Table Of ContentMODIFICATIONS TO THE SYSTEMATIC LAYOUT PLANNING
PROCEDURE TO ALLOW DEPARTMENTAL DIVISION AND IRREGULARLY
SHAPED SUBDEPARTMENTS
A thesis presented to
the faculty of the
Fritz J. and Dolores H. Russ
College of Engineering and Technology
of
Ohio University
in partial fulfillment
of the requirements for the degree
Master of Science
Stephen E. Martin
August 2004
This thesis entitled
MODIFICATIONS TO THE SYSTEMATIC LAYOUT PLANNING PROCEDURE TO
ALLOW DEPARTMENTAL DIVISION AND IRREGULARLY SHAPED
SUBDEPARTMENTS
BY
STEPHEN E. MARTIN
has been approved
for the Department of Industrial and Manufacturing Systems Engineering
and the Russ College of Engineering and Technology
Trevor S. Hale
Assistant Professor of Industrial and Manufacturing Systems Engineering
Dennis Irwin
Dean, Fritz J. and Dolores H. Russ College of Engineering and Technology
MARTIN, STEPHEN E. M.S. August 2004. Industrial Engineering
Modifications to the Systematic Layout Planning Procedure to Allow Departmental
Division and Irregularly Shaped Subdepartments (133 pp.)
Director of Thesis: Trevor S. Hale
The purpose of this research is to develop extensions and enhancements to Systematic
Layout Planning (SLP) that allow more complex problems to be addressed during new
facility layout construction. Specifically, the modified SLP technique allows for
departments to be separated into subdepartments that may or may not necessitate
placement beside other subdepartments of the same department. This scenario was
previously unable to be addressed by traditional SLP. Also, the alternate subdepartment
unit shapes of triangles and hexagons are tested against squares for their effect on the
quality of the layout. Finally, new relationship variables, “viscosity” and “affinity” are
defined to describe the intradepartmental and interdepartmental attraction, respectively.
Layouts produced using the modified SLP technique are compared to those produced
using traditional SLP on the basis of lowest cost and are computed using a tool created in
Microsoft Excel. The modified SLP procedure produces layouts of statistically equal or
lower cost than traditional SLP for the experimental data set.
Approved:
Trevor S. Hale
Assistant Professor of Industrial and Manufacturing Systems Engineering
4
TABLE OF CONTENTS
Abstract...............................................................................................................................3
List of Tables......................................................................................................................5
List of Figures.....................................................................................................................6
1 Introduction.................................................................................................................7
1.1 Background.........................................................................................................7
1.2 Research Purpose................................................................................................8
1.3 Specific Aims of Research..................................................................................9
1.4 Thesis Organization..........................................................................................10
2 Literature Review......................................................................................................11
2.1 Classification of the Facility Layout Problem..................................................11
2.2 Solution Algorithms..........................................................................................13
2.3 Graph Theoretic Approaches............................................................................20
3 Formulation...............................................................................................................23
3.1 Introduction.......................................................................................................23
3.2 Problem Definition............................................................................................25
3.3 Assigning Viscosity and Affinity Values.........................................................26
3.4 Objective Function............................................................................................27
3.5 Experimental Details.........................................................................................35
3.6 A Note on Layout Development from Results.................................................40
4 Results.......................................................................................................................43
4.1 Implementation.................................................................................................43
4.2 Layout Generation............................................................................................43
4.3 Experimental Results and Analysis..................................................................45
4.4 Problem Size.....................................................................................................54
5 Conclusions...............................................................................................................58
5.1 Review of Results.............................................................................................58
5.2 Application........................................................................................................59
5.3 Future Work......................................................................................................60
References.........................................................................................................................61
Appendix A: Step by Step Layout Generation Using Modified SLP...............................64
Appendix B: Experimental Data.....................................................................................129
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LIST OF TABLES
Table 3.1: Differences between SLP and Modified SLP..................................................25
Table 3.2: Insertion Method Example Data......................................................................28
Table 4.1: Layout Cost Results.........................................................................................46
Table 4.2: Calculated T and P Values for Shapes and Insertion Methods........................52
Table 4.3: Calculated T and P Values for Shape/Insertion Method Combinations..........53
Table 4.4: Cost Results for Each Problem Size................................................................55
Table 4.5: T and P values for Problems of Different Sizes..............................................55
6
LIST OF FIGURES
Figure 2.1: Facility Layout Problem Hierarchy................................................................12
Figure 2.2: The Steps of SLP............................................................................................14
Figure 3.1: Blank Facility Grid.........................................................................................29
Figure 3.2: Placement of First Subdepartment.................................................................30
Figure 3.3: Four-way Tie..................................................................................................31
Figure 3.4: Placement of Third Subdepartment................................................................32
Figure 3.5: Placement of Next Department......................................................................32
Figure 3.6: Calculations for Placement of Final Department...........................................33
Figure 3.7: Addition of a New Column to the Facility Grid.............................................34
Figure 3.8: Space Relationship Diagram Developed by Modified SLP...........................34
Figure 3.9: Triangular Tessellation (Weisstein [23])........................................................36
Figure 3.10: Hexagonal Tessellation (Weisstein [22]).....................................................36
Figure 3.11: Example Layout Generated Using Modified SLP........................................41
Figure 3.12: Resultant Facility Grid After Manipulation.................................................42
Figure 4.1: Traditional SLP Layout..................................................................................44
Figure 4.2: Modified SLP Layout.....................................................................................44
Figure 4.3: Viscosity Ranked Cost Chart.........................................................................47
Figure 4.4: Affinity Ranked Cost Chart............................................................................48
Figure 4.5: Sum Ranked and SLP Cost Chart..................................................................49
Figure 4.6: Average Costs of Shape/Insertion Method.....................................................50
Figure 4.7: Average Number of Departmental Separations per Problem.........................56
7
1 INTRODUCTION
1.1 Background
The facility layout problem (FLP) has historically had many different applications
varying greatly in approach, scale, and type. The vast nature of the FLP has prompted
much research on solution algorithms, heuristics, and measures aimed to find good
layouts. FLP solution methods are generally categorized according to the type of
problem being solved and their approach to the solution: improvement techniques for
existing (brown-field) problems and construction techniques for new facility (green-field)
problems. Construction layout techniques offer analysis for new facilities while
improvement techniques analyze an existing facility. Also, methods generally take either
a qualitative or quantitative approach where either intuition or mathematical analysis,
respectively, is applied to produce a good layout. Although the currently available
algorithms are very different, all methods rely on human decision making to generate
good layouts.
A particular cornerstone in the facility layout research is the Systematic Layout
Planning (SLP) procedure created by Muther [18]. SLP is a comprehensive technique to
address the facility layout problem from conception to completion while delineating all
necessary steps in between. The fundamental purpose of SLP is to utilize inter-
departmental relationships (or flow weights) to generate a two-dimensional unit square
block layout. The value of SLP is seen in the simplicity of both the data to be collected
and the algorithm itself. The drawbacks of SLP also involve its simplicity, as it typically
is only able to address non-complex problems. Also, layouts generated by SLP are
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sometimes over simplified and require user manipulation to produce application-specific
layouts. For these reasons, SLP is often the starting point when generating solutions to
the FLP, but not the ending point of final layout generation.
1.2 Research Purpose
SLP considers all departments to have an adjacency constraint and sometimes
shape constraints that require an entire department to be contained within a rectangular
border in only one location of a facility. In specific cases where these constraints do not
apply, SLP produces a layout which may be more costly then necessary. For instance, a
facility may exist where there are several individual process stations. Some processes
because of similar flow weights and relationships may have been grouped together into
departments. Since these processes do not necessarily require placement near each other
and are considered to have no binding shape constraints, they could be evaluated as
individual departments. However, since they do share similar properties, it is less
complex to evaluate them as individual units of the same department instead of
computing the layout for each process as an individual department.
SLP generally suggests the use of unit squares as subdepartment shapes due to the
fact that they produce simple and feasible department shapes that can fit within a
rectangular facility. However, since the above scenario denotes that there are no
departmental shape or adjacency constraints, other shapes can therefore be tested for their
effect on the quality of the layout. Specifically, regular (used in the strict mathematical
sense meaning both equilateral and equiangular) triangles and hexagons may produce
9
different results due to their different number of sides and subsequently different number
of possible adjacent subdepartments.
The purpose of this research is to develop extensions and enhancements to SLP
that will allow more complex problems to be addressed during new facility layout
construction. Specifically, the modified SLP technique will allow for departments to be
separated into subdepartments that may or may not necessitate placement beside other
subdepartments of the same department. While the separation into subdepartments has
been addressed before by Kusiak and Heragu [13] and Liao [14], research by Bozer and
Meller [4] suggests that segregation into subdepartments creates a resultant quadratic
assignment problem that is too complex to solve. However, the algorithm proposed
herein allows a relaxed adherence the adjacency constraint and departmental shape
factors that are traditionally mandatory during FLP calculations, therefore simplifying the
problem.
1.3 Specific Aims of Research
In order to create a modified SLP procedure that can be applied to a new problem
set, research must be done to test the proposed steps of the algorithm for their
effectiveness. The specific aims of the research are as follows.
1. To test the effect of incremental department placement while using an attraction
factor in place of adjacency constraints on the quality of the layout.
2. To evaluate alternate subdepartment unit shapes such as triangles and hexagons
based upon the performance objective.
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3. To test separate insertion algorithms for their sensitivity to the incremental
departmental placement and their effect on the quality of layout.
4. To combine the subdepartmental shape and attraction factors into a modified
version of the graph based layout portion of SLP that will allow for greater
flexibility in solving the FLP.
1.4 Thesis Organization
This thesis is organized as follows: Chapter 2 presents a review of the literature in
the field of facility layout and a hierarchical structure showing the relevance of the
modified SLP procedure to the facility layout problem. Chapter 3 presents the
formulation of the modified SLP procedure and explains the calculations behind the
algorithm. The experimental details and variables are also defined in Chapter 3. An
explanation of the tool used for experimental data collection is included in Chapter 4
along with the experimental results and their statistical significance. Chapter 5
summarizes the conclusions and implications of the results from the previous chapters
and presents areas where future research may occur.
Description:modifications to the systematic layout planning procedure to allow departmental division and irregularly shaped subdepartments a thesis presented to
