application of axiomatic design, triz, and mixed integer...

ORIGINAL ARTICLE

Application of axiomatic design, TRIZ, and mixed integerprogramming to develop innovative designs: a locomotiveballast 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# Springer-Verlag London Limited 2011

Abstract In this paper, we present a method incorporatingaxiomatic design, TRIZ, and mixed integer programming(MIP) to solve engineering design problems. Axiomaticdesign decomposes the problem into several mutually

independent sub-problems, TRIZ generates all feasibledesign concepts, and MIP optimizes cost and the numericalconfiguration among available design options. The methodis illustrated on a locomotive ballast arrangement casestudy. Ballast arrangement is a key process for a locomotiveassembly, which determines the carrying capacity. Due tothe unsophisticated technology requirements, the ballastarrangement process has received little attention. The trendof mass customization, however, demands locomotive man-ufacturers to provide diverse products with affordable cost andreduced time. Thus, a flexible and easy to implement ballastarrangement process design is sought. The proposed methoddetermines what material combinations, in what quantity, andwhere in the limited cavities should the ballast be allocated tominimize cost. Using the case study, we demonstrate theadvantages in cost reduction and time savings. The synergy ofthese improvements not only can enhance productivity andagility but also competitive advantage.

Keywords Axiomatic design . TRIZ .MIP.

Design for manufacturability

NotationsIndex setsf The ballast located in center front area of

the locomotiveg The ballast located in center back area of

the locomotiveh The ballast located in front end area of

the locomotivei The ballast located in back-end area of

the locomotiveJ={1,…, Nj} The different locomotive models, j ∈JK={1,…, Nk} Different types of ballast materials, k ∈K

G. O. Kremer (*)School of Engineering Design, The Pennsylvania State University,213T Hammond Building,University Park, PA 16802, USAe-mail: [email protected]

G. O. Kremer :C.-Y. Lin : S. GuptaDepartment of Industrial and Manufacturing Engineering,The Pennsylvania State University,310 Leonhard Building,University Park, PA 16802, USA

C.-Y. Line-mail: [email protected]

S. Guptae-mail: [email protected]

M.-C. ChiuDepartment of Industrial Engineering and EngineeringManagement, National Tsing Hua University,Hsinchu, Taiwan 30013, Republic of Chinae-mail: [email protected]

D. ClaudioDepartment of Mechanical and Industrial Engineering,Montana State University,Bozeman, MT 59717-3800, USAe-mail: [email protected]

H. ThevenotGE Transportation,2901 East Lake Road,Erie, PA 16531, USAe-mail: [email protected]

Int J Adv Manuf TechnolDOI 10.1007/s00170-011-3752-1

Decision variablesWkfj Total weight of ballast type k in the center front

center area f of model jWkgj Total weight of ballast type k in the center back area

g of model jWkhj Total weight of ballast type k in the front end area

h of model jWkij Total weight of ballast type k in the back-end area i

of model jC Total cost which is the summary of all modelsBPj 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 areaof f and g of model j

PYj Number of standard Y weight box in the center areaof f and g of model j

PZj Number of standard Z weight box in the center areaof f and g of model j

ParametersDk Density of ballast type kVF Available volume in front end of all modelsVE Available volume in back-end of all modelsVC Available volume in center end of all modelsCk Unit cost of ballast type kTWj Total weight requirement of model jBI Balance index of the weight difference between

frond-end and back-end of locomotiveWX Unit weight of the standard ballast type XWY Unit weight of the standard ballast type YWZ Unit weight of the standard ballast type Z

1 Introduction

As global technology competition becomes fiercer, anability to solve engineering and technology problemsexpeditiously becomes critical for the survival of individualbusinesses and entire industries [1]. As such, numerousproblem solving techniques have been devised to solve avariety of industrial problems. However, every tool doesnot suit every application, and hence, it is essential that theright tool be selected for the application at hand. Based ontheir review of the state of the art, Shirwaiker and Okudan[2] have proposed and demonstrated the effective use ofTRIZ and axiomatic design as appropriate tools forengineering design problems in general (e.g., productdesign and manufacturing process design problems). In thispaper, we append to the synergistic use of TRIZ and

axiomatic design (AD) by showing the need for optimiza-tion, and then illustrate the use of the modified method on alocomotive ballast arrangement case study.

Ballast to a locomotive is a “sweet loading.” It aims toprovide sufficient force so that a locomotive can pull thecars by increasing its weight. Extra weight will wasteenergy, while insufficient weight will reduce the capacity ofa locomotive. Hence, the precise weight control of theballast is important. In addition to weight, balance isanother critical concern in ballast arrangement. The weightdifference between the front half and the back half, as wellas the left-hand side and the right-hand side of a locomotiveshould be less than 1%.

Traditional ballast construction process is completedthrough stacking both metal scrap and slab into specificballast cavities inside the locomotive platform. The space islimited and metal slab is expensive, so the metal scrap isallocated 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 recyclingfacilities, has a variant density. Accordingly, the operatorshave to measure weight and balance of locomotive body usinghuge scales several times during the stacking process.

Furthermore, unsteady market demand pressures themanufacturers to produce locomotives in various weights fordiverse purposes, bringing chaos to the shop floor whenshipping schedules change. The ballast construction depart-ments have high work in process (WIP) and very long cycletimes. Finally, the rising cost of metal slab and metal scrapcompresses the revenue. Survey of cheaper alternatives isnecessary. Based on the abovementioned reasons, the need forthe development of a flexible ballast loading process design isdeemed important, and hence is the focus. In the paper, wepresent a synergistic approach, which utilizes axiomaticdesign (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 forthe proposed method. In Sections 3 and 4, we present theproposed methodology, and then provide its illustration onthe ballast arrangement case study. Finally, conclusions areprovided in Section 5.

2 Literature review

Theory of inventive problem solving technique (TRIZ),developed by Genrich Altshuller in 1946, is a systematicideation technique. After studying more than one millionpatents, Altshuller found that problems and their solutionstend to be repeated across a range of industrial andscientific situations, and that the patterns of technologicalevolution incline to repeat both in industrial applications

Int J Adv Manuf Technol

and sciences. Accordingly, inventions often made use ofscientific effects that were developed in unrelated areas.Therefore, the problem solving ways may be repeatable andpredictable. From viewpoint of TRIZ, every factor thataffects a system can be defined as a parameter. There is adependency relationship between the parameters of thesystem. While improving some parameters with positiveeffects to system, some of the other parameters might havenegative effects. This results in a contradiction. Altshullerasserts that an invention occurs when a contradictionbetween parameters is solved. Based on this hypothesis,TRIZ structures a problem into a “contradiction statement”and derives solutions that address the problem statementboth from technical and system perspectives. Hence, theideality of the design increases while a parameter isimproved without worsening the other parameter [3–5]. Inthis manner, TRIZ demonstrates the capability as a supporttool for original idea creation. In this study, we applied the 39engineering parameters, 40 innovative principles, and thecontradiction matrix to generate new ballast design concepts.

TRIZ has been used in synergistic ways with othermethods (e.g., QFD [5], AHP [6, 7], DFMA [8], andfunction-based design [9]). Its effectiveness in idea gener-ation 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 mostappropriate idea, and hence, using it in unison withappropriate tools is recommended.

Axiomatic design has been implemented in tandem withTRIZ. Developed by Suh [12], AD method interrelates fourdomains: customer needs (CNs), functional requirements(FRs), design parameters (DPs), and process variables(PVs). It first transfers the customer needs (CNs) tofunctional requirements (FRs) of a product. The functionalrequirements are further mapped to design parameters(DPs). Each design parameter connects to a processvariable (PV). Each customer need is viewed as a function,which can be further decomposed into subfunctions. Accord-ingly, every subproblem again decomposes to one or morelower level subproblems until it reaches the “axiomatic” level.Therefore, the problem forms a hierarchical structure. In thesame way, functional requirements (FRs), design parameters(DPs), and process variables PVs have a correspondinghierarchical structure. In axiomatic design, every subfunctionof these domains has one on one mapping and this organizes a“zigzagging” relationship between two architectures.

Two major axioms of AD are independence axiom andinformation axiom. The independence axiom maintains theindependence of the functional requirements where eachfunctional requirement (FR) is satisfied without affectingthe other FRs. The information axiom aims to minimize theinformation content of the design. The design that satisfiesboth independence and information axioms will be the

optimal concept. Independence axiom first screens out thesolutions which are “not good.” Then, the informationaxiom will analyze the remaining solutions to pick the bestone. The role of axiomatic design in this study is to begin atthe system level and decompose the design problem intosmaller design objects until all design objects are clearlyrepresented. The details are provided in Section 4.

2.1 Compatibility of AD and TRIZ

In a review of the manufacturing related applications ofTRIZ and AD from literature, Shirwaiker and Okudan [2]pointed out the major strengths of these tools as: (1) TRIZhas the capability of generating innovative solutions, and(2) AD has the capability to analyze effectiveness ofsolutions in terms of satisfying the two axioms. Similarly,Mann [13] discusses the effectiveness of applying TRIZand AD concurrently to solve a problem. From the ADperspective, TRIZ fits very elegantly into the “Ideate andCreate” element of Suh’s design process map. From a TRIZperspective, AD offers the potential for improving theproblem definition and problem solving processes throughaxioms offering means of assessing the effectiveness of adesign concept, and new perspectives on the specificationof functional requirements and the handling of multilayeredproblems [13]. Consequently, a synergistic problem solvingapproach using TRIZ and AD has been proposed byShirwaiker and Okudan [2].

Ruihong et al. [14] have also proposed an approachcombining AD and TRIZ and explained it using the casestudy of a paper machine. However, the synergistic problemsolving approach is a more robust and enhanced approach.While the Ruihong et al. [14] approach employs TRIZ onlyin cases where the design matrix of AD is coupled, thesynergistic approach utilizes TRIZ more effectively in thatTRIZ is used not only for decoupling in case of a coupleddesign matrix but is also used for the mapping andzigzagging processes between the functional domain andphysical domain of the AD hierarchy. This brings efficiencyinto the problem solving process.

However, neither the synergistic approach [2] nor Ruihonget al.’s way of using TRIZ and AD together tackles thequantitative issues in a design problem. Accordingly, weexpand the synergistic approach to include an optimizationmodule. Below, we present the modified method and thenshow its implementation on the case study.

3 Methodology

The synergistic approach uses TRIZ and AD in concert byassigning specific functions to the two tools. By applyingTRIZ within an AD framework, we try to capitalize on the


strengths of both tools. The synergistic approach primarilyuses AD in order to analyze the problem and decompose themain problem into a hierarchy of basic level problems. TRIZis applied to separate functional requirements (FRs) (if theyare coupled) and to generate innovative solutions to the basicproblems in the AD hierarchy. Thus, the framework attemptsto synergistically use detailed analysis capability of AD withthe innovative idea generation prowess of TRIZ.

As indicated before, however, the adopted synergisticapproach does not tackle the quantitative issues in a designproblem. Quantitative issues mostly arise during materialselection and form design phases in a design problem.Various material properties impact the design in eitherpositive or negative way, or positively and negatively bothat the same time; hence, material search requires specificattention. Likewise, form issues in design problems amplifythe complexities in design scenarios, and should beconsidered. Accordingly, we expand the synergistic methodto include specific steps for material search and formideation in order to expand the design space, and useoptimization 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. Axiomaticdesign first decomposes the ballast arrangement probleminto several mutually independent subproblems. Then TRIZserves as a systematic ideation technique that generatesall feasible design concepts according to contradictionsof 39 parameters. With different combinations of theseconflicting situations, some among 40 inventive principlesare suggested as generic solutions. Designers can createspecific solutions by interpreting these principles. Finally, amixed integer mathematical programming model is devel-oped to optimize total cost and generate a standardizedballast allocation model for various locomotive platforms.We present the details of our implementation below.

4 Case study

Company A is a locomotive manufacturing company thatseeks to redesign its existing platform ballast arrangementsystem. In their current system, two different types of ballastare loaded to the locomotive platform to reach five specificweight requirements requested by customers. However, theircurrent system lacks efficiency in addition to severalmanufacturing problems. These problems include:

1. Lack of standardization: Company A currently uses nu-merous ballast arrangement models to reach the fiveweight requirements from multiple customers. Thosemodels are mostly acquired either by trial and error or bypast experience, and thus lack standardization. However,

standard ballast arrangement models can enable quickreaction to changing customer needs, alternating marketdemands, and better utilization of ballast and workforceresources, and hence a reduction in the long processtime under existing manufacturing conditions.

2. Cost consideration: The company currently uses twotypes of ballast materials—metal scrap and metal slab.Metal scrap is the major ballast material in use, and it ismuch cheaper than slab. However, due to the increasingraw material cost, finding replacement low-cost materi-als with relatively more stable market prices can benefitthe company in huge savings and prevent it from losingmarket competitiveness. Moreover, the transportationcost for acquiring ballast materials also need to betaken into account.

3. Complex ballast loading process: The existing ballastloading process is complex and inefficient. A betterway is required to simplify current ballast loadingprocess in order to eliminate redundant procedures andincrease the overall efficiency.

Above are the on-going problems that force the companymanagement to consider ways to improve from the currentstatus. To solve this problem, we applied the proposedmethodology incorporating axiomatic design, TRIZ andoptimization, and followed the steps closely that wereoutlined in Fig. 1.

Problem Definition

Functional Requirements

Design Parameters (DP)

Can DPs be decomposed

further?

Express DPs as Technical Contradictions (TC)

Utilize 40 Inventive Principles

Materials Search Form Ideation

Optimization

No

Yes

Fig. 1 Proposed method


4.1 Ballast functional requirements structure

To begin with, AD is introduced to analyze the problem. ADhierarchically decomposes the problem into independentfunctional requirements (FRs) in a top-down manner. In eachhierarchy, brainstorming is used to generate numerouspossible functional requirements, and then group-thinking isadopted to eliminate inappropriate or dependent ones. For ourproblem, we first divided all platforms to be produced basedon the type of the motor: AC-motor platforms and DC-motorplatforms. This consideration is based on the two main typesof product lines that company A produces. In fact, both motor-based platforms can share the same set of hierarchicalstructures. For the next lower level hierarchy, the selectionof ballast arrangement methods is considered. Two functionalrequirements are built: the standard ballast and the variantballast. In our case study, we only focus on the variant ballastcondition, which is the more complex part of the problem. Forthe next lower level, the available ballast loading cavities areenumerated (front, back, and center). Some constraints need tobe taken into account, such as weight constraints and requiredair flow capacity. Lastly, for the lowest hierarchy level,different material alternatives are considered. Figure 2presents the entire functional requirements structure for theAC-based platform.

4.2 TRIZ contradictions

After defining all the hierarchical functional requirementsusing the AD approach, we introduce TRIZ to determine theselection 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 thatcan focus idea generation. It enables users to resolvesophisticated problems in a systematic fashion by relatingthe 40 inventive principles to the problem context.

TRIZ starts with the identification of technical contra-dictions, which are conflicting engineering parameter pairs.To determine technical contradictions, the first step is to

inspect the problem, find out potential improvement directionsand replace them with specific TRIZ parameters. Indeed,improving from one parameter usually may conflict with oneor more other parameters. To clarify the problem morethoroughly, it is important to define all the technical contra-dictions by indicating all the possible conflicts. For our case,we have 10 improvable engineering parameters potentiallyconflicting with 12 unique parameters. These result in 16 pairsof technical contradictions as shown in Table 1.

In the platform design, the standard ballast will remain fixedirrespective of the weight requirements of the particular model,and variant ballast will be adjusted to meet particular require-ments. As a result, our team decided to work on the design ofthe variant ballast only after finalizing the “form design” and“total weight” of the standard ballast. Once the FRs hierarchywas determined, our team proceeded to determine the materialand its attributes (e.g., cost, availability, manufacturability, andhuman factors) by using TRIZ. Therefore, the next step was toformulate different contradictions and their correspondingTRIZ principles from TRIZ matrix. After achieving all thesolutions for each pair of technical contradictions from theTRIZ principles, we organized the most commonly appliedrecurring principles in Table 2. In this table, we can see thatmost suggested principles related to finding better ballastmaterials 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 proposedtwo categories of materials: (1) metals and metal alloys and(2) non-metal materials.

1. Metals and metal alloys: Table 3 shows the density andcost information for a number of materials in thiscategory. After careful consideration of design criteria,we decided to use cast iron and steel as our majormaterials for the metals and metal alloys category. Castiron is the material of metal scrap, and steel is thematerial 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 costinformation for the four non-metal materials. However,after acquiring detailed information for these materials,we found that all of the four non-metal materials havelow-density levels. Density is a critical determinant thatexcludes alternatives from being potential replacementsto steel-based ballast. However, non-metal materials allhave cost advantages in comparison to metals or metalalloys. Thus, mixing non-metal materials with metals ormetal allows might be a good way to reduce totalballast cost. Nevertheless, concrete, brick, and stone arestill not suitable as auxiliary ballast since they haveFig. 2 Hierarchy of ballast functional requirements structure


additional drawbacks. Brick and stone cost a lot totransport while concrete has the manufacturability

problem. Therefore, sand is decided as the only non-metal material that will be further considered.

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) 19 Periodic action

35 Physical or chemical properties

4 Volume of stationary object (8) Shape (12) 7 Nesting dolls

2 Separation or extraction


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


7 Durability of stationary object (16) Amount of substance (26) 3 Local quality


31 Porous materials

8 Level of automation (38) Complexity of device (36) 15 Dynamism

24 Intermediary


9 Durability of stationary object (16) Manufacturability (32) 35 Physical or chemical properties


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


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


29 Pneumatics or hydraulics

38 Strong oxidants


4.3 Form ideation

Before acquiring the standardized ballast loading model for alldifferent platform types, we needed to consider a standardprocess to load the ballast. In this section, we apply TRIZ toassist in generating different ways to load ballast by either

redesigning the cavity or redesign the shape of ballast. Wegenerated a variety of concepts for company A to enable it toselect from after reviewing pros and cons.

4.3.1 Conceptual designs incorporating variabilityin the front and back-end cavities

Concept A. Ice cube tray designIn this conceptual design, an ice-cube tray

frame is designed to accommodate the vari-able weights in the front and back-endcavities. Therefore, the first step wouldinvolve fabricating the ice-cube tray frame,which could be made of steel/sheet metal andshould be of the size of the two end cavitieswith adequate tolerances for easy insertionand retrieval. The cavities would first be filledwith the standard quantity of loose ballast asshown in Fig. 3a. The next step would requireputting the ice-cube tray frame on top of theloose ballast, and welding it with the platformbase (though welding may not be necessaryfor a properly dimensioned tray). This mightalso be a part of the standard platformfabrication process as illustrated in Fig. 3b.Depending on the variable ballast to be addedto a particular platform model, removable

Table 2 Recurring TRIZ principles

TRIZ principles Number ofoccurrences

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 optimizedcondition

10 Preliminary action 4 Pre-arrange objects or system such that they can come into action at themost convenient time and place

13 “The other way around” 4 Make movable objects fixed, and fixed objects movable

15 Dynamization 4 Allow a system or object to change to achieve optimal operation underdifferent conditions

31 Porous materials 4 Make an object porous or add porous element OR if an object is alreadyporous, add something useful into the pores

40 Composite materials 4 Change from uniform to composite (multiple) materials where eachmaterial is optimized to a particular function requirement

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 418.0 1.25–2.50

Arsenic 354.0 0.72

Beryllium 505.7 160.00

Bismuth 611.0 3.60–4.05

Cadmium 540.0 1.84

Cast iron 424.5 0.03–0.11

Chromium 428.0 0.33–0.43

Cobalt 546.0 27.37–31.74

Copper 557.5 1.33

Gold 1,206.1 5,598.00

Iridium 1,383.0 874.00

Lead 711.0 0.23–0.35

Manganese 475.0 0.60

Mercury 848.6 800.00

Molybdenum 636.0 7.03

Nickel 541.0 2.50–4.73

Platinum 1,336.0 5,850.00

Silver 654.9 65.00

Steel 467.0 0.40

Tin 454.0 2.90

Tungsten 1,223.6 12.50

Uranium 1,179.9 9.65–12.20

Vanadium 343.0 3.90–5.00

Zinc 445.4 0.43–0.52

Table 4 Density and cost of non-metal materials

Non-metal Density (lb/cu ft) Cost ($/lb)

Sand, dry 111.1 0.03–0.04

Concrete, limestone 148.0 0.03–0.04

Stone (common, generic) 168.5 0.08–0.16

Brick, common red 120.0 0.12


weights can be added into the ice-cubecavities either as boxes or slabs, as shown inFig. 3c. The ballast hopper may also bedirectly used in order to fill the loose ballastonto the ice-cube tray frame, which is muchsimilar to filling of a regular ice-cube trayunder a running water tap. One possibledisadvantage of this design would be thepotential over-utilization of the overheadcrane for transporting individual removableweights to the ice-cube cavities on thestandard platform in shop floor.

Concept B. Stacked ice-cube tray designThis design utilizes an ice-cube tray frame

similar to concept A but differs in the way that itstacks ice-cube trays in order to add variability.The ice-cube tray is pre-filled with a standardquantity of loose ballast, which is denselypacked. In the cavities, they are placed one overthe other in order to add variability. Therefore,the number of trays determines the variable

weight. Figure 4a shows a standard ice-cubetray, while Fig. 4b shows the conceptualdesign. One disadvantage may be the changein compactness of the loose ballast in the traysafter the platform is turned upside down,thereby displacing all the densely packed looseballast from the ice-cube trays.

Concept C. Stacked boxes designThis idea is an extension of abovementioned

concept B. The main purpose of this design is todesign a standard box (either variable looseballast or slab) to increase the manufacturabilityand flexibility. As Fig. 5 shows, these standardboxes can be assembled in both vertical andhorizontal directions depending on the variableweight requirements. In order to horizontallyjoin two boxes, a jig-saw puzzle connection isproposed.

Concept D. Sliding plates designThis conceptual design is quite similar to

the first ice-cube tray design (concept A), but

Fig. 3 Ice-cube tray design

Fig. 4 Stacked ice-cube traysdesign


instead of the cubic-shaped cavities in the ice-cube tray frame, this design utilizes thinrectangular plates that slide into the slots.The slots are fabricated on the ice-cube trayframe, which is welded on to the platformafter the fixed quantity of loose ballast ispoured into the end cavity. Depending on thevariable weight needed for that particularmodel, the required number of plates may beinserted in the slots. Figure 6 shows theplatform design utilizing the sliding platesdesign. One disadvantage of this design maybe the high precision and time required by theoperator to accurately position the thin rect-angular slabs into their respective slots. Theoverhead crane would be utilized to pick upthe plates, which may also lead to its over-utilization.

Concept E. Tetris designThis design utilizes the combination of

three standard components in different waysto achieve different weights. As shown inFig. 7a–d, four rectangular shapes are possibleby welding the standard components indifferent ways and each resultant shape hasthe same width. Figure 7e shows that once thestandard loose ballast quantity is put, these

weights can be put in the slot on the side ofthe end cavity. The advantage here is the easycontrol of variable weight.

Concept F. Weight training slab designIn this design, the end cavity is first filled

with the standard quantity of loose ballast.After that, a lid is placed over the looseballast, which contains five cylindrical rodsthat are equidistant from each other. Figure 8illustrates the standard slabs, which may beput over the cylindrical rods in order toconstrain them from any translatory motion.Figure 9 shows an alternative concept for theweight training design, where the standardslabs are fabricated in a slightly differentmanner than in Fig. 8.

Concept G. Ice-tray frame designFigure 10 shows the ice-cube tray frame,

whose total height extends to the base of thecavity. A number of cavities may be filled upto the standard quantity with the loose ballastand the remaining cavities may be filled withthe slabs in order to individually balance eachend cavity. The major difference of thisconceptual design from the previous ice-cube tray designs is that in this design, thelength of the frame extends the whole height

Fig. 5 Stacked boxes design

Fig. 6 Sliding plates design


of the cavity. The ice-cube tray frame is firstwelded on to the end cavity, and then thestandard quantity of loose ballast is poured inthe standard cavity as shown in the followingfigure.

Concept H. Box with spring-loaded chamberThe purpose of the big box is to reduce the

process time while providing flexibility to addand remove variable weight (Fig. 11). There aretwo cabins in this box. The left side of thecabin is for loose ballast which accommodatesthe standard weight. The right side of the cabinhas a spring-controlled adjustable volume. We

can put slabs in this spring-loaded chamberdepending on the weight requirements. Themain advantage of the spring is to clamp, andtherefore, constrain the variable slabs frommoving inside the chamber.

4.3.2 Conceptual designs incorporating variabilityin the central cavity

A. Nesting dolls designThis design is mainly for the central cavity, and it

utilizes the nested doll principle by keeping the airflow

Fig. 7 Tetris design

Fig. 8 Weight training slabdesign – I


considerations in mind. The cavity frame (Fig. 12) is tobe welded on to the central cavity, and is designedsimilar to the ice-cube tray (concept A in Sec-tion 4.3.1). The shape of the frame provides a pathfor the airflow travel (similar to a virtual pipe). Thisdesign can be used for AC platforms as well as DCplatforms since the ice-tray like cavities at the two endsare symmetric along the central axis, and only one sidemay be filled with loose/box/slab as per the variableweight requirements.

4.3.3 Conceptual designs incorporating variabilityon the lid of the front/back-end cavities

A. Folder designThis 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 accommodatingvariable weights in the form of slabs. There are fourdifferent slabs as shown in Fig. 13. In Fig. 13a, thecavity is filled with the standard quantity of the looseballast. Figure 13b–c shows the standard frame, whichhas slots for inserting the four different slabs. The

standard frame is then hinged along with the cavity andcan be swiveled between 0° and 90° because of its pin-hole system for hinging (Fig. 13d). After hinging boththe frames on to the cavity, the cavity is closed. Thisaction also compresses the loose ballast material,thereby increasing the density. The rotating standardframe can also be substituted as the cover for the endcavities.

B. Deck-plate designIn this design, the variable weight is added to the

existing deck plate instead of placing it over the fixedquantity of standard ballast in the end cavities. Thedeck plate is lifted using the overhead crane, and anouter frame containing the variable weights is weldedto the bottom of the deck plate as shown in Fig. 14b.The operator then utilizes the overhead crane, andloads the slab ballasts into the horizontal slots(Fig. 14e). Finally, the whole deck plate is loweredon to the standard platform. There are several benefitsof this design. Firstly, the outer frame for the variableweight compresses the loose ballast material. Anothermajor advantage is that this design allows two or moreoperators to simultaneously load variable weights (inthe form of slabs) in to the frame. At the same time, the

Fig. 9 Weight training slabdesign – II

Fig. 10 Conceptual ice-trayframe design


other operators can fill the front/back-end cavities withthe loose ballast material. This decreases the overallcycle time. This design is also ergonomically beneficialto the technicians as the crane height can control theheight of the deck plate (from the ground) based on theoperator height.

C. Cavity lid designAlternatively, instead of adding weight to the whole

deck plate (as in concept B in Section 4.3.3), separatelids can be manufactured for both the front and back-end cavities. These lids contain the slots for placing thevariable weights and can be lowered on to theindividual cavities with the help of the overhead crane.Figure 15 shows this design concept.

D. Cavity lid design–2This design concept is another alternative to the

cavity lid design, and offers an additional advantage ofthe ice-cube tray design. It comprises of standard slotsbelow the lid (Fig. 16), where the operators can placethe variable weights after the standard weight has beenpoured in the cavity. The lid is then placed on to thecavity and perhaps welded. However, if further weightneeds to be added, it can be added on to the sliding icetray, which is placed in the center of the top of the lid.There are slots on top of the ice tray so that a slidinglid can seal the ice tray. The main advantage of thisdesign is that it allows flexibility at the shop floor asthe weight can be removed from the top (ice tray).

4.3.4 Conceptual ideas for densely packing the looseballast material into the front/back-end cavities

A. Pneumatic hydraulic pressFigure 17 shows the use of a pneumatic/hydraulic

(pulsating) press for densely packing the loose ballast intothe two end cavities. A (portable press) might beintegrated to the overhead crane actions, particularly rightafter lifting the loose ballast hopper to fill the end cavities.

B. Vacuum suction compressionThe purpose of this idea is to compress the volume

of loose materials to increase its density, and mean-while, the compressed materials can keep a unitedrectangle shape so as to efficiently stock them in thecavity or a cell in the ice-cube frame. As illustrated inFig. 18, this idea needs a heat sealer, plastic bag, a steelcontainer, a filter, and an air compressor.

4.4 Optimization module

After determining the appropriate ballast materials andpotential forms of ballast arrangement, we built optimiza-tion models to find out the best ballast arrangementsolutions. In this step, we used integer programmingtechnique to build two optimization models. For bothmodels, the objectives are the same, which is to minimizetotal material costs. In addition, we also want to achieve astandardized ballast arrangement scenario from both opti-

Fig. 11 Box with spring-loadedchamber

Fig. 12 Central cavity framedesign


mization models. The two models are referred to as the“base model,” and the “material-mix model.”

4.5 Mathematical formulation

The objective function of the MIP model, as shown inEqs. 1 and 2 is to achieve the minimum material cost whilesatisfying all the constraints. Here, the total material cost isthe summary of all types of unit material cost multiplied bythe allocated weight.

Min C ð1ÞWhere

C ¼XK

k¼1

Ck»Wkfj þ Ck»XK

k¼1

Ck»Wkgj þXK

k¼1

Ck»Wkhj þXK

k¼1

Ck»Wkij

ð2Þ

Following are the four major constraints considered inthe model.

Volume constraint: In a locomotive platform, ballast can beloaded in four locations: the front cavity, center front path,center back path, and rear cavity. We rename these areas asfront end h, front center f, back center g, and back-end i.Both front end and back-end cavities have unique volu-metric constraints. Front center (f) and back center (g) arephysically connected. It is divided into two sectionsbecause of the balance requirement. Equations 3–6 repre-sent the relationships that satisfy the weight requirementunder volume limitations. Front center f and back center ghave airflow constraints. The center path is reserved for theair flow to reduce the engine temperature. Thus, theminimum air flow requirement is considered to be themaximum ballast loading constraint.

Fig. 13 Folder design

Fig. 14 Variability with the deck plate


XK

k¼1

Wkfj þXK

k¼1

Wkgj þXK

k¼1

Wkhj þXK

k¼1

Wkij � TWj ð3Þ

XK

k¼1

Wkhj

Dk� VF ð4Þ

XK

k¼1

Wkij

Dk� VE ð5Þ

XK

k¼1

ðWkfj þWkgjÞDk

� VC ð6Þ

Balance: The balance of the platform is very important tomaintain the stability; accordingly, ballast loadings shouldnot 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, thedifference of total weights from both sides of the modifiedcenter of gravity should be limited to be lower than abalance index, BI. Equations 7 and 8 represent thisrelationship.

ðPK

k¼1Wkfj þ

PK

k¼1WkhjÞ � ðP

K

k¼1Wkgj þ

PK

k¼1WkijÞ

TWjðBPj � BNjÞ � BI ð7Þ

BPj þ BNj ¼ 1 ð8Þ

Fig. 16 Cavity lid design – 2

Fig. 15 Cavity lid design


Standardized ballast: All the possible types of ballastloaded to the different models are standardized ballast withstandardized weights. We also try to limit the number ofdifferent weights of ballast used in the models. In ourmodel, we use three different weights of standard ballast,which are included in the model with WX, WY, and WZnotations. This scenario is formulated in Eqs. 9–13.

WZ < WY ð9Þ

WY < WX ð10Þ

TWj �XK

k¼1

Wkij �XK

k¼1

Wkhj �WX »PXj �WY»PYj�WZ»PZj ¼ 0

ð11Þ

TWj �XK

k¼1

Wkij �XK

k¼1

Wkhj �WX »PXj < WX ð12Þ

TWj �XK

k¼1

Wkij �XK

k¼1

Wkhj �WX »PXj �WY»PYj < WY

ð13Þ

Variable-type constraints There are three different types ofvariables in the MIP, which are shown in Eqs. 14–16.

Wkfj;Wkgj;Wkhj;Wkij;C � 0 ð14Þ

BPj;BNj 2 0; 1f g ð15Þ

PXj; PYj; PZj;� 0; Integer ð16Þ

4.6 The base model

For this model, we generated a standardized ballast arrange-ment model based on currently used ballast, metal slab andmetal scrap. Company A currently produces five types oflocomotive platforms with different total weight requirements.

Fig. 18 Vacuum suction compression technique

Fig. 17 Pneumatic/hydraulic press

Table 6 Cost comparisons of material-mix model, current model, andthe base model

Cost Current ballastcost (%)

Base model(%)

Material-mixmodel (%)

Cost saving(%)Model

Model 1 100.00 71.29 55.94 44.06

Model 2 134.87 97.10 77.26 57.61

Model 3 112.90 110.00 84.12 28.79

Model 4 137.10 122.90 93.19 43.91

Model 5 216.13 253.47 252.14 −36.01Total Cost 701.00 654.76 562.64 138.36

Table 5 Cost savings for the base model

Cost Current ballastcost (%)

Cost from thebase model (%)

Cost saving(%)Model

Model 1 100.00 71.29 28.71

Model 2 134.87 97.10 37.77

Model 3 112.90 110.00 2.90

Model 4 137.10 122.90 14.19

Model 5 216.13 253.47 −37.34Total Cost 701.00 654.76 46.24


Other factors also need to be considered during the modelconstruction process. For example, after loading all the ballastto the platform, the difference across two halves of thelocomotive weight should be less than 0.5%. Three types ofstandardized ballast are 2,000, 3,000, and 4,000 lbs. Metal slabcosts $0.41 per pound, and metal scrap costs $0.21 per pound.

Based on the information above, we formulated andsolved the base model in the mathematical optimizationsoftware, Lingo. Results are provided in Table 5, where thesolution is provided for one locomotive platform per model.We can see that, despite the fact that we do not consider theadoption of additional ballast materials in the base model,using standardized model can still benefit company A witha total cost saving of 46.24%. Note that cost values areprovided in percentage terms taking the current ballast formodel 1 as the nominal value (100%). However, adoptingstandardized ballast arrangement model can increase thecost for the highest weight requirement platform. Thereason is that standardized model reduces the ballastloading flexibility. The standardized model can simplifythe ballast loading process, improve WIP, and better react tothe changing demand.

4.7 The material-mix model

For the material-mix model, while we apply all theconstraints used in the base model, we also consider thepossible combination of three types of ballast—metal slab,metal scrap, and sand. The cost information used in thematerial-mix model for metal slab and meal scrap are thesame. For sand, the unit cost is assumed to be $0.02 perpound. The total cost of material-mix model, the currentballast model, and the base model are shown in Table 6. Wecan see that the material-mix model has huge cost savingsin comparison to the base model (138.36%).

5 Discussion and conclusions

In its essence, design for manufacturability is the goal ofthis case study. We investigated the current ballast processand constructed a MIP model to optimize the ballastmaterial cost. The rough estimates indicate considerablesavings in the material cost for the case study company. Inaddition, we developed several platform-based ballastdesign concepts that fit the current shop floor environment.Hence, investment on migration to new ballast process istrivial. With the modular design perspective, ballast sizesand types are classified as several different standardizedweights. In the meantime, the whole ballast constructionprocess will be simple. This design can be modified intodifferent weight specifications within a short time. Thebenefit of these new designs is obvious and significant. The

simplicity of the ballast construction process can decreasethe process time and enhance shop floor capacity. Highflexibility in achieving different weight configurations willalso reduce the WIP level and keep the production schedulerobust under dynamic demand conditions. Hence, the shopfloor space can be saved. The synergy of these improve-ments not only enhances the productivity and responsive-ness but also competitive advantage.

More importantly, the actual industrial case study presentedin this paper, not only shows that TRIZ and AD usage inunison is a powerful tool for solving complex industrialproblems, but also blends the power of optimization.

Acknowledgements We acknowledge contributions from ourcolleagues Mr. Teahyun Kim and Dr. Denise Bauer.

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