Int J Adv Manuf Technol DOI 10.1007/s00170-011-3752-1

ORIGINAL ARTICLE

Application of axiomatic , TRIZ, and mixed integer programming to develop innovative : 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 # Springer-Verlag London Limited 2011

Abstract In this paper, we present a method incorporating independent sub-problems, TRIZ generates all feasible axiomatic design, TRIZ, and mixed integer programming design concepts, and MIP optimizes cost and the numerical (MIP) to solve design problems. Axiomatic configuration among available design options. The method design decomposes the problem into several mutually 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 G. O. Kremer (*) the unsophisticated technology requirements, the ballast School of Engineering Design, The Pennsylvania State University, arrangement process has received little attention. The trend 213T Hammond Building, University Park, PA 16802, USA of mass customization, however, demands locomotive man- e-mail: [email protected] ufacturers to provide diverse products with affordable cost and : : reduced time. Thus, a flexible and easy to implement ballast G. O. Kremer C.-Y. Lin S. Gupta arrangement is sought. The proposed method Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, determines what material combinations, in what quantity, and 310 Leonhard Building, where in the limited cavities should the ballast be allocated to University Park, PA 16802, USA minimize cost. Using the case study, we demonstrate the advantages in cost reduction and time savings. The synergy of C.-Y. Lin e-mail: [email protected] these improvements not only can enhance productivity and agility but also competitive advantage. S. Gupta e-mail: [email protected] Keywords Axiomatic design . TRIZ . MIP. M.-C. Chiu Design for manufacturability Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Notations Hsinchu, Taiwan 30013, Republic of China Index sets e-mail: [email protected] f The ballast located in center front area of D. Claudio the locomotive Department of Mechanical and Industrial Engineering, g The ballast located in center back area of Montana State University, the locomotive Bozeman, MT 59717-3800, USA e-mail: [email protected] h The ballast located in front end area of the locomotive H. Thevenot i The ballast located in back-end area of GE Transportation, the locomotive 2901 East Lake Road, … ∈ Erie, PA 16531, USA J={1, , Nj} The different locomotive models, j J e-mail: [email protected] K={1,…, Nk} Different types of ballast materials, k ∈K Int J Adv Manuf Technol

Decision variables axiomatic design (AD) by showing the need for optimiza-

Wkfj Total weight of ballast type k in the center front tion, and then illustrate the use of the modified method on a center area f of model j locomotive ballast arrangement case study.

Wkgj Total weight of ballast type k in the center back area Ballast to a locomotive is a “sweet loading.” It aims to g of model j provide sufficient force so that a locomotive can pull the

Wkhj Total weight of ballast type k in the front end area cars by increasing its weight. Extra weight will waste h of model j energy, while insufficient weight will reduce the capacity of

Wkij Total weight of ballast type k in the back-end area i a locomotive. Hence, the precise weight control of the of model j ballast is important. In addition to weight, balance is C Total cost which is the summary of all models another critical concern in ballast arrangement. The weight

BPj Binary variable that controls the balance percentage. difference between the front half and the back half, as well It will be 1 when front end is heavier than back-end, as the left-hand side and the right-hand side of a locomotive otherwise 0. should be less than 1%.

BNj Binary variable that controls the balance percentage. Traditional ballast construction process is completed It will be 1 when back-end is heavier that front end, through stacking both metal scrap and slab into specific otherwise 0. ballast cavities inside the locomotive platform. The space is

PXj Number of standard X weight box in the center area limited and metal slab is expensive, so the metal scrap is of f and g of model j allocated as much as possible during the construction process.

PYj Number of standard Y weight box in the center area However, there are several drawbacks in the current process. of f and g of model j First of all, the metal scrap, which is purchased from recycling

PZj Number of standard Z weight box in the center area facilities, has a variant density. Accordingly, the operators of f and g of model j have to measure weight and balance of locomotive body using huge scales several times during the stacking process. Parameters Furthermore, unsteady market demand pressures the Dk Density of ballast type k manufacturers to produce locomotives in various weights for VF Available volume in front end of all models diverse purposes, bringing chaos to the shop floor when VE Available volume in back-end of all models shipping schedules change. The ballast construction depart- VC Available volume in center end of all models ments have high work in process (WIP) and very long cycle Ck Unit cost of ballast type k times. Finally, the rising cost of metal slab and metal scrap TWj Total weight requirement of model j compresses the revenue. Survey of cheaper alternatives is BI Balance index of the weight difference between necessary. Based on the above mentioned reasons, the need for frond-end and back-end of locomotive the development of a flexible ballast loading process design is WX Unit weight of the standard ballast type X deemed important, and hence is the focus. In the paper, we WY Unit weight of the standard ballast type Y present a synergistic approach, which utilizes axiomatic WZ Unit weight of the standard ballast type Z 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: 1 Introduction Section 2 presents a literature review and the rational for the proposed method. In Sections 3 and 4, we present the As global technology competition becomes fiercer, an proposed methodology, and then provide its on ability to solve engineering and technology problems the ballast arrangement case study. Finally, conclusions are expeditiously becomes critical for the survival of individual provided in Section 5. 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 2 Literature review not suit every application, and hence, it is essential that the right tool be selected for the application at hand. Based on Theory of inventive problem solving technique (TRIZ), their review of the state of the art, Shirwaiker and Okudan developed by Genrich Altshuller in 1946, is a systematic [2] have proposed and demonstrated the effective use of ideation technique. After studying more than one million TRIZ and axiomatic design as appropriate tools for patents, Altshuller found that problems and their solutions engineering design problems in general (e.g., product tend to be repeated across a range of industrial and design and manufacturing process design problems). In this scientific situations, and that the patterns of technological paper, we append to the synergistic use of TRIZ and evolution incline to repeat both in industrial applications Int J Adv Manuf Technol and sciences. Accordingly, inventions often made use of optimal concept. Independence axiom first screens out the scientific effects that were developed in unrelated areas. solutions which are “not good.” Then, the information Therefore, the problem solving ways may be repeatable and axiom will analyze the remaining solutions to pick the best predictable. From viewpoint of TRIZ, every factor that one. The role of axiomatic design in this study is to begin at affects a system can be defined as a parameter. There is a the system and decompose the design problem into dependency relationship between the parameters of the smaller design objects until all design objects are clearly system. While improving some parameters with positive represented. The details are provided in Section 4. effects to system, some of the other parameters might have negative effects. This results in a contradiction. Altshuller 2.1 Compatibility of AD and TRIZ asserts that an invention occurs when a contradiction between parameters is solved. Based on this hypothesis, In a review of the manufacturing related applications of TRIZ structures a problem into a “contradiction statement” TRIZ and AD from literature, Shirwaiker and Okudan [2] and derives solutions that address the problem statement pointed out the major strengths of these tools as: (1) TRIZ both from technical and system perspectives. Hence, the has the capability of generating innovative solutions, and ideality of the design increases while a parameter is (2) AD has the capability to analyze effectiveness of improved without worsening the other parameter [3–5]. In solutions in terms of satisfying the two axioms. Similarly, this manner, TRIZ demonstrates the capability as a support Mann [13] discusses the effectiveness of applying TRIZ tool for original idea creation. In this study, we applied the 39 and AD concurrently to solve a problem. From the AD engineering parameters, 40 innovative principles, and the perspective, TRIZ fits very elegantly into the “Ideate and contradiction matrix to generate new ballast design concepts. Create” element of Suh’s design process map. From a TRIZ TRIZ has been used in synergistic ways with other perspective, AD offers the potential for improving the methods (e.g., QFD [5], AHP [6, 7], DFMA [8], and problem definition and problem solving processes through function-based design [9]). Its effectiveness in idea gener- axioms offering means of assessing the effectiveness of a ation has also been demonstrated in classroom settings [10, design concept, and new perspectives on the specification 11]. Despite its success in aiding idea generation, however, of functional requirements and the handling of multilayered TRIZ (implemented alone) falls short in selecting the most problems [13]. Consequently, a synergistic problem solving appropriate idea, and hence, using it in unison with approach using TRIZ and AD has been proposed by appropriate tools is recommended. Shirwaiker and Okudan [2]. Axiomatic design has been implemented in tandem with Ruihong et al. [14] have also proposed an approach TRIZ. Developed by Suh [12], AD method interrelates four combining AD and TRIZ and explained it using the case domains: customer needs (CNs), functional requirements study of a paper machine. However, the synergistic problem (FRs), design parameters (DPs), and process variables solving approach is a more robust and enhanced approach. (PVs). It first transfers thecustomerneeds(CNs)to While the Ruihong et al. [14] approach employs TRIZ only functional requirements (FRs) of a product. The functional in cases where the design matrix of AD is coupled, the requirements are further mapped to design parameters synergistic approach utilizes TRIZ more effectively in that (DPs). Each design parameter connects to a process TRIZ is used not only for decoupling in case of a coupled variable (PV). Each customer need is viewed as a function, design matrix but is also used for the mapping and which can be further decomposed into subfunctions. Accord- zigzagging processes between the functional domain and ingly, every subproblem again decomposes to one or more physical domain of the AD hierarchy. This brings efficiency lower level subproblems until it reaches the “axiomatic” level. into the problem solving process. Therefore, the problem forms a hierarchical structure. In the However, neither the synergistic approach [2] nor Ruihong same way, functional requirements (FRs), design parameters et al.’s way of using TRIZ and AD together tackles the (DPs), and process variables PVs have a corresponding quantitative issues in a design problem. Accordingly, we hierarchical structure. In axiomatic design, every subfunction expand the synergistic approach to include an optimization of these domains has one on one mapping and this organizes a module. Below, we present the modified method and then “zigzagging” relationship between two . show its implementation on the case study. Two major axioms of AD are independence axiom and information axiom. The independence axiom maintains the independence of the functional requirements where each 3 Methodology functional requirement (FR) is satisfied without affecting the other FRs. The information axiom aims to minimize the The synergistic approach uses TRIZ and AD in concert by information content of the design. The design that satisfies assigning specific functions to the two tools. By applying both independence and information axioms will be the TRIZ within an AD framework, we try to capitalize on the Int J Adv Manuf Technol strengths of both tools. The synergistic approach primarily standard ballast arrangement models can enable quick uses AD in order to analyze the problem and decompose the reaction to changing customer needs, alternating market main problem into a hierarchy of basic level problems. TRIZ demands, and better utilization of ballast and workforce is applied to separate functional requirements (FRs) (if they resources, and hence a reduction in the long process are coupled) and to generate innovative solutions to the basic time under existing manufacturing conditions. problems in the AD hierarchy. Thus, the framework attempts 2. Cost consideration: The company currently uses two to synergistically use detailed analysis capability of AD with types of ballast materials—metal scrap and metal slab. the innovative idea generation prowess of TRIZ. Metal scrap is the major ballast material in use, and it is As indicated before, however, the adopted synergistic much cheaper than slab. However, due to the increasing approach does not tackle the quantitative issues in a design raw material cost, finding replacement low-cost materi- problem. Quantitative issues mostly arise during material als with relatively more stable market prices can benefit selection and form design phases in a design problem. the company in huge savings and prevent it from losing Various material properties impact the design in either market competitiveness. Moreover, the transportation positive or negative way, or positively and negatively both cost for acquiring ballast materials also need to be at the same time; hence, material search requires specific taken into account. attention. Likewise, form issues in design problems amplify 3. Complex ballast loading process: The existing ballast the complexities in design scenarios, and should be loading process is complex and inefficient. A better considered. Accordingly, we expand the synergistic method way is required to simplify current ballast loading to include specific steps for material search and form process in order to eliminate redundant procedures and ideation in order to expand the design space, and use increase the overall efficiency. optimization to make a final design alternative selection. Above are the on-going problems that force the company The flow of the methodology is provided below. management to consider ways to improve from the current To solve the locomotive ballast arrangement problem, status. To solve this problem, we applied the proposed we implement the above presented method. Axiomatic methodology incorporating axiomatic design, TRIZ and design first decomposes the ballast arrangement problem optimization, and followed the steps closely that were into several mutually independent subproblems. Then TRIZ outlined in Fig. 1. 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 Problem Definition are suggested as generic solutions. can create specific solutions by interpreting these principles. Finally, a Functional Requirements mixed integer mathematical programming model is devel- oped to optimize total cost and generate a standardized ballast allocation model for various locomotive platforms. Design Parameters (DP) We present the details of our implementation below.

Yes Can DPs be 4 Case study decomposed further?

Company A is a locomotive manufacturing company that No seeks to redesign its existing platform ballast arrangement system. In their current system, two different types of ballast Express DPs as Technical are loaded to the locomotive platform to reach five specific Contradictions (TC) weight requirements requested by customers. However, their current system lacks efficiency in addition to several Utilize 40 Inventive Principles manufacturing problems. These problems include:

1. Lack of standardization: Company A currently uses nu- Materials Search Form Ideation merous ballast arrangement models to reach the five weight requirements from multiple customers. Those Optimization models are mostly acquired either by trial and error or by past experience, and thus lack standardization. However, Fig. 1 Proposed method Int J Adv Manuf Technol

4.1 Ballast functional requirements structure inspect the problem, find out potential improvement directions and replace them with specific TRIZ parameters. Indeed, To begin with, AD is introduced to analyze the problem. AD improving from one parameter usually may conflict with one hierarchically decomposes the problem into independent or more other parameters. To clarify the problem more functional requirements (FRs) in a top-down manner. In each thoroughly, it is important to define all the technical contra- hierarchy, is used to generate numerous dictions by indicating all the possible conflicts. For our case, possible functional requirements, and then group-thinking is we have 10 improvable engineering parameters potentially adopted to eliminate inappropriate or dependent ones. For our conflicting with 12 unique parameters. These result in 16 pairs problem, we first divided all platforms to be produced based of technical contradictions as shown in Table 1. on the type of the motor: AC-motor platforms and DC-motor In the platform design, the standard ballast will remain fixed platforms. This consideration is based on the two main types irrespective of the weight requirements of the particular model, of product lines that company A produces. In fact, both motor- and variant ballast will be adjusted to meet particular require- based platforms can share the same set of hierarchical ments. As a result, our team decided to work on the design of structures. For the next lower level hierarchy, the selection the variant ballast only after finalizing the “form design” and of ballast arrangement methods is considered. Two functional “total weight” of the standard ballast. Once the FRs hierarchy requirements are built: the standard ballast and the variant was determined, our team proceeded to determine the material ballast. In our case study, we only focus on the variant ballast and its attributes (e.g., cost, availability, manufacturability, and condition, which is the more complex part of the problem. For human factors) by using TRIZ. Therefore, the next step was to the next lower level, the available ballast loading cavities are formulate different contradictions and their corresponding enumerated (front, back, and center). Some constraints need to TRIZ principles from TRIZ matrix. After achieving all the be taken into account, such as weight constraints and required solutions for each pair of technical contradictions from the air flow capacity. Lastly, for the lowest hierarchy level, TRIZ principles, we organized the most commonly applied different material alternatives are considered. Figure 2 recurring principles in Table 2. In this table, we can see that presents the entire functional requirements structure for the most suggested principles related to finding better ballast AC-based platform. materials and more appropriate ballast arrangement methods. Accordingly, we decided to focus our solution efforts around: 4.2 TRIZ contradictions (1) ballast material research, (2) concept generation, and (3) optimization. After defining all the hierarchical functional requirements After investigating a variety of materials, we proposed using the AD approach, we introduce TRIZ to determine the two categories of materials: (1) metals and metal alloys and selection of materials with the consideration of their physical (2) non-metal materials. (e.g., density, state, etc.) and other (e.g., cost, availability, manufacturability, etc.) features. TRIZ is a systematic tool that 1. Metals and metal alloys: Table 3 shows the density and can focus idea generation. It enables users to resolve cost information for a number of materials in this sophisticated problems in a systematic fashion by relating category. After careful consideration of design criteria, the 40 inventive principles to the problem context. we decided to use cast iron and steel as our major TRIZ starts with the identification of technical contra- materials for the metals and metal alloys category. Cast dictions, which are conflicting engineering parameter pairs. iron is the material of metal scrap, and steel is the To determine technical contradictions, the first step is to 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 Fig. 2 Hierarchy of ballast functional requirements structure still not suitable as auxiliary ballast since they have Int J Adv Manuf Technol

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 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 problem. Therefore, sand is decided as the only non- transport while concrete has the manufacturability metal material that will be further considered. Int J Adv Manuf Technol

Table 2 Recurring TRIZ principles

TRIZ principles Number of Description of principle occurrences

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 Pre-arrange objects or system such that they can come into action at the most 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 under different conditions 31 Porous materials 4 Make an object porous or add porous element OR if an object is already porous, add something useful into the pores 40 Composite materials 4 Change from uniform to composite (multiple) materials where each material is optimized to a particular function requirement

4.3 Form ideation redesigning the cavity or redesign the shape of ballast. We generated a variety of concepts for company A to enable it to Before acquiring the standardized ballast loading model for all select from after reviewing pros and cons. different platform types, we needed to consider a standard process to load the ballast. In this section, we apply TRIZ to 4.3.1 Conceptual designs incorporating variability assist in generating different ways to load ballast by either in the front and back-end cavities

Table 3 List of materials with their density and cost Concept A. Ice cube tray design In this , an ice-cube tray Metal Density (lb/cu ft) Cost ($/lb) frame is designed to accommodate the vari- able weights in the front and back-end Aluminum bronze (3–10% A1) 480.7 0.74–0.97 cavities. Therefore, the first step would Antimony, cast 418.0 1.25–2.50 involve fabricating the ice-cube tray frame, Arsenic 354.0 0.72 which could be made of steel/sheet metal and Beryllium 505.7 160.00 should be of the size of the two end cavities Bismuth 611.0 3.60–4.05 with adequate tolerances for easy insertion Cadmium 540.0 1.84 and retrieval. The cavities would first be filled Cast iron 424.5 0.03–0.11 with the standard quantity of loose ballast as – Chromium 428.0 0.33 0.43 shown in Fig. 3a. The next step would require – Cobalt 546.0 27.37 31.74 putting the ice-cube tray frame on top of the Copper 557.5 1.33 loose ballast, and welding it with the platform Gold 1,206.1 5,598.00 base (though welding may not be necessary Iridium 1,383.0 874.00 for a properly dimensioned tray). This might – Lead 711.0 0.23 0.35 also be a part of the standard platform Manganese 475.0 0.60 fabrication process as illustrated in Fig. 3b. Mercury 848.6 800.00 Depending on the variable ballast to be added Molybdenum 636.0 7.03 to a particular platform model, removable Nickel 541.0 2.50–4.73 Platinum 1,336.0 5,850.00 Silver 654.9 65.00 Table 4 Density and cost of non-metal materials Steel 467.0 0.40 Non-metal Density (lb/cu ft) Cost ($/lb) Tin 454.0 2.90 Tungsten 1,223.6 12.50 Sand, dry 111.1 0.03–0.04 Uranium 1,179.9 9.65–12.20 Concrete, limestone 148.0 0.03–0.04 Vanadium 343.0 3.90–5.00 Stone (common, generic) 168.5 0.08–0.16 Zinc 445.4 0.43–0.52 Brick, common red 120.0 0.12 Int J Adv Manuf Technol

Fig. 3 Ice-cube tray design

weights can be added into the ice-cube weight. Figure 4a shows a standard ice-cube cavities either as boxes or slabs, as shown in tray, while Fig. 4b shows the conceptual Fig. 3c. The ballast hopper may also be design. One disadvantage may be the change directly used in order to fill the loose ballast in compactness of the loose ballast in the trays onto the ice-cube tray frame, which is much after the platform is turned upside down, similar to filling of a regular ice-cube tray thereby displacing all the densely packed loose under a running water tap. One possible ballast from the ice-cube trays. disadvantage of this design would be the Concept C. Stacked boxes design potential over-utilization of the overhead This idea is an extension of abovementioned crane for transporting individual removable concept B. The main purpose of this design is to weights to the ice-cube cavities on the design a standard box (either variable loose standard platform in shop floor. ballast or slab) to increase the manufacturability Concept B. Stacked ice-cube tray design and flexibility. As Fig. 5 shows, these standard This design utilizes an ice-cube tray frame boxes can be assembled in both vertical and similar to concept A but differs in the way that it horizontal directions depending on the variable stacks ice-cube trays in order to add variability. weight requirements. In order to horizontally The ice-cube tray is pre-filled with a standard join two boxes, a jig-saw puzzle connection is quantity of loose ballast, which is densely proposed. packed. In the cavities, they are placed one over Concept D. Sliding plates design the other in order to add variability. Therefore, This conceptual design is quite similar to the number of trays determines the variable the first ice-cube tray design (concept A), but

Fig. 4 Stacked ice-cube trays design Int J Adv Manuf Technol

Fig. 5 Stacked boxes design

instead of the cubic-shaped cavities in the ice- weights can be put in the slot on the side of cube tray frame, this design utilizes thin the end cavity. The advantage here is the easy rectangular plates that slide into the slots. control of variable weight. The slots are fabricated on the ice-cube tray Concept F. Weight training slab design frame, which is welded on to the platform In this design, the end cavity is first filled after the fixed quantity of loose ballast is with the standard quantity of loose ballast. poured into the end cavity. Depending on the After that, a lid is placed over the loose variable weight needed for that particular ballast, which contains five cylindrical rods model, the required number of plates may be that are equidistant from each other. Figure 8 inserted in the slots. Figure 6 shows the illustrates the standard slabs, which may be platform design utilizing the sliding plates put over the cylindrical rods in order to design. One disadvantage of this design may constrain them from any translatory motion. be the high precision and time required by the Figure 9 shows an alternative concept for the operator to accurately position the thin rect- weight training design, where the standard angular slabs into their respective slots. The slabs are fabricated in a slightly different overhead crane would be utilized to pick up manner than in Fig. 8. the plates, which may also lead to its over- Concept G. Ice-tray frame design utilization. Figure 10 shows the ice-cube tray frame, Concept E. Tetris design whose total height extends to the base of the This design utilizes the combination of cavity. A number of cavities may be filled up three standard components in different ways to the standard quantity with the loose ballast to achieve different weights. As shown in and the remaining cavities may be filled with Fig. 7a–d, four rectangular shapes are possible the slabs in order to individually balance each by welding the standard components in end cavity. The major difference of this different ways and each resultant shape has conceptual design from the previous ice- the same width. Figure 7e shows that once the cube tray designs is that in this design, the standard loose ballast quantity is put, these length of the frame extends the whole height

Fig. 6 Sliding plates design Int J Adv Manuf Technol

Fig. 7 Tetris design

of the cavity. The ice-cube tray frame is first can put slabs in this spring-loaded chamber welded on to the end cavity, and then the depending on the weight requirements. The standard quantity of loose ballast is poured in main advantage of the spring is to clamp, and the standard cavity as shown in the following therefore, constrain the variable slabs from figure. moving inside the chamber. Concept H. Box with spring-loaded chamber The purpose of the big box is to reduce the process time while providing flexibility to add 4.3.2 Conceptual designs incorporating variability and remove variable weight (Fig. 11). There are in the central cavity two cabins in this box. The left side of the cabin is for loose ballast which accommodates A. Nesting dolls design the standard weight. The right side of the cabin This design is mainly for the central cavity, and it has a spring-controlled adjustable volume. We utilizes the nested doll principle by keeping the airflow

Fig. 8 Weight training slab design – I Int J Adv Manuf Technol

Fig. 9 Weight training slab design – II

considerations in mind. The cavity frame (Fig. 12)isto standard frame is then hinged along with the cavity and be welded on to the central cavity, and is designed can be swiveled between 0° and 90° because of its pin- similar to the ice-cube tray (concept A in Sec- hole system for hinging (Fig. 13d). After hinging both tion 4.3.1). The shape of the frame provides a path the frames on to the cavity, the cavity is closed. This for the airflow travel (similar to a virtual pipe). This action also compresses the loose ballast material, design can be used for AC platforms as well as DC thereby increasing the density. The rotating standard platforms since the ice-tray like cavities at the two ends frame can also be substituted as the cover for the end are symmetric along the central axis, and only one side cavities. may be filled with loose/box/slab as per the variable B. Deck-plate design weight requirements. 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 4.3.3 Conceptual designs incorporating variability deck plate is lifted using the overhead crane, and an on the lid of the front/back-end cavities outer frame containing the variable weights is welded to the bottom of the deck plate as shown in Fig. 14b. A. Folder design The operator then utilizes the overhead crane, and This folder design is based on the principle of loads the slab ballasts into the horizontal slots rotation along the hinges (i.e., like a door). However, (Fig. 14e). Finally, the whole deck plate is lowered the hinged frame consists of slots for accommodating on to the standard platform. There are several benefits variable weights in the form of slabs. There are four of this design. Firstly, the outer frame for the variable different slabs as shown in Fig. 13. In Fig. 13a, the weight compresses the loose ballast material. Another cavity is filled with the standard quantity of the loose major advantage is that this design allows two or more ballast. Figure 13b–c shows the standard frame, which operators to simultaneously load variable weights (in has slots for inserting the four different slabs. The the form of slabs) in to the frame. At the same time, the

Fig. 10 Conceptual ice-tray frame design Int J Adv Manuf Technol

Fig. 11 Box with spring-loaded chamber

other operators can fill the front/back-end cavities with 4.3.4 Conceptual ideas for densely packing the loose the loose ballast material. This decreases the overall ballast material into the front/back-end cavities cycle time. This design is also ergonomically beneficial to the technicians as the crane height can control the A. Pneumatic hydraulic press height of the deck plate (from the ground) based on the Figure 17 shows the use of a pneumatic/hydraulic operator height. (pulsating) press for densely packing the loose ballast into C. Cavity lid design the two end cavities. A (portable press) might be Alternatively, instead of adding weight to the whole integrated to the overhead crane actions, particularly right deck plate (as in concept B in Section 4.3.3), separate after lifting the loose ballast hopper to fill the end cavities. lids can be manufactured for both the front and back- B. Vacuum suction compression end cavities. These lids contain the slots for placing the The purpose of this idea is to compress the volume variable weights and can be lowered on to the of loose materials to increase its density, and mean- individual cavities with the help of the overhead crane. while, the compressed materials can keep a united Figure 15 shows this design concept. rectangle shape so as to efficiently stock them in the cavity or a cell in the ice-cube frame. As illustrated in D. Cavity lid design–2 Fig. 18, this idea needs a heat sealer, plastic bag, a steel This design concept is another alternative to the container, a filter, and an air compressor. 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 4.4 Optimization module the variable weights after the standard weight has been poured in the cavity. The lid is then placed on to the After determining the appropriate ballast materials and cavity and perhaps welded. However, if further weight potential forms of ballast arrangement, we built optimiza- needs to be added, it can be added on to the sliding ice tion models to find out the best ballast arrangement tray, which is placed in the center of the top of the lid. solutions. In this step, we used integer programming There are slots on top of the ice tray so that a sliding technique to build two optimization models. For both lid can seal the ice tray. The main advantage of this models, the objectives are the same, which is to minimize design is that it allows flexibility at the shop floor as total material costs. In addition, we also want to achieve a the weight can be removed from the top (ice tray). standardized ballast arrangement scenario from both opti-

Fig. 12 Central cavity frame design Int J Adv Manuf Technol

Fig. 13 Folder design mization models. The two models are referred to as the Following are the four major constraints considered in “base model,” and the “material-mix model.” 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, The objective function of the MIP model, as shown in center back path, and rear cavity. We rename these areas as Eqs. 1 and 2 is to achieve the minimum material cost while front end h, front center f, back center g, and back-end i. satisfying all the constraints. Here, the total material cost is Both front end and back-end cavities have unique volu- the summary of all types of unit material cost multiplied by metric constraints. Front center (f) and back center (g) are the allocated weight. physically connected. It is divided into two sections because of the balance requirement. Equations 3–6 repre- Min C ð1Þ sent the relationships that satisfy the weight requirement Where under volume limitations. Front center f and back center g have airflow constraints. The center path is reserved for the XK XK XK XK » » » » » C ¼ Ck Wkfj þ Ck Ck Wkgj þ Ck Wkhj þ Ck Wkij air flow to reduce the engine temperature. Thus, the k¼1 k¼1 k¼1 k¼1 minimum air flow requirement is considered to be the ð2Þ maximum ballast loading constraint.

Fig. 14 Variability with the deck plate Int J Adv Manuf Technol

Fig. 15 Cavity lid design

XK XK XK XK Balance: The balance of the platform is very important to Wkfj þ Wkgj þ Wkhj þ Wkij TWj ð3Þ k¼1 k¼1 k¼1 k¼1 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. XK Wkhj After loading all the ballast onto the platform, the VF ð4Þ difference of total weights from both sides of the modified Dk k¼1 center of gravity should be limited to be lower than a balance index, BI. Equations 7 and 8 represent this relationship. XK W kij VE ð5Þ D PK PK PK PK k¼1 k ð Wkfj þ WkhjÞð Wkgj þ WkijÞ k¼1 k¼1 k¼1 k¼1 BI ð7Þ TWjðBPj BNjÞ XK ðW þ W Þ kfj kgj VC ð6Þ Dk k¼1 BPj þ BNj ¼ 1 ð8Þ

Fig. 16 Cavity lid design – 2 Int J Adv Manuf Technol

Table 5 Cost savings for the base model

Cost Current ballast Cost from the Cost saving Model cost (%) base 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 −37.34 Total Cost 701.00 654.76 46.24

XK XK » TWj Wkij Wkhj WX PXj < WX ð12Þ k¼1 k¼1 Fig. 17 Pneumatic/hydraulic press

XK XK » » TWj Wkij Wkhj WX PXj WY PYj < WY Standardized ballast: All the possible types of ballast k¼1 k¼1 loaded to the different models are standardized ballast with ð13Þ 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, Variable-type constraints There are three different types of which are included in the model with WX, WY, and WZ variables in the MIP, which are shown in Eqs. 14–16. notations. This scenario is formulated in Eqs. 9–13. Wkfj; Wkgj; Wkhj; Wkij; C 0 ð14Þ

WZ < WY ð9Þ BPj; BNj 2 fg0; 1 ð15Þ

WY < WX ð10Þ PXj; PYj; PZj; 0; Integer ð16Þ

XK XK » » » TWj Wkij Wkhj WX PXj WY PYjWZ PZj ¼ 0 k¼1 k¼1 4.6 The base model ð11Þ For this model, we generated a standardized ballast arrange- ment 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 Current ballast Base model Material-mix Cost saving Model cost (%) (%) 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 −36.01 Total Cost 701.00 654.76 562.64 138.36 Fig. 18 Vacuum suction compression technique Int J Adv Manuf Technol

Other factors also need to be considered during the model simplicity of the ballast construction process can decrease construction process. For example, after loading all the ballast the process time and enhance shop floor capacity. High to the platform, the difference across two halves of the flexibility in achieving different weight configurations will locomotive weight should be less than 0.5%. Three types of also reduce the WIP level and keep the production schedule standardized ballast are 2,000, 3,000, and 4,000 lbs. Metal slab robust under dynamic demand conditions. Hence, the shop costs $0.41 per pound, and metal scrap costs $0.21 per pound. floor space can be saved. The synergy of these improve- Based on the information above, we formulated and ments not only enhances the productivity and responsive- solved the base model in the mathematical optimization ness but also competitive advantage. software, Lingo. Results are provided in Table 5, where the More importantly, the actual industrial case study presented solution is provided for one locomotive platform per model. in this paper, not only shows that TRIZ and AD usage in We can see that, despite the fact that we do not consider the unison is a powerful tool for solving complex industrial adoption of additional ballast materials in the base model, problems, but also blends the power of optimization. using standardized model can still benefit company A with a total cost saving of 46.24%. Note that cost values are Acknowledgements We acknowledge contributions from our provided in percentage terms taking the current ballast for colleagues Mr. Teahyun Kim and Dr. Denise Bauer. model 1 as the nominal value (100%). However, adopting standardized ballast arrangement model can increase the cost for the highest weight requirement platform. The References reason is that standardized model reduces the ballast loading flexibility. The standardized model can simplify 1. Jugulum R, Sefik M (1998) Building a robust manufacturing the ballast loading process, improve WIP, and better react to strategy. Comput Ind Eng 35(1/2):225–228 the changing demand. 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 4.7 The material-mix model 3. Low MK, Lamvik T, Walsh K, Myklebust O (2001) Manufactur- ing a green service: engaging the TRIZ model of innovation. IEEE For the material-mix model, while we apply all the Trans Electron Packag Manuf 24(1):10–17 constraints used in the base model, we also consider the 4. Akay D, Demiray A, Kurt M (2008) Collaborative tool for solving — human factors problems in the manufacturing environment: the possible combination of three types of ballast metal slab, theory of inventive problem solving technique (TRIZ) method. Int metal scrap, and sand. The cost information used in the J Prod Res 46(11):2913–2925 material-mix model for metal slab and meal scrap are the 5. Yamashina H, Ito T, Kawada H (2002) Innovative product same. For sand, the unit cost is assumed to be $0.02 per development process by integrating QFD and TRIZ. Int J Prod Res 40(5):1031–1050 pound. The total cost of material-mix model, the current 6. Li T-S, Huang H-H (2009) Applying TRIZ and Fuzzy AHP to ballast model, and the base model are shown in Table 6.We develop innovative design for automated manufacturing systems. can see that the material-mix model has huge cost savings Expert Syst Appl 36(4):8302–8312 in comparison to the base model (138.36%). 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 5 Discussion and conclusions and TRIZ approach to the simplification of product structure. 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