A neural network approach to facility layout problems

A near-optimum parallel algorithm for solving facility layout problems is presented in this paper where the problem is NP-complete. The facility layout problem is one of the most fundamental quadratic assignment problems in Operations Research. The goal of the problem is to locate N facilities on an N-square (location) array so as to minimize the total cost. The proposed system is composed of N × N neurons based on an artificial two-dimensional maximum neural network for an N-facility layout problem. Our algorithm has given improved solutions for several benchmark problems over the best existing algorithms.     

The facility layout problem

In this paper, the facility layout problem is surveyed. Various formulations of the facility layout problem and the algorithms for solving this problem are presented. Twelve heuristic algorithms are compared on the basis of their performance with respect to eight test problems commonly used in the literature. Certain issues related to the facility layout problem and some aspects of the machine layout problem in flexible manufacturing systems are also presented.     

A spring-embedding approach for the facility layout problem

The facility layout problem is concerned with finding the most efficient arrangement of a given number of departments with unequal area requirements within a facility. The facility layout problem is a hard problem, and therefore, exact solution methods are only feasible for small or greatly restricted problems. In this paper, we propose a spring-embedding approach that unlike previous approaches results in a model that is convex. Numerical results demonstrating the potential of our model and the efficiency of our solution procedure are presented.     

On unboundedness of maximal operators for directional Hilbert transforms

We show that for any infinite set of unit vectors in the maximal operator defined by

is not bounded in .

     

Applying the sequence-pair representation to optimal facility layout designs

We present a new formulation for the facility layout problem based on the sequence-pair representation, which is used successfully in VLSI design. By tightening the structure of the problem with this formulation, we have extended the solvable solution space from problems with nine departments to problems with eleven departments.     

A polyhedral approach to the single row facility layout problem

The single row facility layout problem (SRFLP) is the NP-hard problem of arranging facilities on a line, while minimizing a weighted sum of the distances between facility pairs. In this paper, a detailed polyhedral study of the SRFLP is performed, and several huge classes of valid and facet-inducing inequalities are derived. Some separation heuristics are presented, along with a primal heuristic based on multi-dimensional scaling. Finally, a branch-and-cut algorithm is described and some encouraging computational results are given.     

A two-stage mathematical-programming method for the multi-floor facility layout problem

We present a two-stage method using mathematical-programming techniques for finding high-quality solutions to the multi-floor facility layout problem. The first stage is a mixed-integer linear program that assigns departments to floors such that the total of the vertical interaction costs between departments on different floors is globally minimized. The second stage finds a locally optimal layout for each floor. Two versions of the proposed approach are considered. The first solves the layout of each floor independently of the other floors, and is suitable for up to one elevator location. The second solves the layout of all floors simultaneously and can handle multiple elevator locations. Preliminary computational results show that both versions of the proposed method can efficiently provide a good variety of high-quality solutions in a short amount of time for medium and large-scale problem instances.     

Heuristics for the dynamic facility layout problem with unequal-area departments

The dynamic facility layout problem (DFLP) is the problem of finding positions of departments on the plant floor for multiple periods (material flows between departments change during the planning horizon) such that departments do not overlap, and the sum of the material handling and rearrangement costs is minimized. In this paper, the departments may have unequal-areas and free orientations, and the layout for each period is generated on the continuous plant floor. Because of the complexity of the problem, only small-size problems can be solved in reasonable time using exact techniques. As a result, a boundary search (construction) technique, which places departments along the boundaries of already placed departments, is developed for the DFLP. The solution is improved using a tabu search heuristic. The heuristics were tested on some instances from the DFLP and static facility layout problem (SFLP) literature. The results obtained demonstrate the effectiveness of the heuristics.     

A convex optimisation framework for the unequal-areas facility layout problem

The unequal-areas facility layout problem is concerned with finding the optimal arrangement of a given number of non-overlapping indivisible departments with unequal area requirements within a facility. We present a convex-optimisation-based framework for efficiently finding competitive solutions for this problem. The framework is based on the combination of two mathematical programming models. The first model is a convex relaxation of the layout problem that establishes the relative position of the departments within the facility, and the second model uses semidefinite optimisation to determine the final layout. Aspect ratio constraints, frequently used in facility layout methods to restrict the occurrence of overly long and narrow departments in the computed layouts, are taken into account by both models. We present computational results showing that the proposed framework consistently produces competitive, and often improved, layouts for well-known large instances when compared with other approaches in the literature.     

An efficient genetic algorithm for single row facility layout

The single row facility layout is the NP-Hard problem of arranging facilities with given lengths on a line, so as to minimize the weighted sum of the distances between all pairs of facilities. Owing to its computational complexity, researchers have developed several heuristics to obtain good quality solutions. In this paper, we present a genetic algorithm called GENALGO to solve large single row facility layout problem instances. Our algorithm uses standard genetic operators and periodically improves the fitness of all individuals. Our computational experiments show that our genetic algorithm yields high quality solutions in spite of starting with an initial population that is randomly generated. Our algorithm improves the previously best known solutions for the 19 instances of 58 benchmark instances and is competitive for most of the remaining ones.     

An improved two-stage optimization-based framework for unequal-areas facility layout

The unequal-areas facility layout problem is concerned with finding the optimal arrangement of a given number of non-overlapping indivisible departments with unequal area requirements within a facility. We present an improved optimization-based framework for efficiently finding competitive solutions for this problem. The framework is based on the combination of two mathematical optimization models. The first model is a nonlinear approximation of the problem that establishes the relative position of the departments within the facility, and the second model is an exact convex optimization formulation of the problem that determines the final layout. Aspect ratio constraints on the departments are taken into account by both models. Our computational results show that the proposed framework is computationally efficient and consistently produces competitive, and often improved, layouts for well-known instances from the literature as well as for new large-scale instances with up to 100 departments.     

An efficient tabu algorithm for the single row facility layout problem

The general goal of the facility layout problem is to arrange a given number of facilities to minimize the total cost associated with the known or projected interactions between them. One of the special classes of the facility layout problem is the Single Row Facility Layout Problem (SRFLP), which consists of finding an optimal linear placement of rectangular facilities with varying dimensions on a straight line. This paper first presents and proves a theorem to find the optimal solution of a special case of SRFLP. The results obtained by this theorem prove to be very useful in reducing the computational efforts when a new algorithm based on tabu search for the SRFLP is proposed in this paper. Computational results of the proposed algorithm on benchmark problems show the greater efficiency of the algorithm compared to the other heuristics for solving the SRFLP.     

A scatter search algorithm for the single row facility layout problem

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, with the objective of minimizing the weighted sum of the distances between all pairs of facilities. The problem is NP-hard and research has focused on heuristics to solve large instances of the problem. In this paper we present a scatter search algorithm to solve large size SRFLP instances. Our computational experiments show that the scatter search algorithm is an algorithm of choice when solving large size SRFLP instances within limited time.     

Flexible facility interior layout: a real options approach

This paper explores a case of flexible facility layout, in which the layout process can be carried out in a dynamic manner responding to changing demands. We consider a facility such as an office building that needs to partition its interior space into units of different sizes and allocate them to different users. Facing different demands, each of which requires a different space size, the management of the facility needs to constantly exercise managerial real options, such as partitioning a big unit to small units and merging small units to a big one. Modelling the demand uncertainties as stochastic processes, we use the Monte Carlo simulation and solve rolling two-stage stochastic programs over time to value the flexible interior layout. Through numerical tests, we demonstrate that effectively and timely exercising the managerial options can significantly increase profit and service quality. Focusing on the dynamic behaviour of the facility interior layout, the proposed options-based approach aims to improve facility management by proactive decision strategies. The approach may also be extended to facility expansion, maintenance and rehabilitation to increase service life and maintain service quality.     

Single- and multi-objective facility layout with workflow interference considerations

The effect of workflow interference is a major concern in facility layout design. Yet, despite the extensive amount of research conducted on the facility layout problem, very little has been done to incorporate interference as part of an overall approach to layout design. This paper examines the impact of workflow interference considerations on facility layout analyses. Linear and nonlinear integer programming formulations of the problem are presented. The structural properties of the resulting formulations, as applied to facility design, are investigated. Finally, a multi-objective approach to facility layout design is presented, incorporating the traditional distance-based objective with that of workflow interference.     

On the birational unboundedness of higher dimensional {\mathbb{Q}}-Fano varieties

We show that the family of (-factorial and log terminal) -Fano n-folds with Picard number one is birationally unbounded for n ≥ 6. T. Okada is partially supported by JSPS Research Fellowships for Young Scientists.