On the Computational Performance of a Semidefinite Programming Approach to Single Row Layout Problems

The single-row layout problem (SRLP) is concerned with the arrangement of a given number of rectangular facilities next to each other along a line so as to minimize the total weighted sum of the center-to-center distances between all pairs of facilities. This problem is a special case of the unequalarea facility layout problem, and is also known in the literature as the onedimensional space allocation problem, see e.g. [12]. An instance of the SRLP consists of n one-dimensional facilities, denoted 1, . . . , n, with given positive lengths `1, . . . , `n, and pairwise weights cij . The objective is to arrange the facilities so as to minimize the total weighted sum of the center-to-center distances between all pairs of facilities. If all the facilities have the same length, the SRLP becomes a special case of the quadratic assignment problem, see e.g. [11]. Several applications of the SRLP have been identified in the literature. One such application arises in the area of flexible manufacturing systems, where machines within manufacturing cells are often placed along a straight path travelled by an automated guided vehicle, see e.g. [10]. Furthermore, the SRLP is closely related to the linear ordering problem, which also has a number of practical applications, see e.g. [5, 6, 13]. The SRLP was first studied by Simmons [14] who proposed a branchand-bound algorithm. Subsequently, Picard and Queyranne [12] developed a dynamic programming algorithm, and mixed integer linear programming models have also been proposed, most recently in [1]. While these algorithms