# Optimization of the Weighted Multi-Facility Location Problem Using MS Excel
### Literature Review  
There are a number of sources in the literature dealing with various types of tasks related to logistics and the use of heuristics algorithms in their solution. Resources focused on the multi-facility and single-facility location problem are important for our work. In [3] is presented a simple and effective Genetic Algorithm for the two-stage capacitated facility location problem (TSCFLP). The TSCFLP is a typical location problem that arises in freight transportation. In this problem, a single product must be transported from a set of plants to meet customers' demands, passing out by intermediate depots. The objective is to minimize the operation costs of the underlying two-stage transportation system thereby satisfying the demand and capacity constraints of its agents. For this purpose, a genetic algorithm is proposed. In paper [4] a new hybrid optimization method called the Hybrid Evolutionary Firefly-Genetic Algorithm is proposed, which is inspired by the social behavior of fireflies and the phenomenon of bioluminescent communication. The method combines the discrete Firefly Algorithm with the standard Genetic Algorithm. In [5] is described a Multiple Ant Colony System to solve the Single Source Capacitated Facility Location Problem (SSCFLP). Lagrangian heuristics have been shown to produce good solutions for the Single Source Capacitated Facility Location Problem. A hybrid algorithm, which combines Lagrangian heuristics and the Ant Colony System, is developed for the SSCFLP. In [6] a discrete version of particle swarm optimization (DPSO) is employed to solve an uncapacitated facility location problem that is one of the most widely studied in combinatorial optimization. In addition, a hybrid version with a local search is defined to get more efficient results. The results are compared with a continuous particle swarm optimization (CPSO) algorithm and two other metaheuristics studies, namely, genetic algorithm and evolutionary simulated annealing. In [7] is proposed a novel model for the reliable facility location problem. Instead of assuming the allocation of a fixed number of facilities to each customer as in the existing works, there is set the number of allocated facilities as an independent variable in the proposed model, which makes the model closer to real-life scenarios but more difficult to be solved by traditional methods. To handle it, EAMILS is proposed. This is a hybrid evolutionary algorithm, which combines a memorable local search (MLS) method and an evolutionary algorithm (EA). Article [8] is focused on the capacitated Multi-Facility Weber problem with rectilinear, Euclidean, squared Euclidean and lp distances. This problem deals with locating m capacitated facilities in the Euclidean plane so as to satisfy the demand of n customers at the minimum total transportation cost. The location and the demand of each customer is known and the transportation cost is proportional to the distance and the amount of flow between customers and facilities. Three new heuristic methods are presented, each of which is based on one of the three well-known metaheuristic approaches: simulated annealing, threshold accepting, and genetic algorithms. Paper [9] is focused on a new variant of the problem known as Single-Source Capacitated Multi-Facility Weber Problem, also known as continuous location-allocation problem, entails determining the locations of a predefined number of facilities in a planar space and their related customer allocations. To tackle the problem efficiently and effectively, an iterative two-phase heuristic algorithm is put forward. This algorithm produces superior results when assessed against the proposed simulated annealing algorithm. In article [10] an extension of the multi-Weber facility location problem is proposed with a rectilinear-distance in the presence of passages over a non-horizontal line barrier. For testing purposes, a benchmark is used based on the transformation of the main problem into an equivalent p-median problem.