A new MILP approach for the facility process-layout design problem with rectangular and L/T shape departments

We propose a new approach for the facility process-layout design problem, and introduce new mixed-integer linear programming (MILP) formulations for solving the problem. In this approach, we consider simultaneously, in a process-layout setting, the shape and location of the departments within the facility as well as the internal arrangement of the machines within the departments. Two models are suggested, the first assumes a rectangular shape of the departments and the second allows non-rectangular departments defined by an L/T shape. For the latter model, new constraints are developed to assure a correct design of the L/T shapes and to avoid irregular department shapes, and cuts are added to shorten the solution time. Finally, we conduct an extensive numerical study, in which we show the capabilities of both formulations in solving problems of medium size, and the superiority of the L/T department shape solutions over the rectangular department solutions.