cascading flowlines and layout modules

Int J Flex Manuf Syst (2006) 17: 119–149

DOI 10.1007/s10696-006-8124-z

Cascading flowlines and layout modules: Practicalstrategies for machine duplication in facility layouts

Shahrukh A. Irani · Heng Huang

C© Springer Science + Business Media, LLC 2006

Abstract The standard approach for design of a layout for a high-variety low-volume

(HVLV) manufacturing facility has been to use either a from-to chart or a multi-product

process chart to design a process layout or a cellular layout, respectively, for the facility.

Considerable research has focused on making a go-no go decision to implement any oneof these two traditional layouts as the preferred layout for an HVLV manufacturing facility.

This paper introduces a variety of Hybrid Cellular Layouts (HCLs) which integrate the at-

tributes of the traditional functional, cellular and flowline layouts. The mathematical models

and methods for design of two HCLs—cascading flowline layout and modular layout—are

discussed in detail. Unlike the standard models in the literature, the design of the cascading

flowline layout introduces a novel string-to-graph aggregation and planar graph embedding

method that allows machine duplication in the layout. Similarly, the design of the Modular

layout introduces a substring clustering method instead of the standard method of cluster

analysis to form part families using the complete routings of the parts. For each HCL, results

from an industry project are presented to demonstrate the real-world viability of the concepts,

methods and software developed to support the design of HCLs for high-variety low-volume

manufacturing facilities.

Keywords Jobshop · FMS · Hybrid cellular layout · Cascading flowline layout · Modular

layout

1. Introduction

The functional layout and cellular layout are traditional layout choices for a HVLV man-

ufacturing facility. The functional layout has advantages such as high machine utilization

at workcenters and high flexibility in allocating operations to alternative machines in any

workcenter. However, it has disadvantages such as high throughput times, high WIP levels,

complex order tracking and production control, long setups, and high frequency of setup

S. A. Irani (�) · H. HuangDepartment of Industrial, Welding and Systems Engineering, The Ohio State University,Columbus, OH 43210

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120 Int J Flex Manuf Syst (2006) 17: 119–149

changes. In direct contrast, the cellular layout has advantages such as low lead times and

low WIP levels. However, high machine utilization is not guaranteed in all cells unless de-

mand for the parts they produce is high enough and stable enough to achieve the desired

utilization of cell resources. Also, in case of machine breakdowns and changes in demand or

product mix, a cell designed to produce a single part family is inflexible and unsuitable for

reconfiguration.

Job shops may be ill-advised to undertake a complete reorganization into physical cells

designed to make specific part families, unless the customer base, part mix and order vol-

umes for the cells will be stable in the long term. Significant changes in product mix and/or

order quantities, which are usually the downfall of a cellular layout, promoted the concept

of virtual cells in an existing functional layout (Irani, Cohen, and Cavalier, 1992; Irani,

Cavalier, and Cohen, 1993; Suresh and Slomp, 2005). In fact, a consulting company, syn-

chronous management has developed and implemented an approach for job shops, called

MTO (Make-To-Order) Kanban (http://www.synchronousmanagement.com/mto-ful.html),

that allows them to retain their existing functional layout and relies on Rough-Cut Capac-

ity Requirements Planning, daily production meetings and shop floor vigilance to progress

and track orders! And, new concepts in factory design that rely on computer-aided commu-

nication and connectivity between workcenters using Enterprise Resource Planning (ERP)

systems, Finite Capacity Scheduling (FCS) systems and Manufacturing Execution Systems

(MES), plus lighter and mobile machines, have allowed jobshops to operate virtual cells and

reconfigurable cells, instead of (rigid and inflexible) physical cells.

Developments in shop floor control technology and material handling systems have re-

duced the impact of travel distances and inter-operation separation of consecutive processes

on the type of physical layout designed for a facility. This paper describes a variety of HCLs

that attempt to avoid the physical separation of identical machines in several cells without

destroying the original cell compositions. All of these layouts are developed from the initial

machine-part grouping analysis used to design independent cells. However, during the layout

phase, creative layout strategies are used to place the shared machines as if they had been

retained in functional groups (“process villages”). Instead of a pure cellular or functional

layout for a jobshop, these layouts represent a novel fusion of partial conversion to a cellular

layout, functional grouping of several shared machine types, limited physical duplication of

shared machines and intercell flows.

2. Review of academic research literature

Recent research literature on facility layout design discusses new layouts — agile, dynamic,

holographic, hybrid, robust, flexible, holonic, cells (fractal, virtual, cascading, linked, re-

mainder, etc.), hybrid flowshops - that are essentially novel combinations of process vs.

product (or part family) focus. A detailed review of these layouts is presented in Huang and

Irani (2003). Here we present only an overview of these layouts and the novel philosophy

underlying each of them. Process fractals (Askin et al., 1996; and Venkatadri et al., 1997)

have the material handling, scheduling, and teamwork advantages of manufacturing cells,

but are more flexible to changes in demand and product mix. Agile manufacturing layouts(Kochhar and Heragu, 1999; and Montreuil, 2000) permit a high degree of adaptability and

responsiveness to changes in product mix and demand across multiple production periods by

rapid reconfiguration of an existing layout. Multi-Channel Manufacturing (Meller, 2000), or

MCM for short, provide multiple channels (or alternative routings) for most manufactured

products flowing through the manufacturing facility through capital investment in additional

workcenters. Flexible layouts (Benjaafar and Sheikhzadeh, 2000) allow for the possibility of

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Int J Flex Manuf Syst (2006) 17: 119–149 121

multiple processing departments of the same type being distributed in different areas of the

same facility, which increases job routing flexibility even in the absence of volume and/or

mix variability. Responsibility networks (Montreuil and Lefrancois, 1996) are comprised of

a variety of cells, such as product cells (each cell is devoted to a single product), group cells

(each cell is responsible for a specific group of products or a part family) and fractal cells

(each cell is a functional group of equipment with similar or identical processing capabilities).

Modular layouts (Irani and Huang, 2000) decompose a facility into a network of different

manufacturing subsystems (layout modules), each of which has well-understood schedul-

ing characteristics. A module could be a machining center, flowline, branched flowline,

multi-product multi-machine flowshop, multi-product multi-machine cell, or a functional

department. Virtual Cells (Drolet, Moodie, and Montreuil, 1989) are groups of machines,

each cell being dedicated to a specific part family; however, there is no physical reconfigu-

ration of the existing facility into a cellular layout. Jensen, Malhotra and Philipoom (1996)

investigated the performance of traditional and GT-based scheduling procedures in different

shops—functional jobshop, pure cell shop and routing flexibility cell shop. They concluded

that “. . . using a shop layout that lies somewhere between a functional layout and a pure cell

layout can work well if significant setup savings can result from machine customization”.

Vakharia, Moily, and Huang (1999) compared the performance of virtual cells and multi-

stage flow shops using analytical models. For a detailed review of new ideas in facility layout

observed across industry please refer to Huang and Irani (2003).

3. Hybrid cellular layouts

A significant portion of the research literature is focused on two areas: (1) Design of cellular

layouts and (2) Comparison of the performance of various layouts (functional vs. cellular

layout vs. virtual cellular). In the former area, despite the considerable research, there is

no accepted software/tool produced for industrial use. In the latter area, there is no specific

method/approach developed for design of virtual cells. Clearly, there is a void between

research/theory and practice/implementation in industry.

The research reported in this paper explores a fundamentally different research direction:� If the design of cells requires significant duplication of identical machines in two or more

cells, why even solve the K-Cluster graph partitioning problem at all? Why even implement

a traditional cellular layout with intercell flows and machine duplication?� Why not identify an intermediate spectrum of layouts that range between the two extremes

of the functional and cellular layouts?� Could we develop methods to design these layouts (HCLs) that are usable in real-world

industry projects, where large data sets with implicit cluster overlap and machine sharing

are the norm?Our preliminary research results indicate that these layouts could be generated by (a)

varying the extent of machine duplication in the layout and (b) eliminating the requirement

that a cell must process a complete family of parts. Examples of these intermediate layouts,

called HCLs, are cascading cells, remainder cells, hybrid flowshops, virtual cells, overlapping

cells, and layout modules (or Partial Cells). The primary design strategy for generating

these layouts is to form the cells. However, during the placement and floor-planning phase,

maximum closeness between all pairs of identical machines in different cells is sought in

order to retain each group of identical machines in a process department, as in a functional

layout. We will now illustrate this spectrum of layouts using a small dataset.

Table 1 shows the routing of each product in a hypothetical facility that consists of 12

machines and produces 19 products. Figures 1 and 2 show a functional layout and a cellular

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Table 1 Operation sequences of products

Product # Sequence Production quantity

1 1→4→8→9 2

2 1→4→7→4→8→7 3

3 1→2→4→7→8→9 1

4 1→4→7→9 3

5 1→6→10→7→9 2

6 6→10→7→8→9 1

7 6→4→8→9 2

8 3→5→2→6→4→8→9 1

9 3→5→6→4→8→9 1

10 4→7→4→8 2

11 6 3

12 11→7→12 1

13 11→12 1

14 11→7→10 3

15 1→7→11→10→11→12 1

16 1→7→11→10→11→12 2

17 11→7→12 1

18 6→7→10 3

19 12 2

Fig. 1 Functional layout

layout with three cells to produce the sample of parts in Table 1, respectively. With reference

to the cells shown in Fig. 2, machine types 1, 6, 7, 9 and 10 have been physically duplicated

among the cells. This physical duplication of identical machines into cells destroys the

flexibility that is attained in a functional layout in which all machines of a shared type are

co-located in a functional group. To avoid physical machine duplication, we propose use of

the following HCLs for design of jobshop layouts:

Cellular Layout with Reorientation of Cells (Fig. 3): Here, by a simple 90-degree rotation of

Cell 2, all machines of types 1 and 7 are located physically adjacent to each other, as if in

a Functional layout, even as the original allocation of machines to cells is retained.

Cellular Layout with Reorientation and Reshaping of Cells (Fig. 4): This HCL was generated

by a reorientation and reshaping of one or more cells. Instead of retaining the U (or

rectangular) shape for all cells, cells are allowed to have L (or S) shapes, which allows

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Fig. 2 Cellular layout with threecells

more machine types that, otherwise would have been distributed among the cells, to remain

co-located in functional groups.

Cellular Layout with S-shaped Flowlines (Fig. 5): This layout is similar to Fig. 3. First,

a Flowline layout was developed for each of the cells. Next, the cells were arranged in

parallel to minimize intercell flows. Finally, their linear shapes were modified into S-shapes

to group identical machines into functional groups.

Hybrid Flowshop Layout (Fig. 6): In this layout, unlike a traditional manufacturing cell,

each group of machines does not process a family of parts. The machines are allo-

cated into several groups of machines (layout modules) and the groups are arranged

in a line. Each module (or stage) in the resulting flowshop can perform one or more

consecutive operations occurring in the operation sequence of almost every part. In a

pure flowshop, the routing of every product is identical to the sequence of machines

that comprises the linear layout of the flowshop. For example, in the HCL shown

in Figure 6, only the pair of operations, 7 → 4, in the routings of parts 2 and 10

cause flow backtracking in the layout. Otherwise, if every part routing in Table 1 is

mapped onto the layout shown in Figure 6, then the travel path of each part for con-

secutive operations will be in-sequence or forward bypass between any two of the five

Fig. 3 Cellular layout with reorientation of cells

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Fig. 4 Cellular layout withreorientation and reshaping ofcells

Fig. 5 Cellular layout with S-shaped flowlines in parallel

Fig. 6 Hybrid flowshop layout

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Fig. 7 Virtual cellular layout

processing stages in the flowshop. If an additional Machine # 4 could have been purchased

and allocated to the third stage in Fig. 6, then no backtracking would have existed. This

HCL has the potential to reduce the complex material flow network in any jobshop into

the linear flow network that is characteristic of a flowshop! The substring identification

and clustering technique used to identify the layout modules that are then arranged in a

linear or network configuration is described elsewhere (Irani and Huang, 2000).

Virtual Cellular Layout (Fig. 7): The layouts in Figs. 3–6 demonstrate the basic objective

of HCLs to minimize the number of machine types that cannot be retained in functional

groups in a pure Cellular Layout. Even though the shared machine types are located

in functional groups, their setups can remain dedicated to a particular family of parts

assigned for production in a specific manufacturing cell. Furthermore, this type of “virtual”

manufacturing focus could also be obtained without creating a cellular layout by dedicating

a particular material handler to move all parts belonging to a particular family among the

necessary machines distributed across the facility. In the virtual cellular layout, machines

shared by several cells are assumed retained in functional groups if these cells can be

located adjacent to each other. This adjacency among the cells allows the machine groups

based on the part families to be virtual, i.e. a particular material handler links machines in

adjacent cells that are required by a part family without necessitating (rigid and inflexible)

physical co-location of the machines in any cell.

Cellular Layout with a Remainder Cell (Fig. 8): In this layout, one or more shared machine

types are retained in a remainder cell accessible to all the cells that need to share capacity

on these machines. The original compositions of Cells 1 and 2 shown in Fig. 3 were relaxed

to facilitate flows of parts through the remainder cell. Machines in the remainder cell were

arranged using standard methods for design of a functional layout.

Cascading Flowline Layout (Table 2): This layout depends on the routing similarity between

parts. The cells are designed such that simple parts get routed to small cells and complex

parts get routed to larger, more complex cells. The complexity of a routing is determined

by the number of unique workcenters (or machines) that are required to make it, regardless

of multiple non-consecutive occurrences that could result in flow backtracking. There is

no intercell movement for any part i.e. every part gets processed in at most one cell. A

new flow mapping technique—Modified Multi-Product Process Chart (MM-PPC)—was

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Fig. 8 Cellular layout with aremainder cell

developed to design this layout for high-mix low-volume manufacturing facilities (Zhou

and Irani, 2003).

4. Design of cascading flowline layouts

A linear embedding of the routing of each part in the product mix of a high-variety low-

volume manufacturing facility is equivalent to a flowline layout for the product. Planar

embedding on a rectilinear grid of a linear permutation of the product routings such that

adjacent flowlines have common substrings of operations results in a Cascading Flow-

line Layout (CFL). Tables 3 and 4 present routings from an actual sample of machine

parts obtained from industry (Sekine and Arai, 1992). In the first phase of development

of the CFL, as shown in Fig. 9, a horizontal permutation of the routings is done to max-

imize adjacencies between pairs of routings that are similar or identical (Askin and Zhou,

1998).

In the second phase of development of the CFL, as shown in Fig. 9, a vertical string

alignment (Gusfield, 1997) between adjacent pairs of routings matches/blends them at com-

mon operations (or substrings of operations), in order to maximize machine co-location into

process (or functional) groups to minimize machine duplication in the entire layout. This

two-phase procedure results in the same machine type appearing in the same row across sev-

eral consecutive columns in the rectilinear grid. Figure 10 illustrates how the non-adjacencies

between locations on the rectilinear grid that represents the (planar) floorplan of the facility

can suggest the need for machine duplication at non-adjacent locations. Figure 11 shows the

resulting CFL. The procedure for design of this HCL is completely unlike any existing layout

design method because, unlike the grid-oriented methods based on the Quadratic Assignment

Problem (QAP), it shapes the layout grid to fit the flow network implicit to the product mix

(Zhou and Irani, 2003).

Recently (based on private communication from Ms. Sharon Hale, Continuous Improve-

ment Consultant, Seattle Children’s Hospital), the authors identified a potential application

of Cascading Flowline Layouts and Layout Modules in the design of the Emergency De-

partment (ED) in any hospital. A Process Sequence Analysis of the three major classes of

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Table 2 Cascading flowline layout

patients (Patient Acuity Level = Fast, Medium or Complex) yielded routings as follows:

Routing for Acuity Level = FAST:

Registration → Triage → Assessment → Treatment → Disposition

Routing for Acuity Level = MEDIUM:

Registration → Triage → Assessment → Treatment → Ancillary Services →Treatment → Disposition

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Table 3 Routings for a sample of parts (Sekine at al., 1992)

Part # Part name Operation sequence Batch quantity

1 Slider (a) 6→9→10→11→12 1

2 Slider (b) 4→6→9→10→11→12 1

3 Press Brace 5→8→9→10 1

4 Bracket #1 4→7→9→10 1

5 Table 3→7→10→12 1

6 Damper 1→7→9→10 2

7 Bracket #2 1→8→9→10 1

8 Support 4→7→9 2

9 Housing 2→7→9 1

10 Flange 2→9 1

11 Shaft 3→9→10→12 1

12 Base 3→6→4→10→12 1

13 Spacer 4→6→4→10→12 1

Table 4 Description of machines in the facility

Machine # Machine name Quantity

1 NC Lathe (LB15) 1

2 NC Lathe (LB20) 1

3 Horizontal Mill (M) 1

4 Upright Mill (VM) 1

5 Compact Mill (BM) 1

6 Upright MC (6VA) 1

7 NC for Screw Holes (TNC) 1

8 Marker (MRK) 1

9 Drilling Machine (B) 1

10 Manual Operations (MAN) 1

11 Honing (H) 1

12 Grinder (G) 1

Routing for Acuity Level = COMPLEX:

Registration → Triage → Assessment → Treatment → Ancillary Services →Consult → Treatment → Ancillary Services → Consult → Treatment → Con-

sult → Ancillary Services → Treatment → Disposition

4.1. Mathematical formulation of the CFL design problem

Let∑

be a finite alphabet for machine types and let∑′ denote

∑∪{−}, where “−” denotes

“space”. The grid representation of P operation sequences, each with length lp for product p,

can be specified by an L × P grid G, where each element of the grid is a member of∑′. L is the

length of the grid based on the worst case alignment of any pair of strings = 2 × maxp(l p).

When a routing is embedded in any column in the grid G, one or more spaces could be

embedded between pairs of consecutive operations in the routing. The problem of optimal

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Fig. 9 Grid embedding of the cascading flowline layout

Fig. 10 Machine duplication at non-adjacent locations in the rectilinear grid [Note: “m#” refers toMachine Number]

Fig. 11 Material flow network for the cascading flowline layout

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allocation of machines and routings on the grid can be formulated as follows:

min

{P∑

p=1

l p∑k=1

cRm pk

−P−1∑x=1

L∑y=1

(P∑

p=1

l p∑k=1

cRm pk

apkxy

)vxy

}(1)

min

{{P∑

p=1

P∑x=1

L∑y=1

(cH

p y · aplp xy) −

P∑p=1

P∑x=1

L∑y=1

(cH

p y · ap1xy)}

−P∑

x=1

L−1∑y=1

(P∑

p=1

l p−1∑k=1

(cH

p apkxyap(k+1)x(y+1)

)) }(2)

subject to:P∑

x=1

L∑y=1

apkxy = 1 p = 1, . . . , P, k = 1, . . . , lp (3)

P∑p=1

l p∑k=1

apkxy ≤ 1 x = 1, . . . , P, y = 1, . . . , L (4)

x · apkxy = x ′ ·px ap(k+1)x ′ y′ k = 1, . . . , l p − 1, p = 1, . . . , P, x = 1, . . . P,

y = 1, . . . , L (5)

y · apkxy < y′ · ap(k+1)xy′ k = 1, . . . , l p − 1, p = 1, . . . , P, x = 1, . . . P,

y = 1, . . . , L (6)

where:

vxy ={

1 if apkxy ap′k ′(x+1) y = 1 and m pk = m p′k ′

0 otherwisex = 1, . . . P − 1, y = 1, . . . , L

apkxy ={

1 if kth operation of product p is assigned to grid location (x,y)

0 otherwise

lp number of operations in the routing of product p, p = 1, . . ., Pmpk machine type used for the kth operation in the routing of product p, m pk ∈ {1, 2,...M}p = 1, . . ., P, k = 1, . . ., lp

L upper limit on the number of rows in the grid = 2 × maxp

(l p)

P total number of products

M total number of machine types

cRm pk

fixed cost of a copy of machine type mpk

cHp material handling cost associated with product

p per unit distance of travel on the grid

The decision variables in the above model are the flow allocations on the grid apkxy , with

the objective of minimizing machine duplication cost and cost of material handling for bypass

moves in any flowline. The first term in the objective function (2) is the total material handling

cost. The second term is the total material handling cost for adjacent flows. Constraint sets

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(3) and (4) ensure that each operation is assigned to exactly one location on the grid and

that each location is either assigned any one operation or is empty. Constraint sets (5) and

(6) guarantee that each column of the grid contains the routing of any one product. Since

graphs are dimensionless and each location in the grid is assumed to have unit dimensions,

duplication costs for each machine type were assumed to be equal, as also the material

handling costs for each product. Also, according to constraint set (3), terms (1) and (2) can

be reduced to terms (7) and (8) respectively. Hence, the earlier mathematical model can be

simplified as follows:

maxP−1∑x=1

L∑y=1

vxy = min

{P∑

p=1

l p −P−1∑x=1

L∑y=1

vxy

}(7)

minP∑

p=1

P∑x=1

L∑y=1

(y · (

aplp xy − ap1xy)) −

P∑x=1

L−1∑y=1

(P∑

p=1

l p−1∑k=1

(apkxyap(k+1)x(y+1)

))(8)

subject to:

P∑x=1

L∑y=1

apkxy = 1 p = 1, . . . , P, k = 1, . . . , lp (9)

P∑p = 1

l p∑k = 1

apkxy ≤ 1 x = 1, . . . , P, y = 1, . . . , L (10)

x · apkxy = x ′ · ap(k + 1)x′y′ k = 1, . . . , lp − 1, p = 1, . . . , P, x = 1, . . . P,

y = 1, . . . , L (11)

y · apkxy < y′ · ap(k + 1)xy′ k = 1, . . . , lp − 1, p = 1, . . . , P, x = 1, . . . P,

y = 1, . . . , L (12)

where:

vxy ={

1 if apkxyap′k′(x + 1)y = 1 and mpk = mp′k′

0 otherwisex = 1, . . . P − 1, y = 1, . . . , L

apkxy ={

1 if kth operation of product p is assigned to grid location (x,y)

0 otherwise

lp number of operations in the routing of product p, p = 1, . . ., Pmpk machine type used for the kth operation in the routing of product p, m pk ∈ {1, 2, . . . M}p = 1, . . ., P, k = 1, . . . , lp

L upper limit on the number of rows in the grid = 2 × maxp

(l p)

P total number of products

M total number of machine types

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In the CFL design problem, dual objectives of minimizing costs of machine duplication

at non-adjacent locations and material handling cost for the products need to be fulfilled. In

the rectilinear grid in which the routings are embedded, each location in the grid is a machine

type assigned to that location. Maximization of the occurrence of a machine type in any

row across consecutive columns is equivalent to the minimization of machine duplications at

non-adjacent locations. Hence, the objective function in objective function (7) is a measure

of adjacencies between identical machines in a grid layout, similar to the Bond Energy in

matrix clustering (McCormick et al., 1972). Minimization of the material handling cost for

a product requires (a) the (vertical) travel distance between the locations of its first and

last operations in the column to be minimized and (b) the number of bypass flows (each

bypass flow corresponds to a pair of consecutive operations in the routing that is separated

by at least one “−” element) in the flowline to be minimized. Hence, objective function (8)

is a surrogate measure of material handling cost in the grid layout for a set of cascading

product-based flowlines (CFL).

4.2. Algorithms used for design of CFL

The optimal embedding of the sample of product routings onto the rectilinear layout grid

to minimize machine duplication and material handling costs, as computed using terms

(7) and (8), requires two problems to be solved—Problem #1: Determination of the hori-

zontal permutation of routings to minimize machine duplication in non-adjacent columns

of the grid, and, Problem #2: Vertical alignment of consecutive pairs of routings to min-

imize material handling cost for each product in its flowline. Since both problems are

NP-complete (Parker and Rardin, 1982), heuristic algorithms were developed for their

solution.

Solution of Problem #1: The solution of Problem #1 requires a similarity matrix for all

pairs of routings where the similarity of any pair of strings (or routings) measures the number

of common machines that match in both routings. The similarity between any pair of product

routings (P = 2) is the length of the Longest Common Subsequence (LCS). Note that the LCS

problem is a special case of the Optimal Alignment Problem (OAP) discussed in (Gusfield,

1997). Given two strings of length n and m, both problems can be solved in O(nm) time using

dynamic programming. Let sp1 p2be the LCS-similarity between the routings of products p1

and p2. It is required to find a permutation of the products that maximizes the LCS-similarity

of all consecutive pairs of columns in the grid. This permutation of products corresponds to

an acyclic Traveling Salesman Problem (TSP) using the LCS-similarity matrix as input. This

problem can be formulated as follows.

max∑

p1,p2∈{1,...P}p1 �=p2

P∑x = 1

sp1 p2bp1 x bp2(x + 1)

subject to:

P∑p = 1

bpx = 1 x = 1, . . . , P

P∑x = 1

bpx = 1 p = 1, . . . , P

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where:

bpx ={

1 if the operation sequence of product p is assigned to column x in the layout grid

0 otherwise

Solution of Problem #2: Problem #2 is the Optimal Alignment Problem (OAP) discussed

in (Gusfield, 1997). The pairwise alignment procedure used in this research can be ex-

plained as follows – Consider two strings S1 and S2 of lengths l1 and l2, respectively and

let S[i . . . j] be a substring in S that starts at position i and ends at position j in the rout-

ing. For any two characters x , y in∑

’, V (x , y) denotes the score (or value) obtained by

aligning character x with character y in the same row and in adjacent columns in the grid.

Similar to the scoring of grid adjacencies in the Bond Energy, the (pairwise) adjacency re-

lationship between the two characters x and y in the grid layout could be scored in several

ways: match (identical characters), mismatch (non-identical characters) or space (a char-

acter and a “−”). Matches are assigned a positive value while mismatches and spaces are

assigned zero (or negative) values. In the computer program, the score for each match, mis-

match, and space is specified by variables smatch, smis, and sspace, respectively. Since

our goal is to maximize the number of matches over all machine types, according to term

(7), we let smis = sspace = 0, smatch = 1. For example, consider the following two

routings:

S1 = (A, B, C)

S2 = (A, C, D)

Before alignment the adjacency score between them is 1. After alignment, the score be-

tween them is 2.

S1 = (A, B, C, −)

S2 = (A, −, C, D)

The above scoring scheme can be adjusted to reflect machine duplication cost, similar

processing capabilities of different machine types, constraints on whether certain machine

types can be located adjacent to each other in the layout grid, etc. For example, if a certain

machine type is expensive, then a high weight can be assigned to each of its matches. This

will force all parts requiring this machine type to be assigned to adjacent columns in the

horizontal permutation in order to reduce machine duplication costs.

In order to extend the algorithm for two-string alignment to the case of alignment of a

sequence of P strings, several modifications needed to be made to the core algorithm as

follows—Suppose that consecutive strings Si and Si+1 are being aligned, then when a space

is inserted after Si [x], all previous strings need to be adjusted to keep intact all prior matches

and spaces must be inserted after the locations S1[x], . . ., Si−1[x] to offset each of the previous

(i−1) strings. This is illustrated using the following simple example:

S1 = (A, B, C)

S2 = (B, C, D)

S3 = (B, E, C).

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After alignment of S1 and S2, the embedding of the strings becomes:

S1 = (A, B, C)

S2 = (B, C, D)

S3 = (B, E, C).

After alignment of S2 and S3 without adjustment, the embedding of the strings becomes:

S1 = (A, B, C)

S2 = (B, C, D)

S3 = (B, E, C).

With adjustment, the embedding of the strings becomes:

S1 = (A, B, C)

S2 = (B, C, D)

S3 = (B, E, C).

The main algorithm is as follows:

1) Initialize P sequences S1, . . . SP ,2) for i = 1 to k−1

for j = 2 to kcall LCS(Si , S j )

3) Generate TSP permutation � = {π (1), π (2), . . ., π (k)} and S′i = Sπ (i ) for i = 1, 2,. . ., k.

4) for i = 1 to k−1call Alignment (S′

i , S′i+1)

5) for i = k to 2call Alignment (S′

i , S′i−1)

For an L × P grid, the time complexity of this algorithm is O(P2L2).The LCS algorithm for two strings is as follows:

procedure LCS(S1, S2)for i = 1 to l1 do

for j = 1 to l2 doif (S1[i] = S2[j]) then cell = 1else cell = 0c1 = C[i−1, j−1] +cellc2 = C[i−1, j]c3 = C[i, j]C[i, j] = max

k∈{1,2,3}{ck}

d(x,y) = C[l1, l2]

The Optimal Alignment algorithm for 2 strings is as follows:

procedure Alignment(S1, S2)for i = 1 to l1 do

for j = 1 to l2 doif (S1[i] = S2[j]) then cell = smatch

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else cell = smisc1 = C[i−1, j−1] + cellc2 = C[i−1, j] + sspacec3 = C[i, j] + sspaceC[i, j] = max

k∈{1,2,3}{ck}

Path[i, j] = k∗, where k∗ = k maxk∈{1,2,3}

{ck}d(x,y) = C[l1, l2]traceback(Path, l1, l2)

procedure traceback(Path, i, j)if i = 0 or j = 0 then returncasePath[i, j] = 2: insert a space after S1[i−1]; traceback(Path, i−1, j)Path[i, j] = 3: insert a space after S2[j−1]; traceback(Path, i, j−1)end casetraceback(Path, i − 1, j − 1)

In the alignment algorithm described above, C[i, j] stores the maximum score for the

alignment of S1[1. . .i], S2[1. . . j]. The locations of the spaces that are inserted into the strings

to obtain their optimal alignment can be recovered from the traces stored in the Path[i, j]during computation of C[i, j].

4.3. Machine duplication with capacity requirements analysis

In the case of a large number of routings, the flowline layouts for the product routings could

necessitate duplication of the same machine type at several non-adjacent locations in the

grid containing the cascading flowlines. The feasibility of assigning a machine type to each

location requires comparison of (a) the machine capacity requirements for the parts routed

through that location with (b) overall availability of machines of any type. The steps in the

process are as follows:

1) Generate the optimal rectilinear grid.

2) Indicate the capacity requirement for each machine type associated with each operation

in the grid.

3) Consolidate the capacity requirements of identical machines that occur in adjacent

columns in the grid.

4) Compute the capacity (and machine) requirements for each machine type in each of the

shaded regions in which it occurs.

5) For each machine type, if the capacity requirements in a region exceed a minimum thresh-

old, assign it to that region; else treat the operations routed to that region as “exceptions”.

The products associated with those operations will require to be routed to some other

locations in the layout.

4.4. Industrial application

This section presents the results generated using routing data for a sample of parts provided

by a Boston-based machining jobshop (www.Tecomet.com). The routings for the sample

of parts are shown in Table 5. Figure 12 shows the CFL embedded on a rectilinear grid.

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Table 5 Routing data from a machining jobshop

Part routings

New index Quantity 1 2 3 4 5 6 7 8 9 10

1 22546 8 94

2 720 8 10 8 O.V. 94

3 720 8 10 O.V. 18 22 94

4 5603 8 O.V. 18 96 92 96 92 8 10 94

5 900 18 96 92 96 92 18 94

6 1800 91 90 O.V. 18 96 92 96 92 8 94

7 1800 91 25 94

8 1620 8 10 94

9 720 20 91 O.V. 18 94

10 720 8 10 8 94

11 720 8 10 92 94

12 3600 8 10 O.V. 18 96 92 96 92 8 94

13 900 91 18 94

14 2520 8 10 O.V. 94

15 900 91 8 94

16 900 8 10 DFLOW 94

17 900 8 10 DFLOW O.V. 18 94

18 900 8 19 O.V. 18 25 94

19 180 19 92 8 10 8 O.V. 18 94

20 720 91 8 92 8 10 22 94

21 720 8 10 19 8 23 94

22 720 19 25 94

Fig. 12 Grid embedding of the cascading flowline layout

Figure 13 shows the machine duplication necessary to eliminate cross flows between non-

adjacent flowlines that require to use the same machine types. Figure 15 shows the equivalent

adjacency graph for the CFL shown in Figs. 12 and 13 that would become the input for any

research code available at a university (Tompkins et al., 2003) or commercially available

software for block layout design (http://www.planopt.com/VIP-PLANOPT/index.htm).

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Fig. 13 Machine duplication at non-adjacent locations in the rectilinear grid

Fig. 14 Cascading flowlines with machine duplication at multiple locations

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Fig. 15 Illustration of layout modules

5. Design of modular layouts

Experience from several machining and fabrication jobshop layout projects undertaken in

industry suggested that the material flow network in any facility layout can always be de-

composed into a network of layout modules (Irani and Huang, 2000) i.e. each layout module

represents a portion of the entire facility layout and there is material flow between various

pairs of modules (unless a module is a stand-alone cell). A layout module is essentially a

group of machines connected by a material flow network that exhibits a flow pattern charac-

teristic of a specific type of layout, such as the flowline, cellular or functional layout. Layout

modules are categorized as follows:� Flowline Module (Fig. 15(a)): A Flowline module is a linear arrangement of machines such

that all inter-machine moves for consecutive pairs of operations on any product moving

through the line would be forward, either in-sequence or bypass. In case of backtracks, due

to multiple non-consecutive operations on the same machine, a decision could be taken

to (a) modify the linear shape into linear segments with circular/loop segments separating

pairs of consecutive linear segments, (b) retain the linear shape but utilize a bi-directional

material handling system for backtrack moves, or (c) duplicate the same machine at multiple

locations to convert backtrack moves into forward moves.� Branched (Convergent/Divergent) Flowline Module (Fig. 15(b)): A Branched Flowline

module results when a set of products have operation sequences with one or more substrings

of operations common to all of them. At several points, the flowline will split into parallel

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branches, each branch containing machines unique to a particular product (or products).

These branches will merge later into a single line wherever all product(s) require the same

substring of operations.� Patterned Flow Module (Fig. 15(c)): The material flow network in a Patterned Flow module

exhibits a flow dominance and precedence hierarchy, characteristic of an directed acyclic

digraph. This module could be further decomposed into a network of Flowline modules

and Branched Flowline modules.� Functional Layout Module (Fig. 15(d)): A functional layout module is analogous to the

process-focused department in a traditional Functional layout in which material flows are

random. The random flows are due to the absence of any flow dominance or patterns in the

sequences in which the different machines within the module are used by different parts.� Cell Module (Fig. 15(e)): Similar to a flowline module, a cell module is a set of dissimilar

machines which, if placed together, could produce a family of parts or products without the

products requiring visiting any additional departments or machines external to the module.

Although the parts in a family may not use all the machines and/or have the same sequence

of operations, their operation sequences have high commonality of machine requirements

and high similarity of operation sequences.

The concept of layout modules extends current thinking on input data requirements and

methods for facility layout, and supports the need for a new generation of facility layouts

beyond the traditional layouts (process, product, cellular and project) that continue to be

taught in leading textbooks (Tompkins et al., 2003) and implemented throughout industry.

Our research on layout modules extends the state-of-the-art in the theory and practice of

facility layout techniques as follows:� The “department” in a facility is allowed to contain a combination of multiple compatible

processes, instead of a single process. Similarly, the formation of a “partial cell” is allowed

since the threshold values of operation sequence similarity for grouping dissimilar products

into families are subjective and vary with each sample of product routings specific to a

particular jobshop.� Facility planners are allowed to take a logical approach to duplicating machines of the

same function at multiple locations in a facility based on their occurrence in different

combinations of operations required for different families of routings.� More than one type of layout can be used to arrange the different machines and resources

in a facility.� Design of modular layouts using operation sequences is a flexible method that could also

be used to design any facility layout.� An approach is proposed for defining the multi-function capabilities of flexible automated

machines by identifying strings of consecutive operations common to a large number of

similar products.

5.1. Mathematical formulation of the modular layout design problem

In this section, we propose a mathematical model of the problem of designing a facility layout

as a network of layout modules. First, we make the following assumptions:

• The planning period is one year;

• The production quantity of each product type in the planning period is known;

• The transfer batch size of each product type is known;

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• The material handling cost per transfer batch of each product type traveling between each

pair of machine types in the planning period is known;

• There is a fixed rate penalty for products traveling between layout modules;

• The rates of the setup cost and processing cost of each product type at each machine type

in the planning period are known;

• The loading/unloading cost of each product type at each machine is ignorable;

• The amortized purchasing price per unit of each machine type in the planning period is

known;

• Each operation of each product type is only processed at one machine;

• The number of layout modules is predetermined;

• The objective is to select the best machine set for each layout module and assign each prod-

uct to the best layout module(s), such that the total production incurred cost is minimized

and all resource constraints are satisfied.

Based on the above assumptions, we formulate the problem of designing a modular layout

as follows:

MinimizeK∑

k=1

Ek ·(

M∑m=1

rkm − Lk

)+

T∑i=1

Ni∑j=1

K∑k=1

M∑m=1

⌈Qi

Bi

⌉· Sijk · xijkm

+T∑

i=1

Ni∑j=1

K∑k=1

M∑m=1

Qi · Ui jk · Pi jk · xi jkm

+T∑

i=1

Ni −1∑j=1

K−1∑k=1

K∑l=k+1

M∑m=1

Hikl · xijkm · xi( j+1)lm

+T∑

i=1

Ni −1∑j=1

K−1∑k=1

K∑l=k+1

M∑m=1

M∑n=1;n �=m

μ · Hikl · xi jkm · xi( j+1)ln (1)

Subject to:K∑

k=1

M∑m=1

xi jkm = 1, for each (i, j) (2)

T∑i=1

Ni∑j=1

Qi · Pi jk · xi jkm

Fk≤ rkm, for each (k, m) (3)

K∑k=1

rkm ≥ 1, for each m (4)

rkm ≥ 0 and integral, for each (k, m) (5)

xi jkm binary, for each (i, j, k, m) (6)

�z� denotes the smallest integer that is larger than or equal to z

Variables:

rkm = Number of units of machine type k assigned to module m.

xijkm = 1 if the jth operation of product type i is processed at machine type k in module m;

= 0 otherwise.

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Parameters:

μ = Penalty factor for products traveling between modules.

Bi = Transfer batch size of product type i.Ek = Annualized cost of purchasing a unit of machine type k.

Fk = Annual production time available per unit of machine type k.

Hikl = Material handling cost for transferring a batch of product type i from machine type kto machine type l.

K = Number of machine types.

Lk = Existing number of units of machine type k.

M = Number of modules in the layout.

Ni = Number of operations in the routing of product type i.Pi jk = Processing time of the jth operation of product type i at machine type k.

Qi = Annual production quantity of product type i.Si jk = Setup cost for the jth operation of product type i at machine type k.

T = Number of product types.

Ui jk = Cost per unit time of processing the jth operation of product type i at machine type k.

The objective function (1) minimizes the sum of prorated machine purchasing cost, setup

cost, processing cost and material handling cost. The first part of term (1) gives the amortized

cost of purchasing extra machines in the planning period; the second part of term (1) calculates

the setup cost of all the products at their assigned machines; the third part of term (1)

is the total processing cost of the products at their designated machines; the fourth and

fifth parts of term (1) calculate the intra-module and inter-module material handling costs

respectively. The inter-module material handling cost is core to the problem – for each pair

of consecutive operations in the routing of a product, we need to track the movement of the

product between the two modules where the operations are performed. We need to check if

both these operations are performed in the same module, or not. If not, it will result in an

inter-module trip that implicitly incurs high material handling costs. The ideal solution would

be to completely process each product in a cell module. Since that would entail significant

investment in extra machines, the practical strategy would be to maximize the number of

consecutive operations in each routing that are performed within the same module.

Constraint set (2) ensures that each operation in the routing of each product is performed

at one and only one machine. Constraint set (3) guarantees enough capacity for each machine

type in each layout module and implies that the integer allocation of machines of the same

type to one or more modules is constrained by the available number of machines of that type

on the shop floor i.e. acquisition of extra machines incurs a capital expense. Constraint set

(4) ensures that at least one machine is assigned to each layout module. Constraint sets (5)

and (6) are nonnegativity, binary and integer requirements.

5.2. Algorithm used for design of a modular layout

The mathematical model of designing a modular layout is a binary quadratic programming

problem containing integral components, which is known to be NP-hard. In this section, a

heuristic approach that integrates the methods for design of functional and cellular layouts will

be described. The underlying algorithms are based on group technology for machine grouping

and similarity analysis of product routings, and the string matching methods used extensively

in genetics, molecular chemistry and the biological sciences (Sankoff and Kruskal, 1983).

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Stage 1: Identification of common substrings, if any, between all pairsof operation sequences

A layout module is a essentially a group of machines connected by a material flow network

that exhibits a flow pattern characteristic of a specific type of layout, and thus could have

a product, process or part family focus. A part may go through multiple layout modules

with each module processing a subset of operations for the part. In other words, a layout

module is responsible for a set of similar partial routings of parts. Hence, naturally, we start

constructing layout modules with capturing partial routings that are common among parts,

i.e. the common substrings among operation sequences. A common substring is defined as

a sequence of consecutive operations that is common to two or more operation sequences.

These operation sequences, in turn, are the superstrings of the substring. In each superstring,

an operation that does not belong to the common substring is called a residual operation with

respect to the common substring.

Stage 2: Cluster analysis of dominant common substrings to generatebasic layout modules

Based on the definition of the layout modules, the relationship between common substrings

and each type of layout module can be related to a cluster of these substrings as follows:

(1) Flowline module: A flowline module consists of a group of common substrings in which

there is one substring that is the superstring of all the other substrings.

(2) Branched flowline module: When two or more common substrings have common sub-

substrings and no common residual operations with respect to the common sub-substrings,

then the set of common substrings can be merged into a branched flowline module by plac-

ing the common sub-substrings in a single main flowline and creating parallel branches

for the residual operations.

(3) Patterned flow module: A patterned flow module also have common sub-substrings, but

the residual operations of the substrings with respect to the common sub-substrings have

common operations and the aggregated travel chart digraph obtained from the merger of

the substrings is a DAG (Directed Acyclic Graph).

(4) Functional layout module: A functional layout module is the same as a patterned flow

Layout module, except that the aggregated travel chart digraph obtained from the merger

of the substrings is cyclic. If the similarity coefficients computed for these substrings ex-

hibits poor clusterability, then a functional layout module would appear suitable for those

operations. Alternatively, if these substrings are aggregated into a travel chart digraph

which either exhibits strong connectivity or contains a large number of cycles, then this

absence of flow patterns would again suggest a Functional Layout module.

(5) Cell module: A cell module is a special type of module, because it can also be one or a

combination of the other four types of layout modules. It consists of a set of substrings,

the merger of which has the same aggregated travel chart digraph as that for the merger

of a set of original routings.

Since flowline, branched flowline, and patterned flowline modules all have preferable

DAG structures, we define these three modules as basic layout modules. The objective of

this stage is to form basic layout modules using dominant common substrings. Dominant

common substrings are those common substrings whose frequencies of occurrence in the

original routings are higher than a user defined threshold. Next, cluster analysis of dominant

common substrings needs to be performed to group similar substrings and generate basic

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layout modules. Here, the homogeneous agglomerative hierarchical clustering method with

the (unweighted pair-group) average linkage algorithm for cluster analysis is adopted. Fol-

lowing Mulvey and Crowder (1979), the mathematical model for homogeneous clustering

of dominant common substrings to form basic layout modules would be as follows:

(P) Minimize∑

I

∑J

mij · xij

Subject to :∑

J

xij = 1, for all i∑J

x j j = K

xij ≤ x j j , for all i, j

xijbinary, for all i, j

Each cluster has a DAG structure

where

I = Set of substrings

J = Set of eligible medians

K j = Number of clusters

mij = Merger coefficient between substrings i and jxij = 1 if substring i is assigned to cluster median j;= 0 otherwise.

Given T as the number of all operation types and N as the number of common substrings,

a common substring can be represented by a T × T matrix A where

A[i, j] ={

1 if there is a flow from operation i to operation j0 otherwise

(7)

Representing each substring by a T × T matrix Ak (k = 1, . . . , N), the merger of two or

more substrings can then be represented by the matrix∑

2sk Ak , where(∑k

Ak

)[i, j] =

{a > 0 if there is a flow from operation i to operation j

0 otherwise(8)

The agglomerative hierarchical heuristic for solving problem (P) is described below:

(1) Let each substring Ak be a cluster, which will result in the set of clusters C = {Ck} ={Ak}, k = 1, . . ., N.

(2) Find all strongly connected components consisting of more than two operations, if any,

contained in each substring Ak (k = 1, . . ., N) and store them in a corresponding set of

strongly connected component Sk . The strongly connected components in Sk are allowed

to occur in a basic layout module generated from Ak .

(3) Do until no clusters can be merged:

Step 1: Mark every pair of clusters as untested.

Step 2: Calculate similarity for each pair of clusters using the average linkage method.

Step 3: From the untested clusters, select the pair Ck1 and Ck2 that has the highest similarity.

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Step 4: Test mergeability of Ck1 and Ck2. If (Ck1 + Ck2) contains strongly connected

components that consist of more than two operations and do not belong to (Sk1∪Sk2),

Ck1 and Ck2 are not mergeable, go to Step 3; else, Ck1 and Ck2 are mergeable, replace

Ck1 and Ck2 by (Ck1 + Ck2) in cluster set C with (Sk1 ∪ Sk2) as its corresponding

strongly connected component set, mark (Ck1 + Ck2) as untested, go to Step 2.

(4) Output each of the clusters in C as a basic layout module.

In the above procedure, the strongly connected components are found using the depth

first search proposed by Tarjan (1972). The basic idea in his algorithm is to study where the

nodes of the strong components are located in the depth first spanning forest of the graph.

The nodes of every strong components form a tree in the spanning forest. To identify the

strong components, the root of each component needs to be labeled first. The root of each

component is the node in the component having the lowest number in the depth first order in

the spanning forest. When the roots are identified, the nodes in a component are obtained as

those descendants of its root that are not descendants of any other component root that is a

descendant of its root.

Stage 3: Generation of functional layout modules if necessary

If two layout modules have many common machines, they may be merged into a Function

Layout module to reduce machine duplication. The commonality between layout modules

Mi and M j is defined asnij

min(ni , n j ), where nij is the number of distinct operations common

to both modules; ni and n j are the number of distinct operations contained in Mi and M j ,

respectively. Given a user-defined threshold level of commonality V (0 ≤ V ≤ 1) for merging

layout modules, the algorithm for merging layout modules is presented as follows:

(1) Calculate the commonality between each pair of layout modules.

(2) Find the pair of layout modules with highest commonality. If the commonality is higher

than the threshold level V, then aggregate the two modules into one, go to (1); else, stop.

The selection of the threshold level V is a specific decision problem that requires the

user to perform the classical tradeoff between inter-module material flow costs and machine

duplication among the modules to eliminate the flows (Arvindh and Irani, 1994).

Stage 4: Expression of the original operation sequences in terms of the layout modules

In this stage, we replace the original part routings by the combination of residual machines

and the layout modules generated using the above procedure.

Given an operation sequence (x1, x2, . . ., xm) and layout modules M1,. . ., Mn , the procedure

is implemented by a greedy heuristic method described as below:

(1) Set i = 1; create a null operation sequence as the new sequence.

(2) If i ≤ m, find the layout module M j which contains the longest substring that matches

(xi , xi+1, . . . , xk), where k ≤ m; else, go to (4).

(3) If k ≤ 1, then put xi as a residual machine at the end of the new sequence, i = i + 1, go

to (2); else, put M j at the end of the new sequence, i = k + 1, go to (2).

(4) Output the new sequence as a modular sequence corresponding to the original operation

sequence.

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To reduce machine duplication, the sequences of modules are adjusted such that any

residual machine occurring in an adjacent layout module is absorbed into the module. This

absorption of the residual machine may cause new strongly connected components to occur

in the layout module into which the machine was absorbed, and thus destroy the flowline,

branched flowline, or patterned flow pattern in that module. In other words, a basic layout

module may become a functional layout module after the adjustment.

Stage 5: Generation of facility layout as a network of layout modules

Based on the adjusted modular sequences, a digraph representation between layout modules

and residual machines in the facility layout are generated. If one or more layout modules

and/or residual machines exhibit no flow from/to other modules and machines, then they

could be merged into a cell module. After machine capacities are calculated, a block layout

can be generated using, for example, the maximum weight planar graph embedding heuristic

proposed by Foulds and Giffin (1985). In the final layout, some process departments are

automatically split and their machines are located at non-adjacent locations; some machines

are shared by two adjacent modules due to limited machine availability. If adjacent modules

in the final layout have a high commonality of machines, then they could be aggregated into

a larger module.

5.3. Industrial application

The method for design of a modular layout was applied during a project sponsored by a

custom forge shop. The sample data provided by the company consisted of 530 products and

57 pieces of equipment. The flow diagram of its current layout (Fig. 16) shows the existing

locations of various machines and support equipment in use at the company, and the flows

in its facility. The flow path of any product starts from Receiving (IN), goes through the

sequence of machines dictated by its routing, and ends in Shipping (OUT). The flow diagram

for the proposed modular layout (Fig. 17) shows the recommended relocation and grouping

of various sets of machines into several layout modules, each of which could be operated by

a single, or small group of associates, and the flows in the proposed layout. Also, the different

modules have been assigned to a new “desired or recommended” location on the forge shop

premises in order to minimize the total distance (and time) of travel between different pairs

of modules. Machines represented as white rectangles are the “monuments” that cannot be

re-located in any new layout that the company decides to implement.

A comparison of the two flow diagrams shows that, without moving the monuments, if the

other machines on the premises were to be grouped into modules and relocated, then there

would be a drastic improvement in (1) the speed of material flows between the modules, (2) vi-

sual connectivity and communication among interdependent machines and (3) multi-machine

operation by individual operators. If it were possible to relocate some of the monuments and

place them at locations that matched their “optional locations” in the improved material flow

network, then even more significant reductions in scrap, order completion time, material

handling costs and wasted labor hours would be achieved.

6. Research contributions

From a research perspective, this paper describes radical departures from standard studies

still being undertaken in two traditionally separate research domains: cellular manufactur-

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Fig. 16 Flow diagram for the current layout

Fig. 17 Flow diagram for the proposed modular layout

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ing and facility layout. In the case of cellular manufacturing, it recommends simply not to

pursue the impractical goal of designing a cellular layout if the data indicates overlapping

clusters of parts (and machine sharing between the cells). In addition, instead of utilizing

the usual approaches of machine-part clustering or operation sequence clustering, it intro-

duces a new approach of common substring detection prior to clustering in order to design

“partial cells” (layout modules). Lastly, it presents heuristic algorithms for design of hybrid

cellular layouts that have actually been, and continue to be used, successfully in numerous

industry projects. Next, in the case of facility layout, while excellent research exists (Sherali

et al., 2003) to optimally design process layouts with unequal-sized departments, this layout

ought never to be implemented in any high-variety low-volume facility! Historically, it causes

batch-and-queue delays, results in high material handling costs and slows down or disrupts

shopfloor communications. In addition, instead of using from-to charts or 0-1 matrices as

input data, it uses the original routings which automatically results in layouts that conform

with the flow patterns implicit to the particular facility under study. Lastly, the string align-

ment algorithm with planar embedding of the resulting graphs suggests logical duplications

of shared resources. Improved material flow as an enabler of shopfloor control is important,

not the optimality of a particular type of layout that does not fit the material flow patterns

specific to each facility.

From a practical industry perspective, the ideas and heuristic methods presented in this

paper are powered by the PFAST software (Irani et al., 2000) for material flow analysis,

facility layout and cell formation. Case studies that describe industrial adoption of the research

described in this paper are available at http://ceti.cse.ohio-state.edu/pfast. PFAST, combined

with a standard block layout package like STORM or SPIRAL is routinely used to support

course projects that IE students, both undergraduate and graduate, do at local companies or as

interns. A major sponsor of this research is the Forging Defense Manufacturing Consortium

(http://fdmc.aticorp.org/shop design.html) because custom forge shops are unable to adopt

Cellular Layouts. With their batch-processing equipment and fixed-location monuments,

they are ideal candidates for Modular Layouts and Virtual Cells. Finally, unlike the approach

proposed in Benjaafar and Sheikhzadeh (2000), the use of routings instead of From-To Charts

as the input data for facility layout significantly increases the flexibility of varying the extent

of machine grouping versus machine duplication and distribution in the layout.

7. Future work

In this research, the authors were primarily focused on solution methods that will prove

viable in industry projects. Consequently, the mathematical formulations presented in this

paper were not implemented as-is using CPLEX or other mathematical programming solvers.

However, there is a need for research to explore the maximum problem sizes that could be

optimally solved prior to resorting to the heuristic solutions proposed in this paper. For

example, how would a linearised formulation look and how do the results obtained from

solving this approximation compare against those produced by our heuristics? Also, the

mathematical formulation for the modular layout problem is essentially a variant of the

formulation for a standard cell formation problem. But that is because a layout module is

essentially a Partial Cell. The more interesting research challenge is the automated recognition

and classification of the weighted directed graph representing a cluster of routings as being

a particular type of module. In the current work, this is done manually by drawing and re-

drawing the graph obtained by aggregation of a cluster of common substrings. Finally, while

simulation may be the preferred tool for comparing alternative layouts in an academic setting,

Springer


research ought to explore cheaper, faster, and less data-intensive methods for performance

evaluation suited for industry projects. The authors are investigating a simple cost model that,

for any HCL, computes the total cost of duplicating machines in that layout. A simple 3-tier

classification of each machine/resource (RED = Monument, impossible to buy additional

equipment and install at another location, YELLOW = Expensive machine, ROI must be

provided to justify purchase of additional equipment, GREEN = Inexpensive machine, no

ROI is necessary to justify purchase of additional equipment) helps to rapidly color code

and assess the feasibility of machine duplication required to implement any HCL layout

alternative to an existing functional or cellular layout.

8. Conclusions

This paper introduced several hybrid cellular layouts that modify a standard Cellular layout

in order to group all shared machines into functional groups, as far as possible. Each HCL

has a different degree of grouping of dissimilar machines and similar machines into cells

and functional groups, respectively. Furthermore, the design of two special types of hybrid

cellular layouts, cascading flowline layout and modular layout, was discussed in detail, along

with examples of their applications in real world cases.

Acknowledgment The authors appreciate the insightful comments and recommendations made by the twoanonymous referees, and the guest editors.

The following federal organizations provided funding that has sustained this R&D project

for several years:

(1) National Science Foundation (NSF): This material is based upon work supported by the

National Science Foundation under Grant Nos. DMI-9521278, DMI-8523809 (later DMI-

9796034), DMI-9734815, DMI-9821033, and DMI-9908437. Any opinions, findings,

and conclusions or recommendations expressed in this material are those of the author(s)

and do not necessarily reflect the views of the National Science Foundation.

(2) PRO-FAST Program supported by the Defense Logistics Agency (DLA): The PRO-FAST

Program is enabled by the dedicated team of professionals representing the Department

of Defense (DOD) and industry. These teammates are determined to ensure the Nation’s

forging industry is positioned for the challenges of the 21st Century. Key team members

include: R&D Enterprise Team (DLA J339), Logistics Research and Development Branch

(DLA - DSCP).

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cascading flowlines and layout modules

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