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This article was downloaded by: [Moskow State Univ Bibliote] On: 20 February 2014, At: 07:00 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK International Journal of Production Research Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tprs20 Machine layout: an optimization and knowledge-based approach SUNDERESH S. HERAGU b & ANDREW KUSIAK b a Department of Management and Marketing , School of Business and Economics, State University of New York , Plattsburgh, New York, 12901, USA. b Department of Industrial and Management Engineering , The University of Iowa , Iowa City, Iowa, 52242, USA. Published online: 30 Mar 2007. To cite this article: SUNDERESH S. HERAGU & ANDREW KUSIAK (1990) Machine layout: an optimization and knowledge-based approach, International Journal of Production Research, 28:4, 615-635 To link to this article: http://dx.doi.org/10.1080/00207549008942744 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

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Page 1: Machine layout: an optimization and knowledge-based approach

This article was downloaded by: [Moskow State Univ Bibliote]On: 20 February 2014, At: 07:00Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

International Journal of Production ResearchPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tprs20

Machine layout: an optimization and knowledge-basedapproachSUNDERESH S. HERAGU b & ANDREW KUSIAK ba Department of Management and Marketing , School of Business and Economics, StateUniversity of New York , Plattsburgh, New York, 12901, USA.b Department of Industrial and Management Engineering , The University of Iowa , Iowa City,Iowa, 52242, USA.Published online: 30 Mar 2007.

To cite this article: SUNDERESH S. HERAGU & ANDREW KUSIAK (1990) Machine layout: an optimization and knowledge-basedapproach, International Journal of Production Research, 28:4, 615-635

To link to this article: http://dx.doi.org/10.1080/00207549008942744

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in thepublications on our platform. However, Taylor & Francis, our agents, and our licensors make no representationsor warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Anyopinions and views expressed in this publication are the opinions and views of the authors, and are not theviews of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should beindependently verified with primary sources of information. Taylor and Francis shall not be liable for any losses,actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoevercaused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Machine layout: an optimization and knowledge-based approach

INT. J. PROD. RES., 1990, VOL. 28, No.4, 615--635

Machine layout: an optimization and knowledge-based approach

SUNDERESH S. HERAGUt and ANDREW KUSIAK!

In this paper the machinelayout problemin an automated manufacturingsystemisaddressed. Two models for solving the machine layout problem are developed. Aknowledge-based system for machine layout (KBML) is presented. KBMLcombines the optimization and expert system approaches and considersquantitative as well asqualitativefactorswhile solvingthe machinelayout problem.The system is coded in Common LISP and implemented on a Symbolics 3650machine. It is illustrated with a numerical example.

I. IntroductionThe machine layout problem involves the arrangement of machines on a factory

floor so that the total time required to transfer material between each pair of machinesis minimized. Factors such as width of the material handling carrier path, clearancebetween machines, etc., are considered while determining the layout. Throughout thispaper, the term 'machine' includes machine tools, in-process storage systems,inspection stations, etc. To our knowledge, the machine layout problem has beendiscussed to a rather limited extent. Jacobs (1987) presented an algorithm for solvingthe machine layout problem in a factory. Francis and White (1974) and Tompkins andWhite (1984) show how existing algorithms may be used to solve the machine layoutproblems. Heragu and Kusiak (1988 a) discussed the machine layout problem inautomated manufacturing systems and developed algorithms for solving it.

In contrast, the facility layout problem, which is related to the machine layoutproblem, has been discussed to a greater extent. Koopmans and Beckmann firstmodelled it as a quadratic assignment problem (QAP). Since then a number ofresearchers, for example, Bazaraa and Sherali (1980), Kaufmann and Broeckx (1978),Frieze and Yadegar (1983) have attempted to linearize the QAP and solve it usingbranch-and-bound and cutting-plane methods. Due to its combinatorial nature, theQAP with more than 15 facilities cannot be optimally solved. Hence, a number ofheuristic algorithms have been developed for solving the QAP. Kusiak and Heragu(1987) have reviewed some of them.

Other formulations, such as the quadratic set covering formulation (Bazaraa 1975),linear mixed-integer programming formulation (Love and Wong 1976), etc., have alsobeen used to model the facility layout problem. A major disadvantage of most existingformulations of the layout problem is that they require the location of sites (to whichthe facilities are to be assigned) be known a priori. The term 'site' corresponding to afacility refers to the physical area to be occupied by the facility.

Revision received May 1989.t Department of Management and Marketing, School of Business and Economics, State

University of New York, Plattsburgh, New York 12901, USA.t Department of Industrial and Management Engineering, The University of Iowa, Iowa

City, Iowa 52242, USA.

0020-7543/90 $3-00 © 1990 Taylor & Francis Ltd.

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616 S. S. Heragu and A. Kusiak

In this paper, a knowledge based system designed to solve the machine layoutproblem is presented. The layout problem in automated manufacturing systems isaddressed in the next section. In section 3, existing expert systems developed for themachine layout problem are briefly discussed. Two efficient models for the machinelayout problem are presented in section 4. Section 5 briefly discusses two heuristicalgorithms frequently used in KBML. The data requirement and input format requiredby the system are discussed in section 6. The problem solving approach of KBML ispresented in section 7. The system is illustrated with a numerical example in section 8.Conclusions are drawn in section 9.

2. Machine layout problem in automated manufacturing systemsFour basic types of machine layouts in automated manufacturing systems have

been identified in Heragu and Kusiak (1988 a) (Fig. 1):

- linear single-row- circular single-row- linear double-row- multi-row.

In Fig. I, the machines are arranged such that the total time required by thematerial handling carrier to transfer products, components, tooks, etc., between themachines is minimized. The transfer time required by the material handling carrier istypically proportional to its operating cost.

Many algorithms designed for the facility layout problem can also be used to solvethe machine layout problem. In the past, the machine layout problem has been solvedusing heuristic algorithms, especially for problems with more than fifteen machines.However, the heuristic algorithms have certain limitations. For example, the shape ofsome machines may be altered in the final layout. Obviously such a solution is notacceptable in practice. Also, most heuristic algorithms have been developed for thefacility layout problem and may not consider factors such as the width of materialhandling carrier path, clearance between machines, etc., while determining the layout.As a result, human expertise is required to modify the solution generated by theheuristic algorithm in order to obtain an implementable machine layout. Thismodification requires the human expert to spend a significant amount of time.

a)

®~b) ®

® 1'; @@®

® '" ® ®

c)

®~®d) ®®®®

®§® ®@®®® ® ®®®@

@ machine

-@D-- automated guided vehicle

® robot

Figure 1. Four types of machine layouts: (a) linear single row; (b) circular single-row; (c) lineardouble-row; and (d) multi-row.

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Machine layout 617

Therefore, it seems that there is a need for expert systems to solve the machine layoutproblem.

The layout problem in manufacturing systems can be divided into three classes:

- layout of machines within product cells- layout of machines within functional cells- layout of machine cells on a floor plan.

2.1. Layout of machines within product cellsGroup technology principles are used to determine groups of machines called

machine cells (Burbidge 1975).The layout of machines within each cell depends uponthe volume of material, parts, tools, etc., to be transported, as well as other relatedfactors. For example, due to safety restrictions two machines may have to be placed innon-adjacent and distant sites although the unit transportation volume of partsbetween these two machines may be large. The layout of machines based on grouptechnology is often called a product layout.

2.2. Layout of machines within functional cellsIn some cases, when the concept of group technology cannot be applied, the

machines are arranged in functional cells, for example, milling cells, drilling cells, etc.

2.3. Layout of machine cells on a floor planThe layout of the machine cells on a floor plan depends upon the interaction

between the cells and also the material handling requirement of each cell. For example,if two machine cells use one or more automated guided vehicles (AGV) for handlingmaterial, then it is advantageous to arrange the two machine cells along a straight lineto allow for efficient utilization of the AGV.

3. Literature surveyTo our knowledge only two expert systems have been developed for solving the

machine layout problem, namely, FADES (Fisher and Nof 1984) andlFLAPS(Tirupatikumara, Kashyap and Moodie 1985). In this section, the two systems arebriefly reviewed. In addition, two knowledge-based systems which, like KBML,interact with a database of models are also discussed.

FADES is an expert system which has been designed for solving the facility designproblem, selecting equipment and performing economic analysis. It consists of aknowledge base, a PROLOG interpreter and a database management system relevantto the application concerned. The database consists of economic models, algorithmsand rules for selecting equipment, developing relationship rating between facilities,selecting and invoking the appropriate algorithm, etc. The knowledge is representedusing first order predicate logic. The PROLOG interpreter employs forward-chainingdepth-first search in order to show that the negated goal does not match any of theassertions in the database.

FADES initially identifies the required technology level and examines the availableequipment. Using production parameters such as number of parts per product, productvolume, assembly time, number of different types of products, etc., the expert systemprepares a candidate list of the available equipment which meets the requiredtechnology level. Once the candidate list of available equipment has been prepared, areplacement analysis module performs economic analysis of the alternative equipment

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618 S. S. Heraqu and A. Kusiak

and recommends the appropriate one. FADES is capable of developing a relationshipchart which provides the closeness desired between each pair of facilities. It alsoconstructs a flow matrix and a distance matrix. The flow matrix consists of flow databetween pairs of facilities and the distance matrix consists of distance data betweenpairs of sites. To construct the former, it uses data concerning product demand,operations performed in each facility, etc. To construct the latter, informationregarding site description is used. Using the flow and distance data, a material handlingcost matrix is constructed. To solve the facility layout problem, a linear assignmentalgorithm is invoked. The algorithm uses the material handling cost matrix and therelationship chart to solve the layout problem. It should be noted that algorithms forthe quadratic assignment problem may also be stored in the data base and for a givenproblem, the appropriate algorithm may be selected.

[FLAPS consists of two basic modules:

(i) an expert system module(ii) a syntactic pattern recognition module.

Both modules can generate solutions for the facility layout problem.The expert system module uses three types of assignment rules to assign facilities to

their respective sites. The rule ofthe first type assigns a facility i to a site j, if the resourcerequired by facility i is available at site j. The rule of the second type assigns facilitieswith high flow value between them to adjacent sites. The rule of the third type assignsfacilities which should· not be located adjacently to non-adjacent sites. The patternrecognition module consists of production rules which determine the facility to beassigned first in the floor plan. The other facilities are added to sites in the floor plansuch that:

(i) hazardous facilities are assigned to their corresponding sites(ii) non-hazardous facilities are assigned based on their interaction with previously

assigned facilities.

The above mentioned systems were discussed in this section because they were thefirst two systems developed for solving the layout problem. In addition, it is necessaryto briefly discuss two knowledge-based systems which employ the modelling approachfor problem solving.

Lending Analysis Support System (LASS) is a prototype knowledge-based systemfor solving commercial loan analysis problems (Duchessi and Belardo 1987). Itsknowledge base contains:

(i) knowledge for problem structuring, i.e. categorizing various aspects of the loananalysis problem and developing a link between these categories-for example,profitability analysis is a component of capital analysis and is modelled byreturn on investment (ROI) and return on equity (ROE)

(ii) rules for selecting the appropriate model for the given problem.

The knowledge for problem structuring is represented by semantic nets, while theknowledge for selecting models is represented using production rules. Examples of themodels used are: inventory turnover analysis model, ROI, ROE, debt-equity ratiomodels, etc. The knowledge base consists of 47 rules. The system runs on an IBM-PCcompatible computer and is coded in OPS5 +.

Dolk and Konsynski (1984) developed a system which is capable of constructingnew models or modifying available models in the knowledge base. They examined the

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Machine layout 619

issues involved in knowledge representation for model management systems andproposed a 'model abstraction' approach to represent models in a data base. It involvesrepresenting a model in three sections, namely: data objects, procedures andabstractions. The data objects section lists the data items of the model. For example, thedata items for a linear programming (LP) model are the objective function, constraintsand decision variables. The procedures section lists:

(i) the procedures available, i.e. addition of constraints, deletion of constraints,etc. -

(ii) the data objects it accesses and(iii) the data objects it returns.

The abstraction section lists information about data objects and procedures and alsotheir relationships. For example, the abstraction section of a LP model may specify thatall the expressions be linear in the decision variables.

Using the above mentioned approach, they show how LP models may berepresented in a system. More importantly, they show how constraints, for exampleintegrality constraints, may be added to a LP problem to convert it into an integerprogramming (IP) problem. The model management system developed by Dolk andKonsynski (1984)constructs a model, based on the statement of the problem providedby the user, and identifies a similar model stored in the database using a patternmatching technique. It then solves the constructed model using an appropriatealgorithm.

The difference between KBML and the systems developed by Dolk and Konsynski(1984) and Duchessi and Belardo (1987) is that KBML modifies parameters withinalgorithms in order to improve the solution, whereas the latter do not. Furthermore,KBML permits modification of the solutions which are not implementable (see section7). The system developed by Dolk and Konsynski (1984) constructs a model for thegiven problem, but KBML and LASSselect one from the available models in the modeland algorithm base.

4. Models for the machine layout problemThe QAP which is frequently used to model the layout problem is known to be NP­

complete (Sahni and Gonzalez 1976). Finke, Burkard and Rendl (1985)have reportedon the computational complexity ofthe QAP. The largest problem they have been ableto solve optimally is a IS-facility layout problem. To derive this solution almost 50minutes of CPU time was required on a CDC CYBER 76. Other formulations, forexample the linear mixed-integer program of Love and Wong (1976), are also notsuitable for solving large scale layout problems. Also, as mentioned previously, most ofthe formulations presented to data, require that the location of sites be known a priori.In a layout problem with machines of unequal area, the location of a site depends uponthe machine that is assigned to it and hence cannot be determined a priori. In thissection, two efficientmodels which can be used to solve large scale layout problems (forexample, a 30-machine layout problem) and do not require a priori knowledge of thelocation of sites, are presented.

In order to formulate the machine layout problem, it is assumed that the orientationof each machine is known a priori. The orientation of a machine refers to the directionin which it is to be positioned in the layout. The machine orientation is frequentlydictated by the location of its loading/unloading area. For example, a machining centre

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Page 7: Machine layout: an optimization and knowledge-based approach

620 S. S. Heragu and A. Kusiak

is usually oriented such that its loading/unloading area is closest to the travelling pathof the material handling carrier.

To formulate a linear.mixed-integer model (which involves absolute values in theobjective function and constraints) for the machine layout problem, the followingnotation is used:

IU time required by a material handling carrier per trip between machines i and jfu frequency of trips required between machines i and jelj vertical clearance, i.e. the minimum distance by which machines i and j are to

be separated if they are positioned in opposite rows in the layouthorizontal clearance, i.e. the minimum distance by which machines i andj areto be separated if they are positioned in the same rows in the layout

b, distance between the' extreme horizontal sides of machine iI; distance between the extreme vertical sides of machine i

M an arbitrarily large positive numberxi' vertical distance between centre of machine i and horizontal reference line hrlx7 horizontal distance between centre of machine i and vertical reference line vrl.

The above parameters Ii' b;, clj, c7j , and decision variables XI, x7 corresponding to a two­row layout problem are illustrated in Fig. 2.

ModellThe objective function of model 1 minimizes the total time involved in making the

required number of trips between machines.n-l II

min L L lij /;J{lxi' - xjl+ Ix7 - ~Il1=1 j=i+l

(I)

s.t. IXi'-xjl+MYij~t(bi+bj)+ei'j

Ix7- x'I+M(I- YU)~Wi+lj)+ct

YU=O,I

i=I, ,n-l, j=i+ I, ,n

i= I, , n-I, j = i + I, , n

i= I, ,n-I, j=i+ I, ,n

(2)

(3)

(4)

Constraints (2) and (3) ensure that no two machines in the layout overlap and therequired clearance between each pair of machines is maintained. Since Yij is a 0,1

vrl

I;hc ij

b; MACHINEi

.I tcijXi

!bj MACHINEj Yj

I Ij Yj

I--Xj .1

h rl

Figure 2. Illustration of parameters and decision variables in a two-row machine layoutproblem.

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Machine layout 621

integer variable (contraint (4)), only one of the constraints (2) and (3) is binding.The following three observations regarding model I are worth mentioning.

l. To obtain positive values for the decision variables, one may add the followingnon-negativity constraint to model I:

i= I, .. . ,n (5)

Addition of constraint (5) to model I enables easy interpretation of the solution anddoes not affect it.

2. The above linear mixed-integer model (I) can be transformed into a non-linearmodel by replacing constraint (4) with the following one:

Yij(1-Yi)=O i=I •...• n,j=i+I, ...• n (6)

3. Hall the machines in the layout problem are ofequal area and square shape, thenconstraints (2), (3)and (4) in model I can be replaced by the following two constraints:

i= I, ... ,n-I, j=i+ I, . . . ,n

xi, x7=integer i= I, . . . ,n

(7)

(8)

Model I and its variants can be used to model the multi-row layout problem in whichmachines are to be arranged in two or more rows. However, in some industrial layoutproblems, machines may have to be arranged along a single-row, as shown in Figs. (I (a)and (b). For such layout problems, an even more compact model 2 is presented.

The parameters bi' eii and the decision variable xi in model I are not considered,since the single-row layout problem is a one-dimensional layout problem.

Model 2The objective function of model 2 minimizes the total time involved in making the

required number of trips between the machines.

"-I "min L L t ii .Mlx7- xm

i=1 j=;+1(9)

s.t. Ix7-x'i;;>t(li+I)+e7i i=I•... ,n-l,j=i+I, ...• n (10)

Note that observation 2 corresponding to model I applies to model 2 as well, i.e. thefollowing non-negativity constraint may be added to model 2 to make theinterpretation of the solutions easier:

i= I, .... n (II)

Models I and 2 involve absolute values in the objective function and constraints andhence cannot be solved using standard linear programming algorithms. A heuristicmodified penalty algorithm that can be used to solve the models efficiently is discussedin the next section. It should also be noted that models I and 2 may be transformed intolinear mixed-integer models that do not involve absolute values, and the resultingmodels may be solved optimally using the well known branch-and-bound procedure(Heragu 1988). Such transformed models are suitable for solving layout problemsinvolving 7 machines or less, since they require very high computational time for largerproblems. For example, the layout problem involving 8 machines requires more than

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622 S. S. Heraqu and A. Kusiak

30 minutes of central processing unit (CPU) time on an AMDAHL-5870 computer.Hence the transformed models are not presented in this paper.

5. Discussion of algorithms used in KBMLExperience has shown that for most industrial layout problems, only two

algorithms are likely to be used in KBML. They are algorithms AI and A2 and brieflydiscussed below.

Algorithm AI involves:

(i) transforming the constrained minimization model I or 2 into an unconstrainedmodel using the penalty method (Bazaraa and Shetty 1979) and

(ii) solving the unconstrained model using the Powell algorithm (Press et al. 1986).

Note that the Powell algorithm requires an initial solution which mayor may not befeasible.

In the penalty method, each constraint of the original (constrained) model issquared, multiplied by a penalty parameter pand placed in the objective function. Thusany violation of the constraints in the original model results in an objective function ofhigher value than the optimal one. Our computational experience indicated that byvarying the penalty parameter p, often a new solution is generated. The same is truewhen the initial solution provided to the Powell algorithm is modified. As will be seenin section 7, the above-mentioned aspect of the algorithm makes it a very usefulproblem-solving tool in KBML. For more details on algorithm AI, the reader mayrefer to Heragu (1988).

Algorithm A2 has relatively low computational time complexity and provides goodquality results (Heragu and Kusiak 1988 a). It uses

(i) the flow matrix [hj], where fij is the flow value between machines i and j(ii) the adjacency-distance matrix [dij]' where dij is the minimum distance between

machines i and j when they are located in adjacent sites

to compute a new matrix called the adjusted flow matrix [tij]' where tij=fijdij' Thealgorithm consists of two phases. In phase I, a number of triangles with maximumcorresponding weight are selected. Each vertex of a triangle represents a machine. Theweight of a triangle refers to the sum of the flow values between each pair of verticesbelonging to the triangle. The number of triangles selected depends upon the totalnumber of machines that are represented as vertices of the triangles. The triangles arethen arranged in decreasing order of their weights in a list L.

In phase 2, the assignment of machines to their respective locations is done asfollows: The ordered triangles in list L obtained from phase I are selected one at a time,starting from the first triangle in L. The vertices of this triangle are then sorted in amanner which depends upon:

(i) the flow value ·between the vertices in the triangle and(ii) whether any of the vertices in the triangle have previously been assigned.

The sorted vertices of each ofthe ordered triangles determine the sequence in which themachines enter the layout.

Algorithm'l\2 has a parameter qo, which if modified often provides a new solutionto the layout problem. Of course, this parameter can be varied only to a certain extent,beyond which the algorithm cannot be executed. For more details, see Heragu and

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Machine layout 623

Kusiak (1988 a). In both algorithms AI and A2, KBML varies certain parameters inorder to generate new solutions.

In addition to the above algorithms, there is a simplex based branch-and-boundalgorithm stored in KBML. Details on this algorithm may be found in any basicmathematical programming text book, for example, Press et al. (1986).

6. Data input in KBMLKBML obtained the declarative knowledge, i.e. data for the problem to be solved,

from the user, in an interactive mode. The user is provided with the exact format inwhich data is to be input. The following data are required by KBML:

(i) number of machines to be assigned(ii) flow matrix

(iii) clearance matrix(iv) relationship indicator matrix(v) machine dimensions

(vi) location restrictions (if any) for the machines(vii) type of layout(viii) type of material handling carrier

(ix) dimensions of the floor plan.

Details regarding the above data are as follows.

Number ofmachines to be assigned. The number of machines to be assigned is thetotal number of machines in the layout problem minus the number of machines whoselocations are restricted to certain sites (item (vi) above).

Flow matrix. The elements of the flow matrix indicate the frequency of trips to bemade by the material handling carrier between each pair of machines in a given timehorizon.

Clearance matrix. Elements of the clearance matrix indicate the minimumdistance by which machines i and j are to be separated if they are located adjacently inthe layout.

Relationship indicator matrix. KBML uses three relationship indicators, namely:Ai j , Oij and Xij, which indicate the adjacency requirement that is to be satisfied whileplacing machines i and j in the layout. An entry AiiXi} in row i and column j of therelationship indicator matrix means that corresponding machines i, j are (not) to belocated in adjacent sites. Entry 0u indicates that the location of machine i with respectto machine j is to be determined by the algorithm which solves the layout problem.

The relationship indicator matrix is somewhat similar to the relationship chartwhich was first suggested in Muther (1973).The relationship chart shows the closenessdesired between pairs offacilities and consists of entries A, E, I, 0, U or X. For any pairof facilities (i,j), the values A, E, I, 0, U and X indicate that the closeness desiredbetween facilities i and j is absolutely necessary, especially important, important,ordinary, unimportant and undesirable, respectively. In contrast, the relationshipindicator matrix used in KBML consists only of A, 0 and X entries whoseinterpretation was provided in the previous paragraph.

The reason for using the relationship indicator matrix as opposed to therelationship chart is as follows. KBML used the relationhip indicator matrix not to

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624 S. S. Heragu and A. Kusiak

determine the closeness desired between facilities, but to determine whether a pair offacilities must:

(i) be located in adjacent sites(ii) not be located in adjacent sites(iii) be located as suggested by the algorithm which solves the layout problem.

The closeness desired between each pair of facilities can be obtained from the flowmatrix, and it was therefore decided not to use the relationship chart in KBML.

Machine dimensions. Machine dimensions refer to the length and breadth of eachmachine and are used to determine whether space constraints are violated in a layout.

Location restrictions. It may sometimes be desirable to restrict the location of aparticular machine(s) to a particular site(s).Such information may be easily recorded in

. KBML.

Type of layout. Type of layout refers to the type of arrangement of machines onthe floor plan. As shown in Fig. Lrhere are four basic types of machine layouts inautomated manufacturing systems.

Type of material handling carrier. The type of material handling carrier selectedhas an impact on the type of layout. In order to determine the type of layout, KBMLrequires the user to input the type of material handling carrier selected. On the otherhand, if the type of layout is provided, KBML suggests a suitable material handlingcarrier. The types of material handling carriers considered in KBML are robot, AGVand gantry robot.

Dimensions of the floor plan. This information is required so that KBML candetermine whether the' arrangement of machines violates space constraints. It isassumed that the floor plan is rectangular in shape and the user is required to input thelength and breadth of the floor plan.

Since LISP is an efficient language for list processing, the declarative knowledge inKBML is mostly represented in the form oflists. Usually flow, clearance, distance andrelationship indicator data are in matrix form, but in KBML they are entered in theform of lists. The flow, clearance, distance and relationship indicator data aresubsequently stored in matrix form. The machine dimension and location restrictiondata for all the machines are also entered in list form. The number of machines to beassigned, type of layout, type of material handling carrier and dimensions of the floorplan are entered as single elements.

If there is a conflict among the data entered by the user, the system immediatelynotifies the user and requests the correct data to be entered. For example, if the user hasspecified that the number of machines in the layout problem is 8 and does not provide8 x 8 = 64 flow matrix elements while entering the flow data, the system notifies the userand requests the flow data to be re-entered. On the other hand, if there is no conflict inthe data entry but the user has entered the data incorrectly, the error can be rectifiedtowards the end of the data input session when the system asks if there are anycorrections to be made. The user then responds appropriately by specifying which datatype has to be re-entered, for example, machine dimension, and then enters thecorresponding data.

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Machine layout 625

7. Problem solving approachKBML has been implemented using the tandem architecture discussed in Kusiak

(1987). The tandem architecture and its variants can be used for many practicalproblems arising in the manufacturing environment. They are capable of solving iII­structured as well as well-structured problems. A tandem architecture combines theexpert system and optimization approaches. It can be thought of as an expert systemlinked to a database of models and algorithms. For a given problem, the expert systemfirst selects an appropriate model and algorithm. The problem is solved by thealgorithm and the solution produced is evaluated. If the solution is implementable, theexpert system accepts it. For example, in the case of the machine layout problem, thesolution (layout) is implementable if space constraints are satisfied and adjacencyrequirements are met in the layout produced by the expert system. If the solution is notimplementable, then the expert system may take one of the following actions:

(i) modify certain parameters in the algorithm (if possible) and apply thealgorithm again to the problem in order to generate a new solution, checkwhether it is implementable and repeat the above procedure until animplementable solution is obtained

(ii) modify the solution in order to make it implementable.

Of course, alternative (i)may not be applicable to all algorithms. Even if it is applicableto a particular algorithm, the corresponding parameter can be modified only to acertain extent, beyond which any modification fails to produce solutions. In such a case,i.e. when the parameter(s) in the algorithm cannot be modified any further, and if thesolutions produced thus far are not implementable, the expert system adoptsalternative (ii) mentioned above. Note that the system may use alternative (i) to alsoimprove the current solution. KBML which is a variant of the tandem system discussedabove, modifies parameters within an algorithm to generate new solutions andalternative (ii) above to make a solution implementable if necessary (Heragu andKusiak 1988b).

The structure of KBML is shown in Fig. 3 and its four main components are asfollows.

Database. The database consists of data related to the machine layout problem.KBML interacts with the user and obtains the required data and stores them in thedatabase.

Model and algorithm base. The models and algorithms related to the layoutproblem are stored in the model and algorithm base. Each model is represented as aframe. The model representation scheme in KBML is illustrated in Fig. 4. In the figure,OBLFUN denotes the objective function of model MI. LHS; and RHS i denote the leftand right hand sides of constraint i respectively. IC i indicates whether constraint i is anequality or inequality constraint. If IC i is an inequality constraint, its sign is alsoindicated.

Knowledge base. The knowledge base consists of rules for solving the machinelayout problem. There are five classes of rules in KBML:

(i) Class 1 rules for determining the type oflayout or the type ofmaterial handlingcarrier

(ii) Class 2 rules for selecting an appropriate model and algorithm for the layoutproblem

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626 S. S. Heragu and A. Kusiak

MODEL

•AlGO'"'H'''

BASE

l>\TABASE

Figure 3. Structure of KBML.

(iii) Class 3 rules for making initial assignments based on input data(iv) Class 4 rules for varying parameters within the algorithm (if applicable)(v) Class 5 rules for checking whether the layout is implementable.

To solve the layout problem, the five classes of rules are applied sequentially beginningfrom Class I rules.

KBML requires the user to indicate the desired type of layout. Based on this data,KBML can suggest a suitable material handling carrier depending upon thedimensions of the floor plan. If the user is not able to provide the type of layout and ifthe type of material handling carrier is known, then based on dimensions of the floorplan, KBML can suggest a suitable type of layout. Two sample rules which do so are asfollows.

Rule R6

Rule RI2

IFAND

AND

THEN

IFTHEN

type of layout is single-rowone of the dimensions of the floor plan is greater than twicethe reach of the robotthe other dimension ofthe floor plan is greater than the reachof the robotuse robot as material handling carrier and adopt a circularlayout.type of material handling carrier is robotuse circular single-row layout.

«MODEL M1) (OBJ_FUN 0) «LHS, RHS, IC,)

(LHS. RHS. IC.)

(u-is. RHS. IC.)))

Figure 4. Model representation in KBML.

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Machine layout 627

From Rule R6 above, it can be observed that ifone of the dimensions of the floor plan isgreater than the reach ofthe robot and the other dimension ofthe floor plan is greaterthan twice the reach of the robot, a circular single-row layout is suggested. If thedimensions ofthe floor plan are such that either a linear single-row layout or a circularsingle-row layout can be accommodated, KBML suggests the latter because an AGYrequired by the linear single-row layout is more expensive than a handling robot (ofcomparable capacity) required by the circular layout. Thus Class I rules allow todetermine either:

(i) the type oflayout given the type of material handling carrier to be used and thedimension of the floor plan, or

(ii) the type of material handling carrier given the type of layout.

When the type of layout and type of material handling carrier are both unknown, thesystem uses a default value of 'single-row' for the layout and determines ifsuch a layoutcan be accommodated within the boundaries of the floor plan. If a single-row layoutcan be accommodated, the system determines whether a Circular single-row layout ispossible. If it is possible, then a robot is suggested as the material handling carrier. Ifnot, an AGY is suggested as the material handling carrier. Ifa single-row layout cannotbe accomodated, the system determines if a double-row is possible. If not, a multi-rowlayout is suggested.

Class I rules consist of 3 meta-rules and 13first-order rules. A sample meta-rule andfirst-order rule are shown below. The meta-rules activate the first-order rules. The firstorder rules are further categorized into three classes of rules, namely: Class 1A, 1Band1C rules. If the type oflayout is known and the type of material handling carrier is not,Class I A rules are activated. If the type of material handling carrier is known and thetype of layout structure is not, Class 1B rules are activated. If the type of materialhandling carrier and type of layout structure are both unknown Class 1C rules areactivated.

Meta-rule R2

First-order rule Rl1

IF

THENIFTHEN

type of layout is unknown and type of materialhandling carrier is knownapply Class 1B rules.type of material handling carrier is gantry robotuse multi-row layout.

Class 2 rules are capable of selecting an appropriate model and algorithm for solvingthe given problem. As shown in section 3, the machine layout problem can be modelledas a linear or a non-linear program. In the past, the machine layout problem has beenmodelled as a linear mixed-integer program, quadratic set covering problem, quadraticassignment problem, etc. The latter models cannot be solved optimally in an acceptabletime, if the number of machines in the layout problem is greater than eight. Moreover,the QAP is applicable only when the machines are of equal sizes. Thus, it can be seenthat each model is applicable to a particular problem scenario. In the table, the modeland algorithm selected by KBML for twelve problem scenarios are provided. A • x 'entry in the table indicates that the modeland algorithm in a row in which x appearscan be used for the layout problem in the corresponding column. References to themodels and algorithms are also proviced in the table. For example, it can be observedthat for a multi-row layout problem involving less than 15 machines of equal sizes,KBML selects model M5, i.e. the quadratic assignment problem (Koopmans andBeckmann 1957) and uses the heuristic algorithm presented in Heragu (1988).

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Model and algorithm selected by KBML for twelve problem scenarios. NMP is the number of machines in the layoutproblem, NLP is the non-linear program, LCP is the linear program with continuous variables, LMIP is the linearprogram with mixed (0, I) integer variables, and QAP is the quadratic assignment problem.

0­N00

Model number,."

MI (NLP) MI (NLP) M2 (LCP) M3 (LMIP) M4 (LMIP) M5 (QAP) ,."

::::Reference t t t Heragu Heragu Koopman and '"....

Q(1988) (1988) Beckman (1957) "".,Problem scenario Q

Machines of equal sizes x x x x ::sl'l..

Machines of unequal sizes x x x x ;0..

NMP <8 x x x~

NMP 8-15 x x x .,NMP >15 '"x x x 5'Single-row layout x x ;.;-

Multi-row layout x x x xAlgorithm number Al A2 Al A3§ Al AlReference Heragu Heragu and Heragu Press et al. Heragu Heragu

(1988) Kusiak (1988) (1988) (1986) (1988) (1988)Optimal algorithm No No No Yes No No

t Presented in section 4.t Model 2 presented in section 4.§Simplex based branch-and-bound algorithm.

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Machine layout 629

A sample rule which selects the model and algorithm for a given problem is asfollows.

Rule R16 IF number of machines to be assigned is ~ 8AND the type of machine layout is single-row

THEN select model M2 and solve the model using algorithm AI.

From the table it can be observed that model M2 and algorithm AI in rule RI6 refer tothe model 2 presented in section 4 and the algorithm Al outlined in section 5.

Thus it can be seen that the model and algorithm selected by KBML depend uponthe nature of the problem, namely, machine sizes, number of machines in the layoutproblem and type of machine layout.

Class 3 rules are used to make initial assignments. The initial assignments may bespecified by the user or decided by KBML. For example, if AGV is used as the materialhandling carrier, then it requires a battery charging station. It is advantageous to assignmachines with maximum flow value between them to adjacent sites near the batterycharging station. For, if this is done, the AGV spends less time in travel to the batterycharging station.

User desired assignments have priority over the assignments done by KBML. Thus,if the user desires to locate machines with maximum flow value between them to siteswhich are not near the battery charging station, the system does not attempt to relocatethese machines near the battery charging station. Class 3 consists of 6 rules.

As mentioned in section 5, it is possible to modify certain parameters in some or thealgorithms. Class 4 rules are used for changing these parameters. For every modifiedvalue of the parameter, the algorithm often provides a different solution (layout).

In the first iteration, Class 4 rules do not attempt to modify the value of theparameter. Instead, the selected algorithm (with the initial value of the parameter) isused to solve the layout problem. The solution generated is evaluated forimplementability by Class 5 rules. If the solution is implementable, its solution cost iscomputed. Ifnot, it is modified so as to make it implementable and then its solution costis computed. Note that a layout is implementable if:

(i) adjacency requirements (between pairs of machines) specified by the user aremet

(ii) location restrictions of machines specified by the user are satisfied and(iii) space constraints are not violated.

Then control is passed back to Class 4 rules which modify the value of the parameter bya pre-determined amount. Then the algorithm (with the new modified value of theparameter) is used to solve the layout problem and the solution produced is modified (ifnecessary) in order to make it implementable by Class 5 rules.

The above procedure of modifying the value of a parameter by a predeterminedamount, solving the layout problem, providing the solution to Class 5 rules, modifying(if necessary) to make it implementable, and computing its solution cost, is carried onuntil the algorithm is able to produce solutions. It is, therefore, an iterative procedure.It should be noted that for each layout problem, if the value of the parameter isincreased beyond a certain point, the algorithm fails to produce a solution. The extentto which a parameter can be modified, or alternatively, the number of iterationsperformed, depends on the layout problem and varies from one problem to another.After a few iterations, the algorithm fails to provide a solution. When this occurs, the

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630 S. S. Heraqu and A. Kusiak

Rule R39

solutions produced thus far are considered and the one with the least solution cost isprovided to the user.

The initial value of the parameter in an algorithm is set in such a manner that thealgorithm is able to produce a solution at least in the first iteration.

In order to explain the application of Class 4 and Class 5 rules, assume that, for agiven layout problem, Class 2 rules have selected algorithm A2 and consider thefollowing Class 4 rule:

IF algorithm selected is A2TH EN increase value of parameter qo by .1. and apply the algorithm.

Class 4 rules direct the system to solve the layout problem using algorithm A2 (for theinitial value of qo). Heragu and Kusiak (1988)discuss how the initial value of qo may beset. Then the solution produced by algorithm A2 is provided to Class 5 rules whichcheck whether the machine layout is implementable.

If the layout is implementable, its solution cost is computed. If not, the solution ismodified to make it implementable. Then control is passed back to Class 4 rules whichmodify the parameter qo by .1. =± [average value of flow matrix elements]. (Experiencehas shown that increasing qo in steps of.1. often leads to solutions of better quality.)Then algorithm A2 with the modified value of qo is applied to the problem and thesolution produced is modified (ifnecessary), in order to make it implementable by Class5 rules.

The above procedure of modifying qo by .1. solving the layout problem andmodifying it if necessary, is carried on until the algorithm A2 is able to producesolutions. After the value of qo reaches a certain level, algorithm A2 is unable toproduce any solution. When this occurs, all the solutions produced thus far areconsidered and the one with the least cost is provided to the user.

Inference Engine. KBML uses a forward-chaining inference strategy. Theinference engine attempts to match the data concerning type of material handlingcarrier and type oflayout with the IF part of the meta-rules in Class 1. Ifthe match withthe IF part of a rule is successful, then the rule fires other first-order rules. The first­order rules suggest either the type of layout or the type of material handling carrier tobe used depending upon which rule has been fired. The control is then directed to Class2 rules. The inference engine attempts to match the data provided by the user (numberof machines to be assigned) and the data created by the first-order Class I rules (type oflayout) with the IF part of Class 2 rules. Ifa successful match is found in any rule, theTHEN part indicates the model and algorithm that is to be used to solve the givenlayout problem.

Similarly, using the forward-chaining strategy, the inference engine uses Class 3rules to perform the user desired assignments, and also some assignments based on thedomain knowledge .stored in the knowledge base. As mentioned before, suchknowledge is represented in the form of production rules in KBML. A sampleproduction rule is as follows.

Rule R34 IF type of material handling carrier used is AGV and type oflayout is linear double-pow,

AND the assignment of machines i,j with maximum flow valuebetween them are not restricted to any particular site

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Machine layout 631

THEN locate battery charging station near one end of the layout andassign machines i and j to sites which are adjacent to thebattery charging station.

Rule 34 ensures that the AGV spends less time in travel to the battery charging station,by assigning machines with maximum llow value between them near the batterycharging station.

The controillow from Class I rules to Class 5 rules in KBML is illustrated in Fig. 5.As shown in the figure, control flows sequentially from Class I rules to Class 4 rules. Butbetween Class 4 and Class 5 rules the control is directed back and forth. As mentionedpreviously, the number of times control is transferred back and forth depends upon thegiven layout problem.

The knowledge base in KBML consists of 59 rules. New rules can be easily addedwhen required. KBML is coded in Common LISP and implemented on a Symbolics3650 machine.

( PROBLEMSPECIFICATION

•CLASS 1 RULES

CLA.SS1A CLASS IB CLASS ICRULES RULES RULES

I I..CLASS 2RULES

•CLASS 3RULES

•CLASS 4RULES

t fCLASS 5RULES

+( MAOiINE

LAYOUT

Figure 5. Control flow in KBML.

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632 S. S. Heragu and A. Kusiak

8. A numerical exampleKBML is illustrated as follows.

Example. Determine a machine layout for the following data:

(i) number of machines to be assigned is 8(ii) flow matrix

Machine

2 3 4 5 6 7 8

I 0 2 8 I I 0 0 2

2 2 0 3 0 2 2 2 0

3 8 3 0 0 0 0 0 0

Machine 4 0 0 0 5 2 2 10 (12)

5 I 2 0 5 0 10 0 0

6 0 2 0 2 10 0 I I

7 0 2 0 2 0 I 0 10

8 2 0 0 10 0 I 10 0

(iii) clearance matrix

Machine

2 3 4 5 6 7 8

I 0 I I I I I I

2 I 0 I I I I I

3 I I 0 I I I I

Machine 4 I I I 0 I I I (13)

5 I I I I 0 I I

6 I I I I I 0 I

7 I I I I 0 I

8 I I I I I 0

(iv) relationship indicator matrix

Machine

2 3 4 5 6 7 8

I 0 0 0 A 0 0 0 0

2 0 0 0 0 0 0 0 X

3 0 0 0 0 0 0 X 0

Machine 4 A 0 0 0 0 0 0 0 (14)

5 0 0 0 0 0 0 A 0

6 0 0 0 0 0 0 0 0

7 0 0 X 0 A 0 0 0

8 0 X 0 0 0 0 0 0

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Machine layout 633

(v) machine dimensions

Machinenumber Dimension

1 20x202 lOxlO3 15 x 154 10 x 105 15 x 206 15 x 257 lOxlO8 lO x 15

(vi) location restriction for machines is as follows: machine 6 is to be located atsite 6

(vii) type of layout is single-row(viii) type of material handling carrier is unknown

(ix) dimensions of floor plan are 115 x 30.

Based on the dimensions ofthe floor plan and type of layout provided by the user, thesystem suggests that an AGV is to be used as the material handling carrier and that alinear single-row layout be adopted. It then selects model M2 in the model andalgorithm base (i.e. model 2 presented in section 4),and solves the model using heuristicalgorithm AI (discussed in section 5). The system uses the solution produced by thealgorithm to generate a layout. Of course, the final layout produced will be such thatthe user-specified constraints, namely: locating machine 6 at site 6, locating machines Iand 4, 7, and 5 adjacently, locating machines 2 and 8, 3, and 7 in non-adjacent sites, aresatisfied. The solution cost for such a layout is 2006'50 and is shown in Fig. 6.

9. ConclusionDuring the last thirty years a great deal ofeffort has been invested in research on the

layout problem. Optimization techniques have been widely used for solving themachine layout problem. If expert systems are to be successfully used for solving themachine layout problem, it is clear that they have to take advantage of the optimizationapproach as well. KBML is an effort in that direction.

Since lists are easily and efficientlymanipulated in Common LISP, KBML requiresthe user to input most ofthe data in list form. It should be noted that KBML is easy toimplement. New rules can be easily added to the knowledge base. Since the number ofrules is relatively small, the computation time required by KBML is low.

•--_o--j~)-__----

1,2, 3, .., 8 machinesAGV automatedguidedvehicle

Figure 6. Layout generated by KBML.

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634 S. S. Heraqu and A. Kusiak

KBML produces solutions of good quality for the machine layout problem becauseit uses tested efficient models and algorithms for solving the layout problem. On theother hand, IFLAPS uses simple rules of thumb in determining the machine layout.The only other existing knowledge-based system for the layout problem, FADES cansolve small scale layout problems in which the machines are of equal area only.

The advantages of KBML are as follows:

- KBML can solve large scale industrial layout problems in a relatively lowcomputation time

- it can be used to solve layout problems with machines of equal or unequal sizes,single-row or multi-row layout problems, etc.it uses efficient models and algorithms to solve the layout problemit allows modification of parameters within an algorithm in order to generatenew solutionsit considers quantitative as well as qualitative data while solving the layoutproblem.

AcknowledgmentResearch presented in this paper has been supported in part by grants from the

Natural Sciences and Engineering Research Council of Canada and the University ofManitoba.

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Naval Logistics Research Quarterly, 30, 287-304.BAZARAA, M. S., and SHERALI, M. D., 1980, Benders' partitioning scheme applied to a new

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BURBIDGE, J. L, 1975, The Introduction of Group Technology (New York: Halsted Press/JohnWiley).

DOLK, D. R., and KONSYNSKI, B. R., 1984, Knowledge representation for model managementsystems. IEEE Transactions on Software Engineering, SE-IO (6),619-628.

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