One-Dimensional Space Allocation: An Ordering Algorithm

Abstract

The space-allocation problem arises when an architect tries to arrange rooms of fixed area but unspecified shape on a floor plan in such a way as to minimize a given linear combination of the distances between all pairs of rooms. In one dimension, this is the problem of ordering line segments along a simple axis or rooms along one side of a corridor. This paper devises an efficient branch-and-bound algorithm for finding the optimal ordering, and shows that the algorithm can solve one special type of facilities-to-locations assignment problem. Space allocation in two dimensions is also discussed briefly.

Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes

“…The first three problems come from Simmons (1969), while the larger two problems were first considered in Heragu and Kusiak (1988 We point out that these five solutions were the best solutions found by the metaheuristics of de Alvarenga et al (2000), but with no proof (or claim) of global optimality. We also observe that for instance Lit-5, a layout of cost 44466.5 was reported in Kumar et al (1995), which our lower bound contradicts.…”

“…The SRFLP was first studied by Simmons (1969) who proposed a branch-and-bound algorithm. Subsequently, Picard and Queyranne (1981) developed a dynamic programming algorithm.…”

Provably near-optimal solutions for very large single-row facility layout problems

“…If all the facilities have the same length, the SRFLP becomes an instance of the linear arrangement problem, see, e.g., [25], which is itself a special case of the quadratic assignment problem; see, e.g., [10]. Several practical applications of the SRFLP have been identified in the literature, such as the arrangement of departments on one side of a corridor in supermarkets, hospitals, or offices [31], the assignment of disk cylinders to files [29], the assignment of airplanes to gates in an airport terminal [33], and the arrangement of machines in flexible manufacturing systems, where machines within manufacturing cells are often placed along a straight path travelled by an automated guided vehicle [20]. We refer the reader to the book of Heragu [18] for more information.…”

“…Simmons [31] was the first to state and study the SRFLP, and proposed a branch-and-bound algorithm. Simmons [32] mentioned the possibility of extending the dynamic programming algorithm of Karp and Held [22] to the SRFLP, which was done by Picard and Queyranne [29].…”

A polyhedral approach to the single row facility layout problem

“…The 'S' instances are due to Simmons [26]. The two 'H' instances were derived by Heragu & Kusiak [15], by modifying the famous instances of the Quadratic Assignment Problem (QAP) due to Nugent et al [21].…”