A mixed-integer programming formulation of the double row layout problem based on a linear extension of a partial order

Abstract

The double row layout problem (DRLP) occurs in automated manufacturing environments, where a material-handling device transports materials among machines arranged in a double-row layout, i.e. a layout in which the machines are located on either side of a straight line corridor. The DRLP is how to minimize the total cost of transporting materials between machines. The problem is NP-Hard and one great challenge nowadays is how to solve problem instances in reasonable computational times. In this paper, we give a new mixed-integer programming model of the DRLP, which is based on a linear extension of a partial order. In addition, we propose a reformulation of this model, which yields stronger results. The new models have the least number of 0–1 variables in comparison with previous models in the literature. Computational experiments demonstrate that the proposed models obtain optimal solutions faster than previously published ones.