The value of the shortest loop covering all work centers in a manufacturing facility layout

In this study we develop mathematical models to design circular material flow systems. We first develop a tight formulation to find the shortest loop covering all work centers within a manufacturing facility layout. The shortest loop is an attractive solution for most types of conveyors and power-and-free systems, where the length of the flow path is the major driver of the total cost. We develop a primal as well as a dual graph formulation and discuss their one-to-one correspondence in node-edge as well as in connectivity constraints.