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  We consider the maximal covering location-allocation problem with multiple servers. The objective is to maximize the population covered, subject to constraints on the number of service centers, total number of servers in all centers, and the average waiting time at each center. Each center operates as an M/M/k queuing system with variable number of servers. The total costs of establishing centers and locating servers should not exceed a predetermined amount. We present a mathematical model for the problem, and propose a heuristic solution procedure with two local search algorithms for improving the solutions. Finally, some computational results are presented.

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  Since late 1960's, the emergency location problems, fire stations and medical emergency services have attracted the attention of researchers. Mathematical models, both deterministic and probabilistic, have been proposed and applied to find suitable locations for such facilities in many urban and rural areas. Here, we review some models proposed for finding the location of such facilities, with an eye on successfully implemented real life applications. We then propose an extension of the QM-CLAM model of Marianov and Serra (1998) to M/G/k systems, and suggest a GRASP type heuristic procedure for solving the problem. To improve the computed solution, local search heuristics are used. Sensitivity analysis and some computational results are also presented.

 

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Here, we investigate the classical p-median location problem on a network in which the vertex weights and the distances between vertices are uncertain. We propose a programming model for the uncertain p-median location problem with tail value at risk objective. Then, we show that it is NP-hard. Therefore, a novel hybrid modified binary particle swarm optimization algorithm is presented to obtain the approximate optimal solution of the proposed model. The algorithm contains the tail value at risk simulation and the expected value simulation. Finally, by computational experiments, the algorithm is illustrated to be efficient.

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Hubs are facilities that can decrease the cost of many-to-many distribution systems by acting as an interconnector between the demand and supply nodes. This type of facility can reduce the number of direct links needed in a logistics network. Hub location problems (HLP) have been discussed by many authors for more than four decades, and different approaches have been developed for modeling and solving this problem. We propose a fuzzy type I and II programming approach for a new model presented in the literature, i.e., the single allocation ordered median problem. The level of flow among the nodes will be considered as a fuzzy parameter. In the fuzzy type I approach, a linear programming problem with fuzzy parameters is used, while for the fuzzy type II approach, the rules of interval arithmetic are developed to simplify the problem to the fuzzy type I case. Finally, we apply our method on Kalleh Dairy Co. data of transportation as a case study and compare crisp and fuzzy situations. We show that the results of the fuzzy approach could be 2% better than the crisp approach and also discuss the pros and cons of fuzzy type I and type II approaches.

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Location theory is one of the most important topics in optimization and operations research. In location problems, the goal is to find the location of one or more facilities in a way such that some criteria such as transportation costs, customer traveling distance, total service time, and cost of servicing are optimized. In this paper, we investigate the goal Weber location problem in which the location of a number of demand points on a plane is given, and the ideal is locating the facility in the distance Ri , from the i-th demand point. However, in most instances, the solution of this problem does not exist. Therefore, the minimizing sum of errors is considered. The goal Weber location problem with the lp  norm is solved using the stochastic version of the LBFGS method, which is a second-order limited memory method for minimizing large-scale problems. According to the obtained numerical results, this algorithm achieves a lower optimal value in less time with comparing to other common and popular stochastic optimization algorithms. Note that although the investigated problem is not strongly convex, the numerical results show that the SLBFGS algorithm performs very well even for this type of problem.
 

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Health care facility systems are hierarchical as they consist of facilities at different levels such as clinics, health centers, and hospitals. Therefore, finding a proper location for the health care system can be categorized as a hierarchical location problem. Besides, partitioning a given region in a geographical area into different zones is very crucial to make sure the health services are available at their highest possible level for everyone in that region.  In this study, an optimization model for the integrated problem of hierarchical location and partitioning under uncertainty in the Iranian healthcare system is proposed. The objective function of this model maximizes the total social utility of districts while workload balance and distance limitation between the zones are considered as the main constraints. Since this study involves NP-hard problems, three metaheuristic algorithms, including Genetic, Salp Swarm Algorithm (SSA), and Grey Wolf Optimizer (GWO) were developed. The numerical results suggest that the Grey Wolf Optimizer (GWO) algorithm indicates a more appropriate level of performance in almost all responses compared to the other algorithms. Therefore, the case study was solved by the Grey Wolf Optimizer (GWO). Based on the results, 10 distrcis with their zones are identified to maximize the overall utility. A sensitivity analysis also performed to show the behavior of the model. It can be stated that the findings of this study can be utilized as a useful management tool in other organizations.

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This paper is concerned with presenting an exact algorithm for the Undirected Profitable Location Rural Postman Problem. This problem combines the profitable rural postman and facility location problems and also has some interesting real-life applications. Fixed costs are associated with end points of each profitable edge and the objective is to choose a subset of profitable edges such that the difference between the profit collected and the cost of opening facilities and traveling cost is maximized. A dominance relation is used to present an integer programming formulation for the problem and a branch and cut algorithm is developed for solving the problem and extensive numerical results on real-world benchmark instances are given to evaluate the quality of presented algorithms.
 

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In an uncapacitated facility location problem, the aim is to find the best locations for facilities on a specific network in order to service the existing clients at the maximum total profit or minimum cost. In this paper, we investigate the uncapacitated facility location problem where the profits of the demands and the opening costs of the facilities are uncertain values. We first present the belief degree-constrained, expected value and tail value at risk programming models of the problem under investigation. Then, we apply the concepts of the uncertainty theory to transform these uncertain programs into the corresponding deterministic optimization models. The efficient algorithms
are provided for deriving the optimal solutions the problem under investigation.