Flow network design for manufacturing systems layout

One way to solve a facilities layout planning problem is to use a component approach; the components being (a) block design, (b) input/output station location, (c) material flow network design, and (d) aisle netting out (accounting for aisle space). Material flow network design is an important component of this approach. In this paper a shortest rectilinear flow network problem is defined and formulated as an optimization problem. A Lagrangean relaxation of the problem gives separable, linear-time solvable, shortest-path problems. A heuristic, with ties to this formulation, is presented. An expression for the gap between the heuristically derived solution and the optimal solution is given. Some computational experiments using the heuristic are reported.