## 1 Introduction
### Literature Review  
The problem of location-allocation was raised by [PERSON]. He determined the location of a market by minimizing the total distance between the markets and their demands [18]. This was a Median problem. With the evolution of hardware and software, several other location-allocation problems were developed and tested with different target functions and constraints. Location-allocation problemsbelong to the category of NP-hard issues [11] and are a subset of combinatorial optimization problems. Solving various location-allocation problems using exact methods is very time-consuming. For this reason, most research is undertaken using metaheuristic algorithms. For example, [PERSON] et al compared the Genetic, Simulated Annealing, and Tabu Search algorithms in determining the location of various facilities under time constraints, solution constraints, and unconstrained criteria. They found that implementation of the Simulated Annealing and Genetic algorithms depended on the type of problem, as well as the problem conditions [19]. For this reason, the authors used the two algorithms Simulated Annealing and Tabu Search, to solve their location-allocation problem. [PERSON] et al. developed an evolutionary Simulated Annealing algorithm to determine the location of uncapacitated facilities on a large scale [20]. The Simulated Annealing method is simple in terms of execution and yields results comparable with the Genetic algorithm. [PERSON] et al. applied the Simulated Annealing algorithm to a location-allocation problem, thereby reducing the solving time [21]. The results of this research show that Simulated Annealing algorithm is a simple and good algorithm in solving location-allocation problems. [PERSON] et al. [14] developed a hybrid algorithm for solving allocation problems of emergency evacuation based on Tabu search algorithm. The results of this research show that metaheuristic algorithms are good ones in solving emergency location-allocation problems. [PERSON] et al. compared Genetic, Tabu Search and Simulated Annealing algorithms in location problem and network modeling in thermal energy generation. The effectiveness of each algorithm was examined, and the results showed the efficiency of the Simulated Annealing algorithm in solving this type of problem [22]. [PERSON] et al. solved the problem of multi-objective location-allocation of fire stations in Tehran using the P-Median model and two Genetic and Simulated Annealing algorithms. The results showed the efficiency of the Genetic algorithm in a great number of demands [23]. All of these investigations were done with the same four location-allocation models. In 2014, [PERSON] and [PERSON] developed the VAOMP unified approach that can solve various location-allocation problems with a target function. This model can identify and construct new models that satisfy human needs. Too, the VAOMP problem is NP-hard, since it encompasses NP-hard problems, such as the P-Center problem and the P-Median problem as special cases. [PERSON] and [PERSON] showed that using ILP takes a long computation time in finding optimal solutions [7]. The authors used the developed [PERSON] and [PERSON] model to solve their problem, which lacks the capacity condition. Therefore, [PERSON] et al. solved the VAOMP problem for the same case study using the Tabu Search algorithm. Their Computational results showed that the Tabu Search algorithm can often find the solutions in seconds, the solutions that are better than those obtained using the ILP method in hours or a day [1]. They proposed using a Simulated Annealing algorithm to solve different location-allocation problems with the VAOMP model. Hitherto, no research has been undertaken with the newly developed VAOMP model. [PERSON] et al. from the perspective of spatial justice, examined the condition of fire stations using two algorithms, Simulated Annealing and Tabu Search, using VAOMP in solving location-allocation problem. The results showed that the location of some of the existing facilities for service is not suitable [24].