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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... 

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... 

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... 

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... 

In this paper, we propose an optimization framework to retrieve an optimal group of experts to perform a given multi-aspect task/project. Each task needs a diverse set of skills and the group of assigned experts should be able to collectively cover all required aspects of the task. We consider three types of multiaspect team formation problems and propose a unified framework to solve these problems accurately and efficiently. Our proposed framework is based on Facility Location Analysis (FLA) which is a well known branch of the Operation Research (OR). Our experiments on a real dataset show significant improvement in comparison with the state-of-the art approaches for the team formation... 

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... 

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 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... 

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  

Nowadays, using Blockchain Technology (BCT) is growing faster in each country. It is essential to apply BCT in Supply Chain Network Design (SCND) and is considered by the designer and manager of SC. This research indicates Viable Supply Chain Network Design (VSCND) by applying BCT. A new form of two-stage robust optimization is suggested. Facility locations and activation BCT for VSCND is the first stage of decisions; finally, we determine flow transshipment between components in the next stage. The GAMS-CPLEX is used for solving the model. The results show that running BCT will decrease 0.99% in costs. There is an economic justification for using BCT when demand is high. A fix-and-optimize... 

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 examines the spoke and hub location decisions in a routing problem. To minimize the total cost, the study analyzes on how to locate the spokes, hubs and the allocation of spoke nodes to hub nodes, the routing among the nodes and the number of vehicles assigned to each hub thoroughly. As there might be no facility assigned to some points, unsatisfied demands must be distributed to other nodes with available facilities. Furthermore, the realized demand is determined by considering the perceived utility of each path, using The Gravity rule. For this purpose, the proposed nonlinear model is transformed into a linear programming model, where some tightening rules and preprocessing... 

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... 

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 research, a maximal covering location problem (MCLP) with real-world constraints such as multiple types of facilities and vehicles with different setup costs is taken into account. An original mixed integer linear programming (MILP) model is constructed in order to find the optimal solution. Since the problem at hand is shown to be NP-hard, a constructive heuristic method and a meta-heuristic approach based on genetic algorithm (GA) are developed to solve the problem. To find the most effective solution technique, a set of problems of different sizes is randomly generated and solved by the proposed solution methods. Computational results demonstrate that the heuristic method is... 

Both governments and health-related organizations must immediately act after a natural disaster happened, i.e., providing essential equipment and medicines to injured people as soon as possible and adequately. To achieve this goal, planning the distribution and the inventory of crucial items during a scenario of disasters, a relief supply chain network with four echelons, namely suppliers, warehouses, disaster locations, and medical centers, is designed. In this work, a bi-objective nonlinear mathematical model that follows two main concerns is proposed. First, we wish to minimize the supply chain costs in terms of both the traveling time between echelons and the inventory costs. Second, we... 

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... 

Bus terminal assignment with the objective of maximizing public transportation service is known as bus terminal location problem (BTLP). We formulate the BTLP, a problem of concern in transportation industry, as a p-uncapacitated facility location problem (p-UFLP) with distance constraint. The p-UFLP being NP-hard (Krarup and Pruzan, 1990), we propose evolutionary algorithms for its solution. According to the No Free Lunch theorem and the good efficiency of the distinctive preserve recombination (DPX) operator, we design a new recombination operator for solving a BTLP by new evolutionary and memetic algorithms namely, genetic local search algorithms (GLS). We also define the potential... 

The maximal covering location problem (MCLP) is a challenging problem with numerous applications in practice. Previous publications in the area of MCLP proposed models and presented solution methodologies to solve this problem with up to 900 nodes. Due to the fact that in real-life applications, the number of nodes could be much higher, this paper presents a customized Genetic Algorithm (GA) to solve MCLP instances, with up to 2500 nodes. Results show that the proposed approach is capable of solving problems with a fair amount of exactness. In order to fine-tune the algorithm, Tukey's Least Significant Difference (LSD) tests are employed on a set of test problems