A maximum capture model with interval facility number and cost objective function

The maximum capture problem seeks to find a suitable location for facilities in the network space and in a competitive condition. In this problem, the new company intends to enter the market with the aim of capturing more demand. In this study, the cost factor is considered to be a separate objective function and a bi-objective model is proposed. The number of facilities parameter is considered to be an interval and for its upper and lower bounds calculations two models are proposed. To obtain upper bound a model with the maximum capture objective and the maximum budget constraint and to obtain lower bound a model with the minimum cost objective and the minimum market share constraint. To solve the proposed model, a goal programming method is used. The steps of the research methodology and modelling are shown in a case study from Yazd city. The results show that if the weight of the objective functions is assumed to be equal and the investor neglect 7 % of the market share, 55% of initial investment could be saved.