A mixed-integer programming formulation for optimizing the double row layout problem

The Double Row Layout Problem (DRLP) asks for an arrangement of machines on both sides of a straight line corridor so as to minimize the total cost for transferring materials among machines. The DRLP is NP-Hard and has practical relevance, specially in manufacturing systems design. In this paper, we drastically reduce the time required to solve the problem by constructing a new and effective mixed-integer linear programming (MILP) model of the DRLP. The new model was obtained by reformulating an existing MILP model. This includes tightening some constraints, introducing new variables, implementing constraints to link the new and original variables; and adding valid inequalities and a valid system of equations. To reduce the size of the reformulated model, we eliminate several of the new introduced variables by a substitution using the system of equations. The computational results demonstrate that the proposed model requires considerably smaller computational times compared to the ones in the literature. As a consequence, optimal solutions can now be efficiently found for larger instances of the problem. Previous studies have been able to optimally solve, within reasonable time, instances with size up to 16 machines, while with the new model four instances with 20 machines could be optimally solved.