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A quadratic assignment problem (QAP), which is a combinatorial optimisation problem, is developed to model the problem of locating facilities with material flows between them. The aim of solving the QAP formulation for a facility layout problem (FLP) is to increase a system’s operating efficiency by reducing material handling costs, which can be measured by interdepartmental distances and flows. The QAP-formulated FLP can be viewed as a discrete optimisation problem, where the quadratic objective function is optimised with respect to discrete decision variables subject to linear equality constraints. The conventional approach for solving this discrete optimisation problem is to use the linearisation of the quadratic objective function whereby additional discrete variables and constraints are introduced. The adoption of the linearisation process can result in a significantly increased number of variables and constraints; solving the resulting problem can therefore be challenging. In this paper, a new appro...

In this paper we discuss two particular layout problems, namely the Single-Row Equidistant Facility Layout Problem (SREFLP) and the Single-Row Facility Layout Problem (SRFLP). Our aim is to consolidate the two respective branches in the layout literature. We show that the SREFLP is not only a special case of the Quadratic Assignment Problem but also a special case of the SRFLP. This new connection is relevant as the strongest exact methods for the SRFLP outperform the best approaches specialised to the SREFLP. We describe and compare the exact approaches for the SRFLP, the SREFLP and Linear Arrangement that is again a special case of the SREFLP. In a computational study we showcase that the strongest exact approach for the SRFLP clearly outperforms the strongest exact approach tailored to the SREFLP on medium and large benchmark instances from the literature.

The Quadratic Assignment Problem (QAP) is a difficult and important problem studied in the domain of combinatorial optimisation. It is possible to solve QAP instances with 10--20 facilities using exhaustive parallel algorithms within a few days on a cluster machine. However, large QAP instances with more than 100 facilities are not solvable using exhaustive techniques. We have explored a variety of Genetic Algorithm crossover operators for this problem and verified its performance experimentally using well-known instances from the QAPLIB library. By increasing the number of processors, generations and population sizes we have been able to find solutions that are the same as (or very close to) the best reported solutions for large QAP instances in QAPLIB. In order to parallelise the Genetic Algorithm we generate and evolve separate solution pools on each cluster processor, using an island model. This model exchanges 10% of each processor’s solutions at the initial stages of optimisation. We show experiment...

In real decision making problems, many conflicting objectives have to be taken into account. With increasing awareness of this, multi-objective problems have become more and more popular. Similarly, the design of the multi-objective facility layout problem (MOFLP) has generally been recognised as an important issue in the modern manufacturing system. The MOFLP is formulated as a quadratic assignment problem (QAP) which is NP-hard and solving MOFLP is a tough problem. A new three-level AHP-based heuristic algorithm for resolving the MOFLP is presented here. It also presents a new normalisation procedure (H-1), and a new heuristic method (H-2) for generating objective weights. The proposed approach consists of three levels. The first level applies AHP to generate paired comparison matrices, the consistency of matrix, to convert inconsistent matrices into consistent ones and then generate a qualitative objective matrix; the second level applies normalisation procedure (H-1) to normalise matrices of qualitati...

The Generalised MAchine Layout Problem (GMALP) is a generalisation of the integrated machine and layout problem, which is an extension of the machine layout problem. More specifically, the GMALP is the designing of a facility layout by defining the product mix, selecting the number of machines to be used, assigning these machines to the plant floor, and assigning products to machines such that total profit is maximised. Moreover, the GMALP integrates the quadratic assignment problem with a multicommodity flow problem. Therefore, the GMALP is a computationally intractable problem. Consequently, a mixed-integer nonlinear programming model was developed and used to solve small problem instances. Also, two simple construction algorithms and a tabu search (TS) heuristic were developed for solving large GMALP instances in acceptable computation times. In addition, a test dataset was used to evaluate the performances of the TS heuristic using the different construction algorithms. The results show that the TS he...

Multi-objective facility layout problem (mFLP) generates a different layout by varying objectives weights. Since the selection of objective weights in mFLP is critical, stages of designing layout having multiple objectives, the objective weights therefore play an important role in the layout design of mFLP. In practice, it is selected randomly by the layout designer based on his/her past experience that restricts the layout designing process completely designer dependent and thus the layout varies from designer to designer. This paper aims to resolve the issues of selecting the objective weight for each objective. We propose four methods to determine objective weight which makes the design process of mFLP completely designer independent.

In this paper, we are considering the quadratic assignment model (QAP) of the facility layout problem (FLP) which is known to be NP-hard. We relax the integer constraints of the QAP and solve it on a commercially available package called LINGO 8. In the optimal solution so obtained, Xij s take real values between zero and one. We identify promising Xij s having a value strictly greater than 0.5 in the optimal solution and set them to one. We add the constraints (Xij = 1) associated with promising Xij s into the QAP (with integer restrictions) and resolve using LINGO 8. In all the cases attempted we obtained a superior feasible solution to the QAP which was further improved by the proposed modified simulated annealing (MSA) procedure. An encouraging comparative performance of this procedure is thus reported.

This paper describes a heuristic algorithm for solving the plant/facility location problem by applying ant-colony optimization meta-heuristic. The facility location problem is discussed, and a mathematical formulation is presented. The problem is then modelled as a quadratic assignment problem. An ant algorithm is developed to solve the problem. The results reveal that the proposed algorithm can be adaptively constructed to solve discrete plant location problems. This has been applied to a set of known test problems and appears to be able to compete with other current solutions with encouraging results.

Because of bottleneck machines, the assignment of machine-cells to locations is interrelated with the machines' relative locations, and it makes the problem complicated to solve optimally. This paper prescribes an assignment of machine-cells to linear locations in order to minimize the inter-cell material handling cost incurred due to bottleneck machines in a cellular manufacturing system. This problem is formulated as a quadratic assignment problem (QAP). The optimal results can be obtained for a limited size of QAP. A 3-pair comparison heuristic is devised to partially overcome the dimensional problem for solving a large example. Later, an improvement heuristic called the 'bubble search' technique is developed to obtain a better solution, followed by the development of a lower bound on the QAP problem. Numerical examples are presented to illustrate the two heuristic procedures. A comparison between the optimal and heuristic solutions is also provided to evaluate the performance of the heuristics. Empiri...

Cellular manufacturing has received a considerable amount of attention in the research literature as an approach for improving the performance of manufacturing facilities. However, recent studies have shown that cellular layouts are not always superior to the traditional functional machine layout. We propose a model that does not require the machines to be placed in a functional layout or in a cellular arrangement, but allows the material flow requirements to dictate the machine placement. The model is formulated as an aggregation of the quadratic assignment problem and several network flow problems coupled with linear side constraints. A mixed integer program is presented to find the optimal solution for small problems, and heuristics are developed to solve larger problems. Computational results evaluating the quality of the solution methodologies are also presented.

This paper addresses two real-life assignment problems. In both cases, the number of employees to whom tasks should be assigned is significantly greater than the number of tasks. In the simple job ...

The traditional quadratic assignment problem (QAP) assumes handling costs between two facilities are directly proportional to the distance between them. This linearity assumption is, in general, untrue in actual industrial settings due to changing equipment requirements as the distance between facilities changes. Therefore, this paper presents a model that reflects actual industrial practice in the design of layouts, assignment of departments to sites, and the selection of proper mode of handling between departments in response to the distances between department pairs. The paper discusses how data can be represented to make it easier to develop such a model and shows the methodology to solve the model. The paper concludes with an analysis of modelling error as a way to illustrate the cost associated with applying the wrong model as seems to be reflected in the traditional applications of the model.

The design of the facility layout of a manufacturing system, usually formulated and solved as a quadratic assignment problem (QAP), is of tremendous importance for its effective utilization. In this paper we discuss a new implementation of the tabu search metaheuristic to solve the QAP. Our tabu search implementation includes recency-based and long term memory structure, dynamic tabu list size strategies, and intensification and diversification strategies. The tabu search algorithm converges with a reasonable speed from any random initial solution to very good layouts. Our extensive computational experiments, including statistical analysis and library analysis, strongly support the superiority of our tabu search implementation (we refer to it as (CK)) over existing algorithms in the literature.

In a dynamic facilities layout problem, the objective is to minimize total costs: the flow costs over a series of discrete time periods plus the rearrangement costs of changing layouts between time periods. By assuming unit department sizes, the problem is modelled as a modified quadratic assignment problem. Five algorithms are modified to include the dynamic aspects. A cutting plane algorithm found the best solutions to a series of realistic test problems, outperforming exchange, branch and bound, dynamic programming and cut tree algorithms. It was able to solve a 30-location 5-time-period problem in 200 CPU seconds.

A methodology is proposed to design a GT cell by considering the intercell parts flow in GT cellular manufacturing systems. The problem of GT cell formation is described in a graph using the quantities to be produced in the specified time period and the process routes for producing the products. The objective of this paper is to minimize the total number of parts produced in more than one cell. The problem, formulated as a quadratic assignment problem (QAP), is solved using both Lagrangean relaxation technique and the optimality conditions of quadratic program. Furthermore, in order to obtain the giobal optimal solution rather than the local optimal solution, a branch-and-bound algorithm is employed. Finally, numerical examples are used to show the effectiveness of the solution techniques and GT cell formation procedure. Moreover, a computer simulation is presented, showing the effectiveness of cellular manufacturing systems

SUMMARY Many manufacturing systems require an assignment of machines to locations along a straight track, so as to optimize material flow. This paper uses a cut approach to the corresponding quadratic assignment problem, and derives a heuristic which generates a good solution. In addition, a modified lower bound to the assignment problem is also developed, which is always better than the classical lower bound. Results showing the performance of the heuristic are demonstrated, along with a comparison of the modified and classical lower bound. In almost all the test problems, the solution generated by the heuristic was either optimal or better than any solution obtained by other methods. Extension of the heuristic to more general cases also is considered.

SUMMARY The problem of grouping of parts has been addressed in the past using clustering methods and integer programming. This paper presents an assignment model to solve the grouping problem. A similarity coefficient matrix is used as the input to the assignment problem. Closed loops in the form of subtours are identified after solving the problem and are used as the basis for grouping. The method has been applied to a number of examples. Compared with the earlier mathematical programming model, viz., the p-median model, the assignment method emerges as a distinctly superior technique both in terms of quality of solution and computational time.

The paper deals with the problem of optimization of a quality inspection process structure. The problem is identified with designing an optimal arrangement of inspection operations in a production process (linkages of the quality inspection process with manufacturing and accessory processes). Three mathematical models for the cases of specialized and versatile inspection stations are formulated. It is shown that the problem can be treated as a particular case of a standard assignment problem. An optimization procedure, grounded on Balas' algorithm, is proposed. A numerical example, based on real data, is given.

In this paper, we formulate the quadratic assignment problem through multiple objective programming in which we can have several objectives. In the facility layout problem, the objectives can be materials handling cost, production rate, and flexibility. We define efficiency and describe how efficient alternatives can be generated. A heuristic procedure based on pairwise exchange of subfacilities is developed to generate the efficient solution associated with a given set of objective weights. Our approach could just as easily implement the graph theoretic or other approaches to solve the quadratic assignment problem and generate efficient points associated with given weights. A paired comparison method based on the strength of preference among alternatives is developed. The paired comparison method generates the decision maker's weights of an assumed unknown utility function. The method asks simple questions and uses linear programming to solve the problem. An experiment with the developed computer package...