Discrete Mathematical Programming for Public Library Location with a Line Barrier and K Passages: a Practical Application in Babolsar City

This paper presents a discrete location problem to find p new public facilities’ location among the potential points with trespassing through K passages on a line barrier that is frequently encountered in practice. Indeed allocation of user points to established public facilities is also obtained by the proposed mathematical programming model. A Lagrangian relaxation algorithm in order to find the best location for a number of public centers is developed. To improve the solution quality, two constructive algorithms for initialization are presented, Myopic Algorithm and Greedy Algorithm. The empirical illustration for location of the public libraries and user allocation at the scale of Babolsar city is implemented.