduces a new consensus protocol whose features are different from known consensus protocols available in the literature. The relation between discrete coverage algorithms over a convex polygon for solving a facility location problem (n-median problem) along with some notions in agreement over acyclic digraphs have been used to establish a novel constrained consensus protocol. Its convergence for the special case of acyclic digraphs with switching topology is presented. Extension of the results for other graph topologies and communication links are left for future works. © 2009 IEEE  

The rising disruptions of interdictors force supply chains’ designers to embody the protection decisions when locating the facilities. In the presence of variability in the intensity of disruptions, a risk measure is incorporated into the decision-making. The designer-interdictor bi-level problem, therefore, optimizes the joint location and protection decisions with respect to the conditional value-at-risk. This configuration has been absent from the literature. An accelerated modified Benders decomposition algorithm is developed and enhanced by being hybridized with a sample average approximation-based genetic algorithm. We examine how this new configuration influences the optimal solutions... 

In this paper, a novel multi-objective location model within multi-server queuing framework is proposed, in which facilities behave as M/M/m queues. In the developed model of the problem, the constraints of selecting the nearest-facility along with the service level restriction are considered to bring the model closer to reality. Three objective functions are also considered including minimizing (I) sum of the aggregate travel and waiting times, (II) maximum idle time of all facilities, and (III) the budget required to cover the costs of establishing the selected facilities plus server staffing costs. Since the developed model of the problem is of an NP-hard type and inexact solutions are... 

This paper addresses a bi-level mixed-integer nonlinear programming (MINLP) model for the competitive facility location problem in a closed-loop supply chain (CLSC), in which a firm (i.e., leader) aims at entering a market by locating new distribution and collection facilities, where a competitor (i.e., follower) already exists. The goal is to find the location and attractiveness of each facility going to be established by the leader who seeks to maximize its profit while also taking the follower's response into account. The attractiveness of each facility is a function of integer variables related to the facility's characteristics. Customer behavior is considered to be probabilistic based... 

This paper addresses a real-world problem faced by the public healthcare sector. The problem consists of both the patients’ and service provider's requirements (i.e., accessibility vs. costs) for locating healthcare facilities, allocating service units to those facilities, and determining the facilities’ capacities. The main contribution of this study is capturing both short-term and long-term uncertainties at the modelling stage. The queuing theory is incorporated to consider stochastic demand and service time as a short-term uncertainty, as well as a service level measurement. The developed nonlinear model is then converted into a linear model after introducing a new set of decision... 

Finding the most suitable location among some alternatives is one of the most important factors which could affect the whole success of the construction of a facility. The facility site selection is a multiple criteria decision making (MCDM) problem including both quantitative and qualitative criteria. Due to some difficulties in many real life cases, defining the exact values for MCDM problems is almost impractical and, it's preferable to use fuzzy values (fuzzy numbers) in this type of problems. In this study, we try to determine a suitable location for a Sewage Treatment Plant by using a new fuzzy weighted average (FWA) method. For this aim, ten different criteria is defined and then, by... 

In this paper, we propose an optimization framework to retrieve an optimal group of experts to perform a multi-aspect task. While a diverse set of skills are needed to perform a multi-aspect task, the group of assigned experts should be able to collectively cover all these required skills. We consider three types of multi-aspect expert group formation problems and propose a unified framework to solve these problems accurately and efficiently. The first problem is concerned with finding the top k experts for a given task, while the required skills of the task are implicitly described. In the second problem, the required skills of the tasks are explicitly described using some keywords but each... 

This paper presents a model for “Domestic Facility and Hub Location” in transportation network. Number of hubs and facilities are unknown and the objective is to minimize the transportation cost, lost demand penalty and facility set up costs. Also the distribution of demand among domestic facilities and hubs adheres to gravity rule. To solve the problem, sequential and integrated approaches were undertaken. In the sequential approach, domestic facilities were allocated and hubs were selected afterwards. However the integrated approach deals with both concurrently, with a more sophisticated steps reaching to the solution. This is mainly because the demand itself is highly dependent to where... 

A facility location problem deals with locating the best place for a group of facilities, among distinct demand points, minimizing a certain locational optimization function. In this paper, distributed, asynchronous, and scalable algorithms are presented for solving a facility location problem known as continuous n-median problem (generalized Fermat-Weber problem) via multi-agent robotic systems. The algorithms are discussed both in continuous and discrete time domain, and their validity is proved. It is also shown that the solution of this facility location problem is the set of points that are the geometric medians of their corresponding Voronoi cells  

The facility location problem and its related financial issues have a significant impact on the configuration of a supply chain structure (SCS). Although affording the setup cost of facilities requires a huge financial investment, a meticulous planning to recoup it has been neglected by an overwhelming majority of previous studies. To fill this gap, an economical investment plan of facilities is determined by striking a trade-off between the contribution of the stockholders’ capital and the loan arrangement. In the context of a multiperiod three-echelon SCS, the model also determines the optimum location of plants and the best supply and distribution patterns. The model maximizes the fill... 

We consider the stochastic queue core problem on a tree network. Our aim is to find an optimal path on a tree network subject to the average travel time of particles moving along the tree for service given by a server traversing along the optimal path. We assume that particles originating at a node on a tree network request their demands for service randomly and the server is modeled first by an M/M/1 and then by an M/G/1 queue using the FIFO discipline. We consider that all paths along which the particles travel are modeled with an M/G/c/c state-dependent queue with the particles being independent of each other having demands according to the Poisson distribution. Two algorithms are... 

We consider the stochastic queue core problem on a tree network. Our aim is to find an optimal path on a tree network subject to the average travel time of particles moving along the tree for service given by a server traversing along the optimal path. We assume that particles originating at a node on a tree network request their demands for service randomly and the server is modeled first by an M/M/1 and then by an M/G/1 queue using the FIFO discipline. We consider that all paths along which the particles travel are modeled with an M/G/c/c state-dependent queue with the particles being independent of each other having demands according to the Poisson distribution. Two algorithms are... 

In this paper, three fundamental properties of a potential field-based flocking algorithm, i.e. merging of neighbouring graphs during the system evolution, collision avoidance and convergence of position of the centre of mass of informed agents to that of virtual leader are discussed. Next, these properties are utilized to determine required number of informed agents based on initial position of uninformed ones and consequently reduce the domain of search in optimization problems defined for finding the optimal number of required informed agents. Finally, a new optimization framework is proposed, which benefits Voronoi diagrams in order to reduce the number of informed agents required for... 

In many service and industrial applications of the facility location problem, the number of required facilities along with allocation of the customers to the facilities are the two major questions that need to be answered. In this paper, a facility location problem with stochastic customer demand and immobile servers is studied. Two objectives considered in this problem are: (1) minimizing the average customer waiting time and (2) minimizing the average facility idletime percentage. We formulate this problem using queuing theory and solve the model by a genetic algorithm within the desirability function framework. Several examples are presented to demonstrate the applications of the proposed... 

We propose modified hybridizations of genetic algorithms with some neighborhood search based metaheuristics. In our hybrid algorithms, we consider gradually increasing probability for the application of the neighborhood search procedure on the best individuals as the number of iterations of the genetic algorithm increases. We implement the proposed hybrid algorithms and compare their performance with two other recently proposed hybrid algorithms which, in contrast, use the neighborhood search procedure on all the individuals of the population, two hybrid algorithms applying simulated annealing on the best individual in the papulation in every iteration and three non-hybrid metaheuristic...