Developing a new model for a competitive facility location problem considering sustainability using Markov chains

In this paper, we consider a competitive facility location problem. The problem is defined for a new company planning to locate some new facilities (chain stores) in a geographical region where some other competitors have already located their facilities. We aim to propose a new model that the attractiveness function of each facility is developed based on the sustainable aspects. The attractiveness is based on the two aspects of sustainable development measurements called flexibility in supplying diverse products by a facility and the productivity of services in a facility. The objective is to maximize the profit in which the revenue is based on the amount of market share captured by the new facilities and the cost includes the cost of locating new facilities, the total tax paid to the government due to emissions of pollutants, and the cost of customers' dissatisfaction. The last type of cost occurs once a customer has to wait too long to receive services. Therefore, for providing justice in servicing, a chance constraint is proposed to control this dissatisfaction according to the Jackson Markov network. For an illustrative case study, the new company can capture 61.49% of the market share and 38.51% of the market remains for the existing companies. This can show that the current methodology leads to capture more market share in a competitive environment. An accelerated Benders' decomposition is used to solve the model, which is enhanced by disaggregating cuts, valid inequalities, and Pareto-optimal cuts. The proposed solution approach can improve the solution about 10% against the best previous method. Managerial implications and numerical examples illustrate the effectiveness and the applicability of the mathematical model and the solution approach. (c) 2020 Elsevier Ltd. All rights reserved.