Mathematical modeling of optimal multi fuzzy locations of facilities based on the assumed step distance among them in a convex set

In current global industries, production units aim to transport goods among suitably located facilities to reduce their production costs. However, rapid changes increase the uncertainty and ambiguity in the environment. Therefore, the use of mathematical optimization models based on fuzzy approaches to locate facilities is particularly important. In this study, we employ fuzzy linear programming to propose a model for locating new facilities among an existing set of facilities. We also give a convex solution and formulate a model for fuzzy data using integer linear programming. We then solve the model using an example where we minimize the total cost related to the placement of facilities based on the assumed step distance among them.