This paper studies the problem of determining optimal facility location and network design decisions over multiple time periods considering equity-based objective. The problem determines optimal locations of facilities and the design of the underlying network, taking into account budget constraints on opening facilities and constructing links for each time period during the planning horizon. The objective is to minimize the sum over all time periods of the maximum travel time between nodes and facilities for each time period. We propose a mixed-integer, non-linear programming model to address the problem. The non-linear terms of the model relevant to the objective function can be easily converted to linear terms. Due to the high complexity of the model, CPLEX could not solve the problem efficiently. Hence, we propose two heuristics based on linear relaxation and a hybrid algorithm based on Variable Neighborhood Search to solve the problem. We tested the performance of the proposed algorithms on two data sets with up to 60 nodes, 708 candidate links, and 20 time periods compared to each other and the CPLEX solver.
