Int J Adv Manuf Technol (2012) 61:827–842
DOI 10.1007/s00170-011-3752-1
ORIGINAL ARTICLE
Application of axiomatic design, TRIZ, and mixed integer
programming to develop innovative designs: a locomotive
ballast arrangement case study
Gül Okudan Kremer & Ming-Chuan Chiu &
Chun-Yu Lin & Saraj Gupta & David Claudio &
Henri Thevenot
Received: 1 September 2010 / Accepted: 7 November 2011 / Published online: 5 January 2012
# Springer-Verlag London Limited 2011
Abstract In this paper, we present a method incorporating
axiomatic design, TRIZ, and mixed integer programming
(MIP) to solve engineering design problems. Axiomatic
design decomposes the problem into several mutually
G. O. Kremer (*)
School of Engineering Design, The Pennsylvania State University,
213T Hammond Building,
University Park, PA 16802, USA
e-mail: gkremer@psu.edu
G. O. Kremer : C.-Y. Lin : S. Gupta
Department of Industrial and Manufacturing Engineering,
The Pennsylvania State University,
310 Leonhard Building,
University Park, PA 16802, USA
C.-Y. Lin
e-mail: czl134@psu.edu
S. Gupta
e-mail: sgupta@dresser-rand.com
M.-C. Chiu
Department of Industrial Engineering and Engineering
Management, National Tsing Hua University,
Hsinchu, Taiwan 30013, Republic of China
e-mail: mcchiu@ie.nthu.edu.tw
D. Claudio
Department of Mechanical and Industrial Engineering,
Montana State University,
Bozeman, MT 59717-3800, USA
e-mail: david.claudio@ie.montana.edu
H. Thevenot
GE Transportation,
2901 East Lake Road,
Erie, PA 16531, USA
e-mail: henri.thevenot@ge.com
independent sub-problems, TRIZ generates all feasible
design concepts, and MIP optimizes cost and the numerical
configuration among available design options. The method
is illustrated on a locomotive ballast arrangement case
study. Ballast arrangement is a key process for a locomotive
assembly, which determines the carrying capacity. Due to
the unsophisticated technology requirements, the ballast
arrangement process has received little attention. The trend
of mass customization, however, demands locomotive manufacturers to provide diverse products with affordable cost and
reduced time. Thus, a flexible and easy to implement ballast
arrangement process design is sought. The proposed method
determines what material combinations, in what quantity, and
where in the limited cavities should the ballast be allocated to
minimize cost. Using the case study, we demonstrate the
advantages in cost reduction and time savings. The synergy of
these improvements not only can enhance productivity and
agility but also competitive advantage.
Keywords Axiomatic design . TRIZ . MIP .
Design for manufacturability
Notations
Index sets
f
g
h
i
J={1,…, Nj}
K={1,…, Nk}
The ballast located in center front area of
the locomotive
The ballast located in center back area of
the locomotive
The ballast located in front end area of
the locomotive
The ballast located in back-end area of
the locomotive
The different locomotive models, j ∈J
Different types of ballast materials, k ∈K
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Decision variables
Wkfj Total weight of ballast type k in the center front
center area f of model j
Wkgj Total weight of ballast type k in the center back area
g of model j
Wkhj Total weight of ballast type k in the front end area
h of model j
Wkij Total weight of ballast type k in the back-end area i
of model j
C
Total cost which is the summary of all models
BPj Binary variable that controls the balance percentage.
It will be 1 when front end is heavier than back-end,
otherwise 0.
BNj Binary variable that controls the balance percentage.
It will be 1 when back-end is heavier that front end,
otherwise 0.
PXj Number of standard X weight box in the center area
of f and g of model j
PYj Number of standard Y weight box in the center area
of f and g of model j
PZj
Number of standard Z weight box in the center area
of f and g of model j
Parameters
Density of ballast type k
Dk
VF
Available volume in front end of all models
VE
Available volume in back-end of all models
VC Available volume in center end of all models
Ck
Unit cost of ballast type k
TWj Total weight requirement of model j
BI
Balance index of the weight difference between
frond-end and back-end of locomotive
WX Unit weight of the standard ballast type X
WY Unit weight of the standard ballast type Y
WZ Unit weight of the standard ballast type Z
1 Introduction
As global technology competition becomes fiercer, an
ability to solve engineering and technology problems
expeditiously becomes critical for the survival of individual
businesses and entire industries [1]. As such, numerous
problem solving techniques have been devised to solve a
variety of industrial problems. However, every tool does
not suit every application, and hence, it is essential that the
right tool be selected for the application at hand. Based on
their review of the state of the art, Shirwaiker and Okudan
[2] have proposed and demonstrated the effective use of
TRIZ and axiomatic design as appropriate tools for
engineering design problems in general (e.g., product
design and manufacturing process design problems). In this
paper, we append to the synergistic use of TRIZ and
Int J Adv Manuf Technol (2012) 61:827–842
axiomatic design (AD) by showing the need for optimization, and then illustrate the use of the modified method on a
locomotive ballast arrangement case study.
Ballast to a locomotive is a “sweet loading.” It aims to
provide sufficient force so that a locomotive can pull the
cars by increasing its weight. Extra weight will waste
energy, while insufficient weight will reduce the capacity of
a locomotive. Hence, the precise weight control of the
ballast is important. In addition to weight, balance is
another critical concern in ballast arrangement. The weight
difference between the front half and the back half, as well
as the left-hand side and the right-hand side of a locomotive
should be less than 1%.
Traditional ballast construction process is completed
through stacking both metal scrap and slab into specific
ballast cavities inside the locomotive platform. The space is
limited and metal slab is expensive, so the metal scrap is
allocated as much as possible during the construction process.
However, there are several drawbacks in the current process.
First of all, the metal scrap, which is purchased from recycling
facilities, has a variant density. Accordingly, the operators
have to measure weight and balance of locomotive body using
huge scales several times during the stacking process.
Furthermore, unsteady market demand pressures the
manufacturers to produce locomotives in various weights for
diverse purposes, bringing chaos to the shop floor when
shipping schedules change. The ballast construction departments have high work in process (WIP) and very long cycle
times. Finally, the rising cost of metal slab and metal scrap
compresses the revenue. Survey of cheaper alternatives is
necessary. Based on the above mentioned reasons, the need for
the development of a flexible ballast loading process design is
deemed important, and hence is the focus. In the paper, we
present a synergistic approach, which utilizes axiomatic
design (AD), theory of inventive problem solving (TRIZ),
and mixed integer programming model, to solve this problem.
The paper is organized in the following manner:
Section 2 presents a literature review and the rational for
the proposed method. In Sections 3 and 4, we present the
proposed methodology, and then provide its illustration on
the ballast arrangement case study. Finally, conclusions are
provided in Section 5.
2 Literature review
Theory of inventive problem solving technique (TRIZ),
developed by Genrich Altshuller in 1946, is a systematic
ideation technique. After studying more than one million
patents, Altshuller found that problems and their solutions
tend to be repeated across a range of industrial and
scientific situations, and that the patterns of technological
evolution incline to repeat both in industrial applications
Int J Adv Manuf Technol (2012) 61:827–842
and sciences. Accordingly, inventions often made use of
scientific effects that were developed in unrelated areas.
Therefore, the problem solving ways may be repeatable and
predictable. From viewpoint of TRIZ, every factor that
affects a system can be defined as a parameter. There is a
dependency relationship between the parameters of the
system. While improving some parameters with positive
effects to system, some of the other parameters might have
negative effects. This results in a contradiction. Altshuller
asserts that an invention occurs when a contradiction
between parameters is solved. Based on this hypothesis,
TRIZ structures a problem into a “contradiction statement”
and derives solutions that address the problem statement
both from technical and system perspectives. Hence, the
ideality of the design increases while a parameter is
improved without worsening the other parameter [3–5]. In
this manner, TRIZ demonstrates the capability as a support
tool for original idea creation. In this study, we applied the 39
engineering parameters, 40 innovative principles, and the
contradiction matrix to generate new ballast design concepts.
TRIZ has been used in synergistic ways with other
methods (e.g., QFD [5], AHP [6, 7], DFMA [8], and
function-based design [9]). Its effectiveness in idea generation has also been demonstrated in classroom settings [10,
11]. Despite its success in aiding idea generation, however,
TRIZ (implemented alone) falls short in selecting the most
appropriate idea, and hence, using it in unison with
appropriate tools is recommended.
Axiomatic design has been implemented in tandem with
TRIZ. Developed by Suh [12], AD method interrelates four
domains: customer needs (CNs), functional requirements
(FRs), design parameters (DPs), and process variables
(PVs). It first transfers the customer needs (CNs) to
functional requirements (FRs) of a product. The functional
requirements are further mapped to design parameters
(DPs). Each design parameter connects to a process
variable (PV). Each customer need is viewed as a function,
which can be further decomposed into subfunctions. Accordingly, every subproblem again decomposes to one or more
lower level subproblems until it reaches the “axiomatic” level.
Therefore, the problem forms a hierarchical structure. In the
same way, functional requirements (FRs), design parameters
(DPs), and process variables PVs have a corresponding
hierarchical structure. In axiomatic design, every subfunction
of these domains has one on one mapping and this organizes a
“zigzagging” relationship between two architectures.
Two major axioms of AD are independence axiom and
information axiom. The independence axiom maintains the
independence of the functional requirements where each
functional requirement (FR) is satisfied without affecting
the other FRs. The information axiom aims to minimize the
information content of the design. The design that satisfies
both independence and information axioms will be the
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optimal concept. Independence axiom first screens out the
solutions which are “not good.” Then, the information
axiom will analyze the remaining solutions to pick the best
one. The role of axiomatic design in this study is to begin at
the system level and decompose the design problem into
smaller design objects until all design objects are clearly
represented. The details are provided in Section 4.
2.1 Compatibility of AD and TRIZ
In a review of the manufacturing related applications of
TRIZ and AD from literature, Shirwaiker and Okudan [2]
pointed out the major strengths of these tools as: (1) TRIZ
has the capability of generating innovative solutions, and
(2) AD has the capability to analyze effectiveness of
solutions in terms of satisfying the two axioms. Similarly,
Mann [13] discusses the effectiveness of applying TRIZ
and AD concurrently to solve a problem. From the AD
perspective, TRIZ fits very elegantly into the “Ideate and
Create” element of Suh’s design process map. From a TRIZ
perspective, AD offers the potential for improving the
problem definition and problem solving processes through
axioms offering means of assessing the effectiveness of a
design concept, and new perspectives on the specification
of functional requirements and the handling of multilayered
problems [13]. Consequently, a synergistic problem solving
approach using TRIZ and AD has been proposed by
Shirwaiker and Okudan [2].
Ruihong et al. [14] have also proposed an approach
combining AD and TRIZ and explained it using the case
study of a paper machine. However, the synergistic problem
solving approach is a more robust and enhanced approach.
While the Ruihong et al. [14] approach employs TRIZ only
in cases where the design matrix of AD is coupled, the
synergistic approach utilizes TRIZ more effectively in that
TRIZ is used not only for decoupling in case of a coupled
design matrix but is also used for the mapping and
zigzagging processes between the functional domain and
physical domain of the AD hierarchy. This brings efficiency
into the problem solving process.
However, neither the synergistic approach [2] nor Ruihong
et al.’s way of using TRIZ and AD together tackles the
quantitative issues in a design problem. Accordingly, we
expand the synergistic approach to include an optimization
module. Below, we present the modified method and then
show its implementation on the case study.
3 Methodology
The synergistic approach uses TRIZ and AD in concert by
assigning specific functions to the two tools. By applying
TRIZ within an AD framework, we try to capitalize on the
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strengths of both tools. The synergistic approach primarily
uses AD in order to analyze the problem and decompose the
main problem into a hierarchy of basic level problems. TRIZ
is applied to separate functional requirements (FRs) (if they
are coupled) and to generate innovative solutions to the basic
problems in the AD hierarchy. Thus, the framework attempts
to synergistically use detailed analysis capability of AD with
the innovative idea generation prowess of TRIZ.
As indicated before, however, the adopted synergistic
approach does not tackle the quantitative issues in a design
problem. Quantitative issues mostly arise during material
selection and form design phases in a design problem.
Various material properties impact the design in either
positive or negative way, or positively and negatively both
at the same time; hence, material search requires specific
attention. Likewise, form issues in design problems amplify
the complexities in design scenarios, and should be
considered. Accordingly, we expand the synergistic method
to include specific steps for material search and form
ideation in order to expand the design space, and use
optimization to make a final design alternative selection.
The flow of the methodology is provided below.
To solve the locomotive ballast arrangement problem,
we implement the above presented method. Axiomatic
design first decomposes the ballast arrangement problem
into several mutually independent subproblems. Then TRIZ
serves as a systematic ideation technique that generates
all feasible design concepts according to contradictions
of 39 parameters. With different combinations of these
conflicting situations, some among 40 inventive principles
are suggested as generic solutions. Designers can create
specific solutions by interpreting these principles. Finally, a
mixed integer mathematical programming model is developed to optimize total cost and generate a standardized
ballast allocation model for various locomotive platforms.
We present the details of our implementation below.
Int J Adv Manuf Technol (2012) 61:827–842
standard ballast arrangement models can enable quick
reaction to changing customer needs, alternating market
demands, and better utilization of ballast and workforce
resources, and hence a reduction in the long process
time under existing manufacturing conditions.
2. Cost consideration: The company currently uses two
types of ballast materials—metal scrap and metal slab.
Metal scrap is the major ballast material in use, and it is
much cheaper than slab. However, due to the increasing
raw material cost, finding replacement low-cost materials with relatively more stable market prices can benefit
the company in huge savings and prevent it from losing
market competitiveness. Moreover, the transportation
cost for acquiring ballast materials also need to be
taken into account.
3. Complex ballast loading process: The existing ballast
loading process is complex and inefficient. A better
way is required to simplify current ballast loading
process in order to eliminate redundant procedures and
increase the overall efficiency.
Above are the on-going problems that force the company
management to consider ways to improve from the current
status. To solve this problem, we applied the proposed
methodology incorporating axiomatic design, TRIZ and
optimization, and followed the steps closely that were
outlined in Fig. 1.
Problem Definition
Functional Requirements
Design Parameters (DP)
Yes
Can DPs be
decomposed
further?
4 Case study
Company A is a locomotive manufacturing company that
seeks to redesign its existing platform ballast arrangement
system. In their current system, two different types of ballast
are loaded to the locomotive platform to reach five specific
weight requirements requested by customers. However, their
current system lacks efficiency in addition to several
manufacturing problems. These problems include:
1. Lack of standardization: Company A currently uses numerous ballast arrangement models to reach the five
weight requirements from multiple customers. Those
models are mostly acquired either by trial and error or by
past experience, and thus lack standardization. However,
No
Express DPs as Technical
Contradictions (TC)
Utilize 40 Inventive Principles
Materials Search
Form Ideation
Optimization
Fig. 1 Proposed method
Int J Adv Manuf Technol (2012) 61:827–842
4.1 Ballast functional requirements structure
To begin with, AD is introduced to analyze the problem. AD
hierarchically decomposes the problem into independent
functional requirements (FRs) in a top-down manner. In each
hierarchy, brainstorming is used to generate numerous
possible functional requirements, and then group-thinking is
adopted to eliminate inappropriate or dependent ones. For our
problem, we first divided all platforms to be produced based
on the type of the motor: AC-motor platforms and DC-motor
platforms. This consideration is based on the two main types
of product lines that company A produces. In fact, both motorbased platforms can share the same set of hierarchical
structures. For the next lower level hierarchy, the selection
of ballast arrangement methods is considered. Two functional
requirements are built: the standard ballast and the variant
ballast. In our case study, we only focus on the variant ballast
condition, which is the more complex part of the problem. For
the next lower level, the available ballast loading cavities are
enumerated (front, back, and center). Some constraints need to
be taken into account, such as weight constraints and required
air flow capacity. Lastly, for the lowest hierarchy level,
different material alternatives are considered. Figure 2
presents the entire functional requirements structure for the
AC-based platform.
4.2 TRIZ contradictions
After defining all the hierarchical functional requirements
using the AD approach, we introduce TRIZ to determine the
selection of materials with the consideration of their physical
(e.g., density, state, etc.) and other (e.g., cost, availability,
manufacturability, etc.) features. TRIZ is a systematic tool that
can focus idea generation. It enables users to resolve
sophisticated problems in a systematic fashion by relating
the 40 inventive principles to the problem context.
TRIZ starts with the identification of technical contradictions, which are conflicting engineering parameter pairs.
To determine technical contradictions, the first step is to
Fig. 2 Hierarchy of ballast functional requirements structure
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inspect the problem, find out potential improvement directions
and replace them with specific TRIZ parameters. Indeed,
improving from one parameter usually may conflict with one
or more other parameters. To clarify the problem more
thoroughly, it is important to define all the technical contradictions by indicating all the possible conflicts. For our case,
we have 10 improvable engineering parameters potentially
conflicting with 12 unique parameters. These result in 16 pairs
of technical contradictions as shown in Table 1.
In the platform design, the standard ballast will remain fixed
irrespective of the weight requirements of the particular model,
and variant ballast will be adjusted to meet particular requirements. As a result, our team decided to work on the design of
the variant ballast only after finalizing the “form design” and
“total weight” of the standard ballast. Once the FRs hierarchy
was determined, our team proceeded to determine the material
and its attributes (e.g., cost, availability, manufacturability, and
human factors) by using TRIZ. Therefore, the next step was to
formulate different contradictions and their corresponding
TRIZ principles from TRIZ matrix. After achieving all the
solutions for each pair of technical contradictions from the
TRIZ principles, we organized the most commonly applied
recurring principles in Table 2. In this table, we can see that
most suggested principles related to finding better ballast
materials and more appropriate ballast arrangement methods.
Accordingly, we decided to focus our solution efforts around:
(1) ballast material research, (2) concept generation, and (3)
optimization.
After investigating a variety of materials, we proposed
two categories of materials: (1) metals and metal alloys and
(2) non-metal materials.
1. Metals and metal alloys: Table 3 shows the density and
cost information for a number of materials in this
category. After careful consideration of design criteria,
we decided to use cast iron and steel as our major
materials for the metals and metal alloys category. Cast
iron is the material of metal scrap, and steel is the
material of metal slab.
2. Non-metal materials: For non-metal materials, initially,
we selected four candidates: (a) concrete, (b) stone, (c)
brick, and (d) sand. Table 4 shows the density and cost
information for the four non-metal materials. However,
after acquiring detailed information for these materials,
we found that all of the four non-metal materials have
low-density levels. Density is a critical determinant that
excludes alternatives from being potential replacements
to steel-based ballast. However, non-metal materials all
have cost advantages in comparison to metals or metal
alloys. Thus, mixing non-metal materials with metals or
metal allows might be a good way to reduce total
ballast cost. Nevertheless, concrete, brick, and stone are
still not suitable as auxiliary ballast since they have
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Table 1 Contradiction matrix and corresponding TRIZ principles
No.
Feature to improve
Conflicting feature
TRIZ principles
1
Manufacturability (32)
Waste of time (25)
35 Physical or chemical properties
28 Replace a mechanical system
34 Recycling (rejecting and regenerating)
4 Asymmetry
2
Weight of stationary object (2)
Manufacturability (32)
1 Segmentation
27 Cheap disposable
36 Use phase changes
13 Other way around
3
Manufacturability (32)
Waste of energy (22)
4
Volume of stationary object (8)
Shape (12)
19 Periodic action
35 Physical or chemical properties
7 Nesting dolls
2 Separation or extraction
35 Physical or chemical properties
5
Weight of stationary object (2)
Volume of stationary object (8)
35 Physical or chemical properties
10 Preliminary action
19 Periodic action
14 Spherical shapes
6
Stability of object (13)
Amount of substance (26)
15 Dynamism
32 Optical changes
35 Physical or chemical properties
7
Durability of stationary object (16)
Amount of substance (26)
3 Local quality
35 Physical or chemical properties
31 Porous materials
8
Level of automation (38)
Complexity of device (36)
15 Dynamism
24 Intermediary
10 Preliminary action
9
Durability of stationary object (16)
Manufacturability (32)
35 Physical or chemical properties
10 Preliminary action
10
Force (10)
Weight of moving object (1)
8 Counter-weight
1 Segmentation
37 Thermal expansion
18 Mechanical vibration
11
Accuracy of measurement (28)
Manufacturability (32)
6 Universality
35 Physical or chemical properties
25 Self-service
18 Mechanical vibration
12
Accuracy of measurement (28)
Convenience of use (33)
1 Segmentation
13 Other way around
17 Moving to another dimension
34 Recycling (rejecting and regenerating)
13
Weight of stationary object (2)
Harmful side effects (31)
35 Physical or chemical properties
22 Blessing in disguise (harm to benefit)
1 Segmentation
39 Inert environment
14
Convenience of use (33)
Harmful side effects (31)
All
15
Reliability (27)
Productivity (39)
1 Segmentation
35 Physical or chemical properties
29 Pneumatics or hydraulics
38 Strong oxidants
additional drawbacks. Brick and stone cost a lot to
transport while concrete has the manufacturability
problem. Therefore, sand is decided as the only nonmetal material that will be further considered.
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Table 2 Recurring TRIZ principles
TRIZ principles
Number of
occurrences
Description of principle
35 Parameter changes
8
Change concentration or consistency
3 Local quality
6
Enable each part of the system to function in a locally optimized
condition
10 Preliminary action
4
13 “The other way around”
4
Pre-arrange objects or system such that they can come into action at the
most convenient time and place
Make movable objects fixed, and fixed objects movable
15 Dynamization
4
31 Porous materials
4
40 Composite materials
4
Allow a system or object to change to achieve optimal operation under
different conditions
Make an object porous or add porous element OR if an object is already
porous, add something useful into the pores
Change from uniform to composite (multiple) materials where each
material is optimized to a particular function requirement
4.3 Form ideation
Before acquiring the standardized ballast loading model for all
different platform types, we needed to consider a standard
process to load the ballast. In this section, we apply TRIZ to
assist in generating different ways to load ballast by either
Table 3 List of materials with their density and cost
Metal
Density (lb/cu ft)
Cost ($/lb)
Aluminum bronze (3–10% A1)
480.7
0.74–0.97
Antimony, cast
Arsenic
Beryllium
418.0
354.0
505.7
1.25–2.50
0.72
160.00
Bismuth
Cadmium
Cast iron
611.0
540.0
424.5
3.60–4.05
1.84
0.03–0.11
Chromium
Cobalt
Copper
Gold
Iridium
Lead
Manganese
Mercury
428.0
546.0
557.5
1,206.1
1,383.0
711.0
475.0
848.6
0.33–0.43
27.37–31.74
1.33
5,598.00
874.00
0.23–0.35
0.60
800.00
Molybdenum
Nickel
Platinum
Silver
Steel
Tin
Tungsten
Uranium
Vanadium
Zinc
636.0
541.0
1,336.0
654.9
467.0
454.0
1,223.6
1,179.9
343.0
445.4
7.03
2.50–4.73
5,850.00
65.00
0.40
2.90
12.50
9.65–12.20
3.90–5.00
0.43–0.52
redesigning the cavity or redesign the shape of ballast. We
generated a variety of concepts for company A to enable it to
select from after reviewing pros and cons.
4.3.1 Conceptual designs incorporating variability
in the front and back-end cavities
Concept A. Ice cube tray design
In this conceptual design, an ice-cube tray
frame is designed to accommodate the variable weights in the front and back-end
cavities. Therefore, the first step would
involve fabricating the ice-cube tray frame,
which could be made of steel/sheet metal and
should be of the size of the two end cavities
with adequate tolerances for easy insertion
and retrieval. The cavities would first be filled
with the standard quantity of loose ballast as
shown in Fig. 3a. The next step would require
putting the ice-cube tray frame on top of the
loose ballast, and welding it with the platform
base (though welding may not be necessary
for a properly dimensioned tray). This might
also be a part of the standard platform
fabrication process as illustrated in Fig. 3b.
Depending on the variable ballast to be added
to a particular platform model, removable
Table 4 Density and cost of non-metal materials
Non-metal
Sand, dry
Concrete, limestone
Stone (common, generic)
Brick, common red
Density (lb/cu ft)
Cost ($/lb)
111.1
148.0
168.5
120.0
0.03–0.04
0.03–0.04
0.08–0.16
0.12
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Fig. 3 Ice-cube tray design
weights can be added into the ice-cube
cavities either as boxes or slabs, as shown in
Fig. 3c. The ballast hopper may also be
directly used in order to fill the loose ballast
onto the ice-cube tray frame, which is much
similar to filling of a regular ice-cube tray
under a running water tap. One possible
disadvantage of this design would be the
potential over-utilization of the overhead
crane for transporting individual removable
weights to the ice-cube cavities on the
standard platform in shop floor.
Concept B. Stacked ice-cube tray design
This design utilizes an ice-cube tray frame
similar to concept A but differs in the way that it
stacks ice-cube trays in order to add variability.
The ice-cube tray is pre-filled with a standard
quantity of loose ballast, which is densely
packed. In the cavities, they are placed one over
the other in order to add variability. Therefore,
the number of trays determines the variable
Fig. 4 Stacked ice-cube trays
design
weight. Figure 4a shows a standard ice-cube
tray, while Fig. 4b shows the conceptual
design. One disadvantage may be the change
in compactness of the loose ballast in the trays
after the platform is turned upside down,
thereby displacing all the densely packed loose
ballast from the ice-cube trays.
Concept C. Stacked boxes design
This idea is an extension of abovementioned
concept B. The main purpose of this design is to
design a standard box (either variable loose
ballast or slab) to increase the manufacturability
and flexibility. As Fig. 5 shows, these standard
boxes can be assembled in both vertical and
horizontal directions depending on the variable
weight requirements. In order to horizontally
join two boxes, a jig-saw puzzle connection is
proposed.
Concept D. Sliding plates design
This conceptual design is quite similar to
the first ice-cube tray design (concept A), but
Int J Adv Manuf Technol (2012) 61:827–842
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Fig. 5 Stacked boxes design
instead of the cubic-shaped cavities in the icecube tray frame, this design utilizes thin
rectangular plates that slide into the slots.
The slots are fabricated on the ice-cube tray
frame, which is welded on to the platform
after the fixed quantity of loose ballast is
poured into the end cavity. Depending on the
variable weight needed for that particular
model, the required number of plates may be
inserted in the slots. Figure 6 shows the
platform design utilizing the sliding plates
design. One disadvantage of this design may
be the high precision and time required by the
operator to accurately position the thin rectangular slabs into their respective slots. The
overhead crane would be utilized to pick up
the plates, which may also lead to its overutilization.
Concept E. Tetris design
This design utilizes the combination of
three standard components in different ways
to achieve different weights. As shown in
Fig. 7a–d, four rectangular shapes are possible
by welding the standard components in
different ways and each resultant shape has
the same width. Figure 7e shows that once the
standard loose ballast quantity is put, these
Fig. 6 Sliding plates design
weights can be put in the slot on the side of
the end cavity. The advantage here is the easy
control of variable weight.
Concept F. Weight training slab design
In this design, the end cavity is first filled
with the standard quantity of loose ballast.
After that, a lid is placed over the loose
ballast, which contains five cylindrical rods
that are equidistant from each other. Figure 8
illustrates the standard slabs, which may be
put over the cylindrical rods in order to
constrain them from any translatory motion.
Figure 9 shows an alternative concept for the
weight training design, where the standard
slabs are fabricated in a slightly different
manner than in Fig. 8.
Concept G. Ice-tray frame design
Figure 10 shows the ice-cube tray frame,
whose total height extends to the base of the
cavity. A number of cavities may be filled up
to the standard quantity with the loose ballast
and the remaining cavities may be filled with
the slabs in order to individually balance each
end cavity. The major difference of this
conceptual design from the previous icecube tray designs is that in this design, the
length of the frame extends the whole height
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Int J Adv Manuf Technol (2012) 61:827–842
Fig. 7 Tetris design
of the cavity. The ice-cube tray frame is first
welded on to the end cavity, and then the
standard quantity of loose ballast is poured in
the standard cavity as shown in the following
figure.
Concept H. Box with spring-loaded chamber
The purpose of the big box is to reduce the
process time while providing flexibility to add
and remove variable weight (Fig. 11). There are
two cabins in this box. The left side of the
cabin is for loose ballast which accommodates
the standard weight. The right side of the cabin
has a spring-controlled adjustable volume. We
Fig. 8 Weight training slab
design – I
can put slabs in this spring-loaded chamber
depending on the weight requirements. The
main advantage of the spring is to clamp, and
therefore, constrain the variable slabs from
moving inside the chamber.
4.3.2 Conceptual designs incorporating variability
in the central cavity
A. Nesting dolls design
This design is mainly for the central cavity, and it
utilizes the nested doll principle by keeping the airflow
Int J Adv Manuf Technol (2012) 61:827–842
837
Fig. 9 Weight training slab
design – II
considerations in mind. The cavity frame (Fig. 12) is to
be welded on to the central cavity, and is designed
similar to the ice-cube tray (concept A in Section 4.3.1). The shape of the frame provides a path
for the airflow travel (similar to a virtual pipe). This
design can be used for AC platforms as well as DC
platforms since the ice-tray like cavities at the two ends
are symmetric along the central axis, and only one side
may be filled with loose/box/slab as per the variable
weight requirements.
4.3.3 Conceptual designs incorporating variability
on the lid of the front/back-end cavities
A. Folder design
This folder design is based on the principle of
rotation along the hinges (i.e., like a door). However,
the hinged frame consists of slots for accommodating
variable weights in the form of slabs. There are four
different slabs as shown in Fig. 13. In Fig. 13a, the
cavity is filled with the standard quantity of the loose
ballast. Figure 13b–c shows the standard frame, which
has slots for inserting the four different slabs. The
Fig. 10 Conceptual ice-tray
frame design
standard frame is then hinged along with the cavity and
can be swiveled between 0° and 90° because of its pinhole system for hinging (Fig. 13d). After hinging both
the frames on to the cavity, the cavity is closed. This
action also compresses the loose ballast material,
thereby increasing the density. The rotating standard
frame can also be substituted as the cover for the end
cavities.
B. Deck-plate design
In this design, the variable weight is added to the
existing deck plate instead of placing it over the fixed
quantity of standard ballast in the end cavities. The
deck plate is lifted using the overhead crane, and an
outer frame containing the variable weights is welded
to the bottom of the deck plate as shown in Fig. 14b.
The operator then utilizes the overhead crane, and
loads the slab ballasts into the horizontal slots
(Fig. 14e). Finally, the whole deck plate is lowered
on to the standard platform. There are several benefits
of this design. Firstly, the outer frame for the variable
weight compresses the loose ballast material. Another
major advantage is that this design allows two or more
operators to simultaneously load variable weights (in
the form of slabs) in to the frame. At the same time, the
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Int J Adv Manuf Technol (2012) 61:827–842
Fig. 11 Box with spring-loaded
chamber
other operators can fill the front/back-end cavities with
the loose ballast material. This decreases the overall
cycle time. This design is also ergonomically beneficial
to the technicians as the crane height can control the
height of the deck plate (from the ground) based on the
operator height.
C. Cavity lid design
Alternatively, instead of adding weight to the whole
deck plate (as in concept B in Section 4.3.3), separate
lids can be manufactured for both the front and backend cavities. These lids contain the slots for placing the
variable weights and can be lowered on to the
individual cavities with the help of the overhead crane.
Figure 15 shows this design concept.
D. Cavity lid design–2
This design concept is another alternative to the
cavity lid design, and offers an additional advantage of
the ice-cube tray design. It comprises of standard slots
below the lid (Fig. 16), where the operators can place
the variable weights after the standard weight has been
poured in the cavity. The lid is then placed on to the
cavity and perhaps welded. However, if further weight
needs to be added, it can be added on to the sliding ice
tray, which is placed in the center of the top of the lid.
There are slots on top of the ice tray so that a sliding
lid can seal the ice tray. The main advantage of this
design is that it allows flexibility at the shop floor as
the weight can be removed from the top (ice tray).
Fig. 12 Central cavity frame
design
4.3.4 Conceptual ideas for densely packing the loose
ballast material into the front/back-end cavities
A. Pneumatic hydraulic press
Figure 17 shows the use of a pneumatic/hydraulic
(pulsating) press for densely packing the loose ballast into
the two end cavities. A (portable press) might be
integrated to the overhead crane actions, particularly right
after lifting the loose ballast hopper to fill the end cavities.
B. Vacuum suction compression
The purpose of this idea is to compress the volume
of loose materials to increase its density, and meanwhile, the compressed materials can keep a united
rectangle shape so as to efficiently stock them in the
cavity or a cell in the ice-cube frame. As illustrated in
Fig. 18, this idea needs a heat sealer, plastic bag, a steel
container, a filter, and an air compressor.
4.4 Optimization module
After determining the appropriate ballast materials and
potential forms of ballast arrangement, we built optimization models to find out the best ballast arrangement
solutions. In this step, we used integer programming
technique to build two optimization models. For both
models, the objectives are the same, which is to minimize
total material costs. In addition, we also want to achieve a
standardized ballast arrangement scenario from both opti-
Int J Adv Manuf Technol (2012) 61:827–842
839
Fig. 13 Folder design
mization models. The two models are referred to as the
“base model,” and the “material-mix model.”
Following are the four major constraints considered in
the model.
4.5 Mathematical formulation
Volume constraint: In a locomotive platform, ballast can be
loaded in four locations: the front cavity, center front path,
center back path, and rear cavity. We rename these areas as
front end h, front center f, back center g, and back-end i.
Both front end and back-end cavities have unique volumetric constraints. Front center (f) and back center (g) are
physically connected. It is divided into two sections
because of the balance requirement. Equations 3–6 represent the relationships that satisfy the weight requirement
under volume limitations. Front center f and back center g
have airflow constraints. The center path is reserved for the
air flow to reduce the engine temperature. Thus, the
minimum air flow requirement is considered to be the
maximum ballast loading constraint.
The objective function of the MIP model, as shown in
Eqs. 1 and 2 is to achieve the minimum material cost while
satisfying all the constraints. Here, the total material cost is
the summary of all types of unit material cost multiplied by
the allocated weight.
ð1Þ
Min C
Where
C¼
K
X
k¼1
Ck »Wkfj þ Ck »
K
X
Ck »Wkgj þ
k¼1
K
X
k¼1
Ck »Wkhj þ
K
X
Ck »Wkij
k¼1
ð2Þ
Fig. 14 Variability with the deck plate
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Int J Adv Manuf Technol (2012) 61:827–842
Fig. 15 Cavity lid design
K
X
Wkfj þ
k¼1
Dk
K
X
Wkij
k¼1
Wkgj þ
k¼1
K
X
Wkhj
k¼1
K
X
Dk
K
X
k¼1
Wkhj þ
K
X
Wkij TWj
ð3Þ
k¼1
VF
ð4Þ
VE
ð5Þ
Balance: The balance of the platform is very important to
maintain the stability; accordingly, ballast loadings should
not lead to big changes in center of gravity of the platform.
An imbalance coefficient is adopted to verify the balance.
After loading all the ballast onto the platform, the
difference of total weights from both sides of the modified
center of gravity should be limited to be lower than a
balance index, BI. Equations 7 and 8 represent this
relationship.
ð
K
P
k¼1
K
X
ðWkfj þ Wkgj Þ
k¼1
Dk
Wkfj þ
K
P
k¼1
Wkhj Þ ð
K
P
Wkgj þ
k¼1
TWj ðBPj BNj Þ
VC
Fig. 16 Cavity lid design – 2
ð6Þ
BPj þ BNj ¼ 1
K
P
k¼1
Wkij Þ
BI
ð7Þ
ð8Þ
Int J Adv Manuf Technol (2012) 61:827–842
841
Table 5 Cost savings for the base model
Cost
Model
Current ballast
cost (%)
Cost from the
base model (%)
Cost saving
(%)
Model 1
100.00
71.29
28.71
Model 2
134.87
97.10
37.77
Model 3
Model 4
112.90
137.10
110.00
122.90
2.90
14.19
Model 5
216.13
253.47
−37.34
Total Cost
701.00
654.76
46.24
TWj K
X
Wkij k¼1
K
X
Wkhj WX »PXj < WX
ð12Þ
k¼1
Fig. 17 Pneumatic/hydraulic press
Standardized ballast: All the possible types of ballast
loaded to the different models are standardized ballast with
standardized weights. We also try to limit the number of
different weights of ballast used in the models. In our
model, we use three different weights of standard ballast,
which are included in the model with WX, WY, and WZ
notations. This scenario is formulated in Eqs. 9–13.
WZ < WY
ð9Þ
WY < WX
ð10Þ
TWj K
X
k¼1
Wkij K
X
TWj K
X
Wkij k¼1
K
X
Wkhj WX »PXj WY »PYj < WY
k¼1
ð13Þ
Variable-type constraints There are three different types of
variables in the MIP, which are shown in Eqs. 14–16.
Wkfj ; Wkgj ; Wkhj ; Wkij ; C 0
ð14Þ
BPj ; BNj 2 f0; 1g
ð15Þ
PXj ; PYj ; PZj ; 0; Integer
ð16Þ
Wkhj WX »PXj WY »PYj WZ »PZj ¼ 0
4.6 The base model
k¼1
ð11Þ
For this model, we generated a standardized ballast arrangement model based on currently used ballast, metal slab and
metal scrap. Company A currently produces five types of
locomotive platforms with different total weight requirements.
Table 6 Cost comparisons of material-mix model, current model, and
the base model
Cost
Model
Fig. 18 Vacuum suction compression technique
Model 1
Model 2
Model 3
Model 4
Model 5
Total Cost
Current ballast Base model Material-mix Cost saving
cost (%)
(%)
model (%)
(%)
100.00
134.87
112.90
137.10
216.13
701.00
71.29
97.10
110.00
122.90
253.47
654.76
55.94
77.26
84.12
93.19
252.14
562.64
44.06
57.61
28.79
43.91
−36.01
138.36
842
Other factors also need to be considered during the model
construction process. For example, after loading all the ballast
to the platform, the difference across two halves of the
locomotive weight should be less than 0.5%. Three types of
standardized ballast are 2,000, 3,000, and 4,000 lbs. Metal slab
costs $0.41 per pound, and metal scrap costs $0.21 per pound.
Based on the information above, we formulated and
solved the base model in the mathematical optimization
software, Lingo. Results are provided in Table 5, where the
solution is provided for one locomotive platform per model.
We can see that, despite the fact that we do not consider the
adoption of additional ballast materials in the base model,
using standardized model can still benefit company A with
a total cost saving of 46.24%. Note that cost values are
provided in percentage terms taking the current ballast for
model 1 as the nominal value (100%). However, adopting
standardized ballast arrangement model can increase the
cost for the highest weight requirement platform. The
reason is that standardized model reduces the ballast
loading flexibility. The standardized model can simplify
the ballast loading process, improve WIP, and better react to
the changing demand.
4.7 The material-mix model
For the material-mix model, while we apply all the
constraints used in the base model, we also consider the
possible combination of three types of ballast—metal slab,
metal scrap, and sand. The cost information used in the
material-mix model for metal slab and meal scrap are the
same. For sand, the unit cost is assumed to be $0.02 per
pound. The total cost of material-mix model, the current
ballast model, and the base model are shown in Table 6. We
can see that the material-mix model has huge cost savings
in comparison to the base model (138.36%).
5 Discussion and conclusions
In its essence, design for manufacturability is the goal of
this case study. We investigated the current ballast process
and constructed a MIP model to optimize the ballast
material cost. The rough estimates indicate considerable
savings in the material cost for the case study company. In
addition, we developed several platform-based ballast
design concepts that fit the current shop floor environment.
Hence, investment on migration to new ballast process is
trivial. With the modular design perspective, ballast sizes
and types are classified as several different standardized
weights. In the meantime, the whole ballast construction
process will be simple. This design can be modified into
different weight specifications within a short time. The
benefit of these new designs is obvious and significant. The
Int J Adv Manuf Technol (2012) 61:827–842
simplicity of the ballast construction process can decrease
the process time and enhance shop floor capacity. High
flexibility in achieving different weight configurations will
also reduce the WIP level and keep the production schedule
robust under dynamic demand conditions. Hence, the shop
floor space can be saved. The synergy of these improvements not only enhances the productivity and responsiveness but also competitive advantage.
More importantly, the actual industrial case study presented
in this paper, not only shows that TRIZ and AD usage in
unison is a powerful tool for solving complex industrial
problems, but also blends the power of optimization.
Acknowledgements We acknowledge contributions from our
colleagues Mr. Teahyun Kim and Dr. Denise Bauer.
References
1. Jugulum R, Sefik M (1998) Building a robust manufacturing
strategy. Comput Ind Eng 35(1/2):225–228
2. Shirwaiker RA, Okudan GE (2008) TRIZ and axiomatic design: a
review of case-studies and a proposed synergistic use. J Intell
Manuf 19(1):33–47
3. Low MK, Lamvik T, Walsh K, Myklebust O (2001) Manufacturing a green service: engaging the TRIZ model of innovation. IEEE
Trans Electron Packag Manuf 24(1):10–17
4. Akay D, Demiray A, Kurt M (2008) Collaborative tool for solving
human factors problems in the manufacturing environment: the
theory of inventive problem solving technique (TRIZ) method. Int
J Prod Res 46(11):2913–2925
5. Yamashina H, Ito T, Kawada H (2002) Innovative product
development process by integrating QFD and TRIZ. Int J Prod
Res 40(5):1031–1050
6. Li T-S, Huang H-H (2009) Applying TRIZ and Fuzzy AHP to
develop innovative design for automated manufacturing systems.
Expert Syst Appl 36(4):8302–8312
7. Li T (2010) Applying TRIZ and AHP to develop innovative
design for automated assembly systems. Int J Adv Manuf Technol
46:301–313
8. Bariani PF, Berti GA, Lucchetta G (2004) A combined DFMA
and TRIZ approach to the simplification of product structure. Proc
Ins Mech Eng Part B: J Eng Manuf 218(8):1023–1027
9. Nix, A.A., Sherrett, B. and Stone, R.B. 2011. A function based
approach to TRIZ. Proceedings of ASME International Design
Engineering Technical Conferences, August 29–31, Washington, D.C
10. Okudan GE, Ogot M, Shirwaiker R (2002) An Investigation on
the Effectiveness Design Ideation Using TRIZ. Proceedings of
IDETC/CIE 2006 Design Education Conference, September 10–
13, 2006, Philadelphia, PA
11. Okudan G.E., Chiu M-C, Lin C., Schmidt L., Vargas N, and
Linsey J. "A pilot exploration of systematic ideation methods and
tools on design learning" Information Technology Based Higher
Education and Training (ITHET), April 29th - May 1 2010
12. Suh NP (1995) Designing-in of quality through axiomatic design.
IEEE Trans Reliab 44(2):256–264
13. Mann, D., 1999. Axiomatic design and TRIZ: compatibilities and
contradictions. The TRIZ Journal (http://www.triz-journal.com)
14. Ruihong, Z., Runhua, T.,and Guozhong, C., 2004. Case study in
AD and TRIZ:A papermachine. TRIZ Journal (http://www.
trizjournal.com)