New heuristics for competitive and hiearchial facility location problem

Abstract

A lot of versions of the facility location problem have been studied for a long time. This work considers the combination of two versions Competitive Facility Location and Hierarchical Facility Location Problem. A company wants to locate hierarchical facilities to a market area where there is a competitor that already located its hierarchical facilities. The objective is to maximize the total net profit which is obtained by subtracting the total cost of constructing a chain from the total captured market share. Hierarchical structure is successively inclusive service hierarchy model and all facilities are assumed to be in two levels. Our main assumption is that a customer splits his/her demand (buying power) among the chains proportional to the attraction level to the closest facility of each chain. This patronizing behavior is a hybrid of probabilistic and deterministic patronizing behavior models. The contribution of this study is treating the attractiveness of facilities as continuous decision variables. Also the number of each level of facilities to be opened is not predetermined. A nonlinear mixed integer model is developed for the problem. Firstly the SBB solver within GAMS suite v22.0 is employed. Then a Simulated Annealing Algorithm is developed and within this algorithm two different strategies each having different add-drop criteria are employed as solution procedure. The first strategy consists of add-drop second closest criteria (SASCAD) whereas the second strategy uses random add-drop criteria (SARAD) for neighborhood search. In both strategies Simplex Search and Fibonacci Search algorithms are employed to find the attractiveness values. Then these strategies are compared and it is seen that SASCAD results better however it is more time consuming. SARAD achieved to catch the same results with the SASCAD in most of the experiments moreover it takes less time.