Jun 1, 2002 - First, a formal framework to help corporations .... of the Indianapolis Motor Speedway, site of the 2000 US Grand Prix, is shown in Figure. 1.2.
A Comprehensive Decision Support Framework For Flexible System Design
by
Andrew T. Olewnik June 1, 2002 A thesis submitted to the Faculty of the Graduate School of State University of New York at Buffalo in partial fulfillment of the requirements for the degree of
Master of Science Department of Mechanical and Aerospace Engineering
Acknowledgments First and foremost I would like to acknowledge the support and insight of Dr. Kemper Lewis. Your encouragement and the endless opportunities you provide to make myself better are, and will always be, much appreciated.
A special thanks to Dr. Debu Talukdar, for your help with aspects of this research.
Of course recognition must be given to my colleagues in the DOES lab – Kurt, John, TK, Ashwin, Scott, Vincent and Adeline.
Thanks for keeping the “work” experience
enjoyable.
Last, but certainly not least. A major thanks to my family and friends. You know who you are and I really couldn’t name you all. It’s nice to share my successes with you, knowing that I need not be successful to share your company.
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Table of Contents List of Figures……………………………………………………………………….
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List of Tables………………………………………………………………………...
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Abstract………………………………………………………………………………
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Chapter 1: Introduction and Motivation……………………………………………
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1.1 A First Flexible System…………………………………………………..
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1.2 A Brief History of Design………………………………………………...
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1.3 Motivation for Flexible Systems………………………………………….
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1.4 Research Issues…………………………………………………………...
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1.5 Thesis Outline…………………………………………………………….
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Chapter 2: Theory and Background………………………………………………..
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2.1 Review of Flexibility in Design…………………………………………..
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2.2 Definition of Flexible Systems…………………………………………...
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2.3 Hierarchy of Open Engineering Systems…………………………………
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2.4 Background Theory………………………………………………………
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2.4.1 Pareto Sets………………………………………………………
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2.4.2 Decision Based Design…………………………………………
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2.4.3 Utility Theory…………………………………………………..
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2.4.4 Consumer Choice Theory………………………………………
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2.5 Summary………………………………………………………………….
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Chapter 3: Decision Support Framework for Flexible System Design……………
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3.1 DBD Framework…………………………………………………………
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3.2 DBD Framework for Flexible Systems…………………………………..
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3.2.1 Details of the Flexible System Framework……………………..
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Chapter 4: Case Study: Design of a Flexible Room………………………………..
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4.1 Introduction to the Flexible Room Problem……………………………...
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4.2 Design of a Flexible Room……………………………………………….
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4.2.1 Single Iteration of the Framework for Flexible Room Problem..
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4.2.2 General Results of the Flexible Room Problem………………..
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4.2.3 Evolution of the Pareto Frontier………………………………..
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Chapter 5: Conclusions and Future Work…………………………………………
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5.1 Revisiting the Research Questions……………………………………….
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5.2 Future Work………………………………………………………………
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5.2.1 Flexible System Design………………………………………...
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5.2.2 Decision Support Frameworks………………………………….
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5.3 Conclusion………………………………………………………………..
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List of Figures Figure 1.1: Evolution of the Design Process..……………………………………….
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Figure 1.2: Indianapolis Motor Speedway…………………………………………...
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Figure 2.1: Open Engineering System Hierarchy……………………………………
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Figure 2.2: Choosing an Open Engineering System…………………………………
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Figure 2.3: Mapping Between Performance and Design Spaces…………………….
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Figure 2.4: Pareto Frontier for Two Objectives……………………………………...
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Figure 2.5: Choice Problem……………………….…………………………………
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Figure 2.6: A von Neumann-Morgenstern lottery...…………………………………
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Figure 2.7: Utility Function Types…………………………………………………..
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Figure 3.1: Hazelrigg’s DBD Framework………...…………………………………
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Figure 3.2: DBD Framework for Flexible Systems..………………………………...
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Figure 3.3: Measuring Flexibility in Two Dimensions……………………………...
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Figure 3.4: Relationship of Attributes to Design Variables…………………………
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Figure 3.5: Utility of NPV for Two Companies…..…………………………………
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Figure 4.1: Flexible Room Banquet Facility……...…………………………………
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Figure 4.2: Assumed Growth Trend for Banquet Facilities.………………………...
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Figure 4.3: Resulting Growth Trend for Banquet Facilities…………………………
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Figure 4.4: Utility Functions for Companies A, B, and C...…………………………
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Figure 4.5: Flexible Room Banquet Facility Design…...……………………………
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Figure 4.6: Pareto Set for Ideal Flexible Room…...…………………………………
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Figure 4.4: Survey of Possible Room Configurations.………………………………
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Figure 4.5: Component Utility Graphs for Wall Attributes………………………….
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Figure 4.6: Results from all Iterations of the Framework...…………………………
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Figure 4.7: Results for Extreme Discount Rates.....…………………………………
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Figure 4.8: Changing Pareto Frontier for Flexible Room……………………………
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List of Tables Table 4.1: Total Number of Banquet Facilities for 2002…………………………….
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Table 4.2: Banquet Facility Growth Calculations…………………………….……...
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Table 4.3: Ideal Flexible Room Configuration Extremes……………………………
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Table 4.4: First Iteration Results for Companies A, B, and C.………………………
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Abstract Flexible systems have been defined as those designed to maintain a high level of performance through real time changes in their configuration when operating conditions or requirements change in a predictable or unpredictable way. The primary purpose of the research conducted here is two-fold. First, a formal framework to help corporations identify the flexible system design that is best is introduced. The objective of the framework is to help designers make engineering/business decisions that will maximize the corporate utility for the system. The second goal of the research is to introduce a metric for flexibility. Such a metric is necessary in order to compare one flexible system to another. This metric would be useful to consumers in comparing one corporation’s flexible system to another. The research conducted here, relies on principles from a broad range of technical and social sciences, including, engineering science, decision theory and marketing. The hope is that this work will further strengthen the case for modeling the design process from a “Decision Based Design” approach.
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CHAPTER 1 Introduction and Motivation
1.1 A First Flexible System Undoubtedly, the concept of a flexible system is an elusive one. What, exactly is a flexible system? That question will be answered in good time; but for now, as a starting point, imagine the toy, Transformers. The basic premise behind the Transformer is the ability to “transform” from a robot to some type of machine and vice-versa. An example would be Optimus Prime, a Transformer who could change from a robot to a semi-truck cab. The basic idea behind a flexible system is similar, though more rooted in reality. Flexible systems are systems which can “transform” in some way to offer improved performance to the customer. If we continue with the Transformer example, some general questions can be raised about the design and implementation of the system. How do the design variables change? How do various functions map to various configurations and how do these configurations coincide?
How should the Transformer shift from one function to
another? These same questions can be asked of flexible systems and they help to make up the fundamental motivations of this research. More formal definitions for flexible systems will come in Chapter 2 but the remainder of this chapter concentrates on the motivation behind such systems. Research questions are also presented but first a look at the history of the design process is covered in order to set the stage for flexibility in design.
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1.2 A Brief History of Design In order to understand the need for flexible systems, knowledge of the history of the design process is necessary. Figure 1.1 shows such a history. Ford’s introduction of Measure of Success
Process Ford’s Design Process
Dictatorial
Accuracy
Mass Production
Iterative Technical
Efficiency
Current Design Process
Iterative Social-Technical
Flexibility
Future Design Processes
Largely Automated
???
Figure 1.1. Evolution of the Design Process
the assembly line was the first step in a formal design process. Though it brought accuracy to manufacturing, the process failed to offer choice to the customer [1]. The evolution of mass production brought about efficiency in design while maintaining accuracy, however, consumer choice was still not an option. The next evolution in the design process strove to incorporate the “voice of the customer.”
The information
revolution and advent of the internet helped to make design the iterative social-technical process it is today [2]. This process allows companies to meet varying consumer needs while maintaining efficiency and accuracy in product development. Success of this approach is measured by the “flexibility” in choice of products offered to consumers. Note that each new process is built upon the previous and each measure of success is extremely important for the next evolution of the process. Although the measure is unknown, the next logical step is a largely automated process. While it may be difficult
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if not impossible to replace the values, preferences, and judgments of designers, many steps of capturing customer preferences and converting them into function and form could be automated. Before this can happen, an understanding of flexibility and its impact on product design must be developed and integrated into the design process. The foundation for understanding, begins with the motivation for “flexibility” in design.
1.3 Motivation for Flexible Systems Zeleny has implied that performance tradeoffs are a result of poorly designed systems [3]. Though this may be a gross overstatement, it serves to highlight the primary motivation of flexible systems. Namely, flexible systems have the ability to eliminate performance tradeoffs by adapting to give optimal performance in predictable situations. To appreciate the optimal performance possibilities a flexible system can offer, consider a racecar. In the design of a racecar, whether it is NASCAR, CART, Formula One, or even local racetracks, the difference between winning a race and not winning comes down to the ability of a driver to get the most out of his or her racecar. While having a talented driver is always desirable, even the most talented driver can do nothing more than realize the full potential of the vehicle. The core vehicle design (how it is setup and tuned by a race team) is aimed at an optimal compromise that allows the driver to repeatedly turn fast lap times at a particular racetrack. Any advantage gained through vehicle design and tuning, however small, increases the vehicle’s potential and, with a talented driver, will translate into an increase in on-track performance.
Vehicle
simulations are now used not only prior to and during a race weekend to guide tuning of the racecar, but also in the design phase where parameters, which are not adjustable, must
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be set and optimized.
The basic configuration of the car (e.g., center of gravity,
suspension systems, steering stiffness, roll stiffness) remains constant. Formula One racetracks are not constant radius tracks and do not consist of only a few turns. A layout of the Indianapolis Motor Speedway, site of the 2000 US Grand Prix, is shown in Figure 1.2. This course, as typical with Formula One racetracks, consists of a number of turns, ranging in radius sizes from 114 ft. to 840 ft. The optimal racecar configuration for each turn is different [4]. However, the team must choose one configuration come race day. In addition, it may rain on race day, it may be humid, or it may be hotter than expected. All these uncontrollable conditions create a difficult job for racecar designers.
Figure 1.2. Indianapolis Motor Speedway
However, consider a flexible racecar design that is able to change its performance features as a function of the current track conditions (ignoring racing restrictions for the time being). Whether on a straightaway, a big turn, or a small hairpin turn, the car could adjust variables such as the center of gravity, roll stiffness, and aerodynamic downforce (via wings and aerofoils). These configuration changes could be more automated through an active control system, or less automated and a result of a driver adjustment. The ability of a racecar to dynamically change is a practical illustration of one aspect of a flexible system, namely, adaptability [5].
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While the racetrack layout provides a highly predictable aspect of a racecar’s operating environment, there is a multitude of equally important factors that cannot be predicted (e.g. temperature, wind, rain, etc.). Such unknown factors are largely the focus of another aspect of flexible design, robustness [5], which strives to minimize the effect of unforeseeable changes in the operating environment on the performance of the system without eliminating the cause of the changes themselves [6]. The effect is to create a system that is less sensitive to variation in uncontrollable design parameters than the traditional optimal design point [7]. Though methods to incorporate robustness into the design process already exist [8-17], incorporation of these methods into a flexible design framework may require revision. The major difference between the two aspects of a flexible system, are the environmental conditions each can deal with. In general, adaptability is associated with conditions that are predictable in nature, while robustness is associated with conditions that are unpredictable in nature [5]. Further motivation for flexible design lies in the idea of multi-tasking. Imagine flipping through the stations on your television. You stop on CNN and start watching a story about NASA’s use of satellites to refuel the space station. A video feed shows a satellite refueling the station at that instant…the same satellite that is providing the video feed to your television.
Systems that can accomplish multiple tasks could prove
economically efficient in situations like the one described above.
However, strong
knowledge of flexibility in design is vital to the future of such systems. Motivation for flexible design is not limited to physical systems.
Consider
companies that generate some kind of output (e.g., manufacturing companies). These
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companies are constantly concerned with how to manage flexible levels of output by changing variables such as capital expenditures and labor forces [18]. A final motivation for examining flexible design methods is the improvement of methods already developed. As stated in section 1.2, before the design process can move to a largely automated one, a thorough understanding of the iterative social-technical process is necessary. This necessitates a thorough understanding of flexibility and its components. Of all these motivations, the most important to this research is the actual design of flexible systems. In the next section, the issues that must be addressed to accomplish this task are discussed. Further, the research questions addressed within this thesis are laid out.
1.4 Research Issues In the design of any engineering system, decisions must be made that ultimately affect the final product. It is for this reason, according to Hazelrigg, that design can never be exclusive of human input [19]. The idea that engineering design is dependent on the decisions made by the designers means that decision support is a primary issue in designing flexible systems and leads to the first research question: 1) How can flexible systems be designed in a manner that provides decision support and accounts for all the stages in the creation of consumer driven products? There are two key secondary issues that must be addressed in order to answer this question. These issues are related to the two aspects of making a system flexible,
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adaptability and robustness, and the additional cost incurred in creating such systems. Dealing with these issues will require: 1.1)
Method/technique for changing the levels of adaptability/robustness.
1.2)
Incorporation of demand modeling to justify cost associated with a flexible system.
Another primary issue is the level of flexibility in the system. This is important because the need to compare one flexible system to another will certainly arise for the designers and potentially the customers. It is evident then, that some metric for flexibility would be desirable for comparison purposes and the second research question becomes: 2) How can flexibility be measured? As with research question one, there are two secondary issues associated with this question. These issues are concerned with the correlation between flexibility and the decisions made with respect to perceived usefulness and levels of adaptability and robustness. Dealing with these relationships requires: 2.1)
Understanding the affects of varied flexibility on the utility of a product to consumer and corporation.
2.2)
Understanding the relationship between the measure of flexibility and the levels of adaptability and robustness.
The questions and issues above are interesting because answering them requires the integration of technical (engineering) and social (business) concepts in a structure that can be incorporated in a typical corporate environment.
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Such a structure and the
concepts necessary to implement it will be laid out in subsequent chapters. The next section outlines the remaining chapters of this thesis.
1.5 Thesis Outline Chapter 2 begins with a literature review of “flexibility” in design. Section 2.1 shows where flexible systems fall in the hierarchy of open engineering systems. Section 2.2 defines flexibility and its associated components, as it pertains to this research. Section 2.3 discusses the necessary background for the concepts that will be implemented in answering the research questions. Chapter 3 begins with a brief description of the Decision Based Design (DBD) Framework as introduced by Hazelrigg [19]. Section 3.2 describes the adaptations to that framework for use in the design of flexible systems and details each step within that framework. In Chapter 4 a case study is presented to demonstrate the decision framework introduced in Chapter 3 and in the final chapter, the research questions and issues are revisited and the degree to which they were answered is explored.
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CHAPTER 2 Theory and Background
2.1 Review of Flexibility in Design Before formal definitions for flexible systems in context of this research are introduced, a literature review of flexibility in design is given. The review stands to show that the idea of flexibility in design is not an entirely new one and that there is some merit to such a concept. Incorporation of flexibility and adaptability into the design process has seen some application recently, especially in the area of robust design. Combining robust design approaches and game theory was used by Chen and Lewis [9] to provide a range of solutions to designers, in effect giving more freedom to the designers and harnessing flexibility. According to Roser and Kazmer [20], “flexible design has the ability to change performance while requiring only minor time and costs to change the design parameters.” Flexible design under this context has been used to improve product design and reduce the economic cost associated with making changes to design parameters through a flexible design methodology [21]. In addition, Parkinson and Chase [22] call for the adoption of adaptive robust design approaches into the conceptual design stage. Adaptive robust design is the addition of features to a design to “control or absorb variability.” Parkinson points out that adaptive robust design has been used in an ad hoc manner for some time and that incorporation of this ideology in the conceptual design stage would be beneficial. Finally, achievement of “flexible” systems has been proposed via product platforms and product families by Simpson [23] and Finch [24]. The idea 9
here is to create a “family” or group of related products that have different functions but have a common “platform”[23]. Swiss Army Knives are an example of a product family based on a common product platform [25]. Although this literature review is not all encompassing, it does show that there is a large body of work dedicated to the concept of flexibility in design. However, to this point, “flexibility” has been an abstract concept in system design. The purpose of this research is to take flexible design from abstract concept to tangible reality.
The
definitions presented in the next section serve as a starting point.
2.2 Definition of Flexible Systems To facilitate an understanding of what a flexible system is in the context of this research and to create a consistent lexicon for future research, formal definitions for flexible systems and its components are presented here.
Flexible systems – Systems designed to maintain a high level of performance through real time changes in their configuration when operating conditions or requirements change in a predictable or unpredictable way [5].
The key concept behind flexible systems is the “real time changes in their configuration.” Design of such sophisticated systems will require a good understanding of the two underlying components of flexible systems, namely adaptability and robustness.
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Adaptability – System parameters (variables) that can be changed to enhance performance of the system in predictable situations; they can be changed when the system is not in use (passive) or in real time (active) [5].
The ability for design variables to adapt, i.e. change, is necessary for a flexible system. To be classified as flexible, a system must have a minimum of one actively adaptable variable. The other extreme is the ideal flexible system, a system in which all of the variables are actively adaptable. However, for complex systems, it is highly unlikely that all design variables will be capable of being adaptable. For this reason, robustness is an important aspect of a flexible system design.
Robustness – System parameters (variables) that are permanently set in such a way as to minimize the effect of unforeseeable changes in the operating environment on the performance of the system without eliminating the cause of the changes themselves [6].
The major reason for robustness is to deal with the uncertainty in operating conditions.
However, there is another situation in which robustness becomes an
important component of a flexible system. This other situation is associated with the cost of making a design variable adaptable. In some cases, it may be too costly to design and/or manufacture the necessary controls to make one or more variables adaptable. In these situations, the variable(s) should be set in such a way to limit the variation from
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ideal flexible system performance. Although this concept is not a focal point in this thesis, it will be discussed further in Section 5.2. Under these definitions, flexible systems are viewed as a type of open engineering system or systems that are capable of indefinite change, growth, and development over time [26]. In the next section, the hierarchy of open engineering systems is presented to show how the addition of flexible systems is beneficial to the future of engineering design.
2.3 Hierarchy of Open Engineering Systems
Open System Modular
Flexible Robustness
Adaptability
Passive
Active
Figure 2.1. Open Engineering Systems Hierarchy
As Figure 2.1 shows, flexible and modular systems are both subsystem types of open engineering systems. A modular architecture, according to Ulrich [25], has the following two properties: 1. Chunks implement one or a few functional elements in their entirety. 2. The interactions between chunks are well defined and are generally fundamental to the primary functions of the product. A truly modular architecture is one in which each “chunk” of the overall system accomplishes one specific function and the interface between chunks is well defined [25].
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The advantage in such an architecture is that a change to one “chunk” can be made without requiring a change to the other “chunks”, in effect offering some amount of flexibility to designers [27]. The approach to product family design in [23] is an example of a method based on a modular architecture. Obviously, modular and flexible systems have a lot in common. Both provide an efficient way to implement the concept of an open system. Both system types utilize robustness to deal with unforeseeable changes in operating environment. Further, both systems offer adaptability to improve performance in predictable situations. The major difference between modular and flexible systems is the type of adaptability utilized. Modular systems would more frequently use passive adaptability to achieve a new set of performance criteria while the system is offline. Flexible systems, on the other hand, use active adaptability in order to enhance performance while the system is in use. It is certainly possible to have a combination of active and passive components in a flexible system, similar to the integrated approaches to active and passive control of structures [28]. It is not the intention that flexible systems replace modular systems. Each of these open system types has distinct advantages. Flexible systems can provide peak performance at all times during use, however the engineering of such sophisticated systems will surely cost more. Thus, if high cost is not justified a modular system can offer a restricted amount of flexibility in a system at a lower cost. This idea of “justified cost” brings to question, when should a designer use a flexible system and when should he/she use a modular system. Figure 2.2 offers a possible solution for dealing with this issue in future research.
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Measure in:
Measure of: Openness
System Type
Flexibility
Robustness
Performance Space
Adaptability
Design Space
Figure 2.2. Choosing an Open Engineering System
Though not an issue in this research, a metric for openness may help the designer choose between system types, i.e., flexible or modular. If, as in the case of Figure 2.2, a flexible system type is chosen, it would be desirable to have some metric for flexibility, as a performance space measure. This issue pertains directly to Research Question 2 and as stated in Section 1.4, is necessary for designers and potentially customers to compare one flexible system to another. It would also be desirable to have metrics for robustness and adaptability, which are design space measures, and to understand the relationship between the flexibility, robustness and adaptability metrics. As evident in Figure 2.2, understanding this relationship is analogous to understanding the relationship in mapping between the performance and design spaces. Figure 2.3 shows the difficulty in mapping from the performance space to the design space.
There is currently no way of
understanding the relationship when moving from the performance space to the design space. Notice in Figure 2.3, that mapping from a single point in the performance space can lead to multiple points in the design space. Also, notice that points far away from one another in the performance space can be located relatively close to one another in the
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design space. Knowledge of the relationship between flexibility, robustness and adaptability may in fact provide useful insights to this problem.
Performance Space
Design Space
X1
F1
F2
X2
Figure 2.3. Mapping Between Performance and Design Spaces
Understanding the open engineering system hierarchy and the location of flexible systems within that hierarchy serves to show that flexible systems are important in the evolution of engineering systems. In the next chapter, the fundamental approach for answering the research questions proposed in Chapter 1 is covered. However, first, some important background theory on underlying methods and techniques is covered in the next section.
2.4 Background Theory In Chapter 3, a framework is proposed to provide a structured way to design flexible systems. There are multiple components to the framework and many of the components have underlying concepts related to it.
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This section provides brief
background on these underlying concepts in order to facilitate better understanding in the coming chapter.
2.4.1 Pareto Sets When multiple competing objectives exist, the optimum is no longer a single design point but an entire set of non-dominated design points. This set is commonly referred to as the Pareto set [29]. The Pareto set, or frontier, is composed of Pareto optimal solutions. A feasible design variable vector, x' , is Pareto optimal if and only if there is no feasible design variable vector, x , with the characteristics,
f i ( x ) ≤ f i ( x ' ) for all i, i =1, n
(Equation 2.1)
f i ( x ) < f i ( x' ) for at least one i, 1 ≤ i ≤ n
(Equation 2.2)
where n is the number of objectives. The inherent problem with multiobjective situations is the lack of a single best, or optimal, point. However, with flexible systems, it may be possible to design a system that could satisfy optimality conditions for multiple f’s. In other words, a flexible system could remain Pareto optimal according to the preceding conditions while actually changing its behavior. Figure 2.4 presents a pictorial explanation of this idea. The hypothetical Pareto set shown, is that for minimizing F1 and F2. The ideal flexible system provides optimal performance by configuring itself to provide the performance associated with the extreme points of the Pareto frontier. That is, when optimal performance with respect to F1 is required the system configuration is such that the performance is 2. If
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during use, optimal performance with respect to F2 is desirable, the system can reconfigure itself to exhibit the performance at 1.
Performance Space 1
F1
Pareto Set 2 F2 Figure 2.4. Pareto Frontier for Two Objectives
The Pareto set is important to this research for two reasons. First, it will be a useful tool for the designer to track how the Pareto set changes as levels of adaptability and robustness change from iteration to iteration in the system design. Second, the Pareto set will provide the basis for a flexibility metric. Though an important aspect in this research, the Pareto set merely provides information to the designer. While this information is vital, it should not be the sole criteria for decision-making. In this research, decisions are based not on multi-objective optimization but on a growing trend known as Decision-Based Design. The important aspects of this approach to engineering design are laid out in the next section.
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2.4.2 Decision-Based Design According to Hazelrigg [19], engineering design is comprised of two parts, identification of options and selection of the best option. He points out however, that there are several inherent problems with this, including, •
the existence of an infinite number of options,
•
the need for a measure of value to rank order options, and
•
the fact that it is computationally infeasible to search all possible options.
Decision-Based Design (DBD) looks to overcome these difficulties by making decisions via information beyond the engineering discipline [19]. Decision-making in general is composed of three parts, namely, identification of options, determination of expectations and expression of values [19]. Consider Figure 2.5. The decision maker must first generate some options, namely A, B and C. Then some expectation, in this case, probabilities are associated with each option. Finally, the value, in this case, utility of each option is calculated. The resulting decision rule is to choose the option that maximizes utility [19, 30].
Options
Expectations
Value
A
Pr(A)
U(A)
B
Pr(B)
U(B)
C
Pr(C)
U(C)
?
d
Figure 2.5. Choice problem
Many researchers have embraced the DBD approach [31-34], however, as pointed out by Chen [35], a lack of agreement still exists on the exact implementation of DBD in
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engineering design. A major issue is the construction of the utility for a design option in order that it reflects the needs of the end user and the economic benefit of the producer [35]. In this research, much like Chen’s [35], a variation of Hazelrigg’s DBD framework [19] is integrated with consumer choice theory in order to handle this issue. The next section briefly describes utility theory and Section 2.4.4 details the fundamentals of consumer choice theory and two methods that could be used.
2.4.3 Utility Theory As discussed in the previous section, selection of a design alternative requires the assignment of a value to the options. According to Hazelrigg [19], the outcomes to a design decision cannot be made with certainty. For this reason, an appropriate value measure must consider uncertainty and risk. One way of assigning values to design is utility theory. The concept of utility theory was developed by John von Neumann and Oskar Morgenstern [36]. Utility theory is based on a lottery, referred to as a von Neumann-Morgenstern lottery and follows six axioms discussed in [36]. The basic premise of utility theory is that given a lottery (set of options with corresponding expectations of occurrence), the option with the highest utility is the option with the highest probability of occurrence. This concept is shown in the example from [19], depicted here as Figure 2.6.
According to von Neumann and Morgenstern, if the
probability of the more desired outcome approaches one, the utility of the lottery should also approach one. However, if the probability of the more desired outcome approaches zero, the utility of the lottery also approaches zero.
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Status quo Decision to enter lottery or remain at status quo.
More desired outcome random event
Less desired outcome
Figure 2.6. A von Neumann – Morgenstern lottery
The purpose of utility theory is to provide a transitive rank order among alternatives. By transitive, it is meant that the decision maker makes choices in a rational way, namely if A is preferred to B and B is preferred to C, then rationally, A must be preferred to C. According to Hazelrigg [19], if the von Neumann-Morgenstern axioms are met, a valid measure for ranking alternatives results. With utility theory, it is possible to map the design options to performance attributes and assess the designer’s preference for tradeoffs between attributes [33]. This ability allows for the creation of utility functions for each attribute of a design, like those shown in Figure 2.7. The figure also shows the different types of risk attitude associated with a decision maker. According to Keeney and Raiffa [30], a “risk averse” person can be thought of as conservative and has a concave utility function, a “risk prone” person can be thought of as willing to take chances and has a convex utility function and a “risk neutral” person has a linear utility function. Utility functions can further be broken into monotonic increasing, monotonic decreasing or non-monotonic.
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Attribute
Risk Neutral
Utility
Risk Prone
Utility
Utility
Risk Averse
Attribute
Attribute
Figure 2.7. Utility Function Types
Keeney and Raiffa [30] have detailed an approach for assessing utility functions for both single attribute and multi-attribute problems and these approaches have been employed in engineering design by Thurston [37, 38] and others. However, in this work, utility functions for the consumers are assessed through a method from consumer choice theory, namely, conjoint analysis. The next section briefly describes consumer choice theory and details the approach used in this research.
2.4.4 Consumer Choice Theory Companies are interested in predicting the probability that their product will be chosen over another, i.e., the demand for a particular product. In order to assess this demand however, the company must understand what drives the consumer to choose one product over another. For a single consumer, this is relatively easy to do. However, consumer markets do not consist of a single individual, rather they are made up of many individuals. It is safe to assume that most of the individuals choose a particular product for different reasons. How then can a company estimate the demand for a single product? Enter, consumer choice theory. The goal of consumer choice theory is to model the
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behavior of a group of individuals based on behavior of the individuals that make up that group [39]. According to Ben-Akiva [39], a specific choice theory is one that defines the decision maker, alternatives, attributes of alternatives and a decision rule.
These
components are briefly defined here: •
Decision maker – Individual with particular tastes who makes decision. Though the term individual is used, a decision maker can be a group of individuals acting together, for example a household.
•
Alternatives – Set of options from which the decision maker chooses. Alternatives can be continuous or more often, discrete in nature.
•
Attributes of alternatives – The individual components that make up a particular alternative. The attributes assume values or levels and it is these values that the decision maker bases his/her choice.
Attributes can be continuous or
discontinuous in nature. •
Decision rule – The mechanism used by the decision maker to arrive at a unique choice. There are a wide variety of decision rules, which can be classified in four categories, namely, dominance, satisfaction, lexicographic rules and utility. The fundamentals of consumer choice theory are rooted in microeconomic
consumer theory [39]; however there is no single accepted choice theory for all problems. In this research one choice theory is applied, namely conjoint analysis and is discussed in the next subsection. However, another choice theory is also discussed briefly to highlight the fact that the choice theory used in conjunction with the framework presented in Chapter 3 is not limited to conjoint analysis.
22
2.4.4.1 Conjoint Analysis According to Dolan [40], conjoint analysis allows for an overall ranking of individual products and through mathematical analysis, the underlying value system of the individual can be assessed. The usefulness of conjoint is that, by understanding a person’s preferences on a subset of products it is possible to make predictions on any products with the same attributes [40]. By using conjoint analysis, it is possible to estimate the aggregate utility of a consumer market for a particular class of products via statistical analysis. The fundamental idea in conjoint analysis is that a product can be represented as a group of attributes and the component utility of each attribute can be assessed through conjoint. There are five stages to conjoint analysis [40]. Those stages are listed here and briefly described: •
Determination of relevant attributes – Before interviewing consumers, there should be confidence that the important attributes are accounted for.
Dolan
suggests that consideration should be given to three attribute types, namely, physical attributes, performance benefits and psychological benefits. •
Stimulus representation – This refers to the way in which the customer is presented the product profile. They could be presented a full profile or partial profile. The choice is highly dependent on the number of attributes and levels. For example, if a product type has two attributes each with three levels, then there are only 3 × 3 = 9 possible product profiles, so a full profile would be reasonable. However, consider a product type with four attributes, each with 5 levels, here there are 5 × 5 × 5 × 5 = 625 possible product profiles. Obviously, a full profile
23
would be unreasonable here.
By using a properly selected partial profile,
however, the preferences for all 625 possible products could be estimated [40]. •
Response type – The consumers interviewed can respond to the product profiles in two ways. They can either rank the products or rate the products. In ranking, the respondents can either choose between paired comparisons or put a list of product profiles in order from most desirable to least desirable. In the rating approach, the respondents are asked to assign a value from a scale on likelihood of purchase or desirability. The major difference between the two approaches, is that ranking allows for comparison of product profiles, while rating is done without a comparison. Ranking and rating have been found to generally produce similar final results [41], although, ranking methods are traditionally preferred because it better mimics the way consumers purchase products, i.e., comparison [40]. However, comparisons (rankings) and specifically pair-wise comparisons can be dangerous when individual responses are aggregated to represent a group preference. The danger results from the fact that individuals that display transitive behavior may and probably will display intransitive behavior as a group [42]. This is known as Arrow’s Impossibility Theorem. To avoid this problem, in this work, ratings will be used.
•
Criterion – Whatever the decision in response type, there is still the related issue of which standard to be used in judgment, namely, preference or likelihood of purchase. Obviously, the product a customer prefers is not always that which they are likely to purchase. Dolan [40], uses the example of a BMW versus a
24
Ford Taurus.
Though the customer may prefer the BMW, due to budget
constraints they may be more likely to purchase the Ford Taurus. The choice of criterion is largely dependent on whether interest is in estimating market share or market size. If the latter is the case, likelihood of purchase is a more appropriate criteria. •
Method of data analysis – The method of data analysis is dependent on choices made in previous stages. Dolan [40] suggests that if ratings are collected, simple regression can be used, for probability of purchase, Logit models can be used and finally if rankings are used, MONANOVA is recommended since “how much” one alternative is preferred to another is not indicated. Once the data is collected and analyzed, it can be used in three ways. It can be used to judge the relative importance of attributes or to identify market segments within the target market or as in this research, to assess market share for different products. Conjoint analysis has seen use recently in engineering design research in [43, 44].
In this research it is used to assess the component utilities or “part-worth’s” for each attribute that makes up a product. With the component utilities known, it is possible to calculate the total utility for a product with Equation 2.3.
Here Ui represents the
component utility of the ith attribute, n is the number of attributes, U(j) is the total utility of the jth product profile and m is the total number of product profiles. This is an additive model and is analogous to assuming no interactions between factors in ANOVA. Though it is possible to deal with interactions in conjoint analysis, an additive model is used here for simplicity, and in many instances an additive model provides a good approximation of reality [45]. Once we calculate the utilities for all the possible product profiles, it is
25
possible to calculate the probability of purchase for each product by use of Equation 2.4. Here Pr(k) represents the probability of purchase of the kth product profile. Equation 2.4 is known as the logit model and its original formulation is attributed to Luce [46], a mathematical psychologist. The model was later adapted by McFadden [47] to model consumer behavior.
n
U ( j ) = ∑ U i for j = 1,…,m
(Equation 2.3)
i =1
Pr(k ) =
exp(U (k )) m
∑ exp(U ( j ))
for k = 1,…,m
(Equation 2.4)
j =1
The next subsection presents another method for assessing consumer behavior, namely, discrete choice analysis, and though not used in this research, it is a viable means of modeling the underlying value system of consumers.
2.4.4.2 Discrete Choice Analysis
In the case of conjoint analysis, the idea is to find the utility of a product and then calculate the probability of purchase. With discrete choice analysis, the converse is applied. That is, the customer is presented with a set of choices and asked to choose one. When this is done for a number of potential customers, the probability of purchase for each option can be calculated. Given the probabilities of choice, the attributes that affect choice and Equation 2.4, it is possible to identify the utility functions behind the decisions.
Simply put, for conjoint analysis, utility functions represent the input and
26
probabilities the output while for discrete choice analysis probabilities represent the input and utility functions the output. The origin of the application of discrete choice analysis lies in transportation engineering and travel demand [39]. The beauty of the approach is that it can be used to assess choice behavior behind seemingly different products or services that have common attributes. For example consider choosing between three travel modes to get to work, namely, car, bus or subway.
While the three do not share attributes related to
performance necessarily, they do share attributes that affect ones decision on usage. For example, convenience, travel time and cost, may all be attributes that affect one’s decision on which mode to use. Both conjoint and discrete choice analyses are useful means for modeling consumer choice. Conjoint analysis can be used with hypothetical product scenarios, i.e., it is possible to calculate demand for a new product concept. Discrete choice analysis on the other hand, is used to calculate demand for existing product scenarios. Conjoint analysis is used in this research because the case study presented represents a hypothetical product concept. Though not used here, discrete choice analysis, has been applied to engineering design recently by Chen [35].
2.5 Summary
This chapter serves as a stepping stone for Chapter 3. Understanding the concepts and theories discussed here is important for comprehension of the coming methodology. In summary, flexible systems and its components were formally defined. The position of flexibility in the open engineering hierarchy was also discussed.
27
Finally, some
background theory was presented on the methods and concepts that are utilized in this research. In the next chapter, a framework under which flexible systems can be designed is laid out in detail.
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CHAPTER 3 Decision Support Framework for Flexible System Design
3.1 DBD Framework As mentioned in Section 1.5, the design of flexible systems is accomplished through adaptations made to the DBD Framework developed by Hazelrigg [19]. The original framework is shown in Figure 3.1. In this framework, the goal is to make design decisions that maximize value [19]. In this case the value is measured in terms of a Von Neumann-Morgenstern Utility. Optimal design for comparison w/ other configurations.
System configuration M
Choose x to max u Choose P(t) to max u System design x
System attributes a
Demand q(a,P,t)
Cost of manufacture and other life cycle costs C
Utility u
Corporate preferences
Exogenous variables y
Figure 3.1. Hazelrigg’s DBD Framework [19]
Though the details of each component are not covered here, a brief discussion is given to highlight the main points of the framework. First, M and x represent that about a system, which the engineer can control, namely the values of the design variables and
29
general system configuration. That which the engineer cannot control, y, is also an important aspect of system design. For example, some uncontrollable variables in the design process may be the weather or the future cost of labor [19]. The attributes of a system, a, represent that which a customer is concerned with and are ultimately dictated by x, y and C. The goal is to model demand, q, which is affected by attributes, a, price, P(t) and time, t. The utility, u, should represent the utility of profit [19] or a similar economic measure, like net present value.
The utility is dictated by corporate
preferences. Ultimately, the right combination of price and demand should be found to maximize utility. It is possible to reiterate through this framework by changing the design variables, x, and once again find the value of price that maximizes utility. For a more detailed discussion the reader is referred to [19]. The original DBD Framework has been adapted by a number of researchers [31, 34, 35, 43] for the purpose of engineering design. In the next section, yet another adaptation of the framework is presented with the goal of designing flexible systems.
3.2 DBD Framework for Flexible Systems The adapted framework for the design of flexible systems is shown in Figure 3.2. The details of the framework will be covered in the subsequent subsection, but first the rational for the adaptation is discussed. The major difference in the frameworks is the mechanics behind the design process. In the original DBD Framework (Figure 3.1) finding a price that maximizes the utility is the end of a single iteration within the framework. However, in the adapted framework of this research, the goal is to generate a budget that constrains designers during the concept generation phase. The constraint
30
provided by a budget should help to reduce the number of possible concepts the designer(s) can consider. It is also felt that identifying a budget more closely mimics the reality of engineering design.
NO
Generate concepts based on budget and minimize cost, C 9
Change levels of robustness and adaptability?
YES
Compare utility of current system with utility of previous system 7
8
Exogenous variables y Flexible system performance M
1
System design x 2
Measure flexibility fx
Identify system attributes and individual importance 3 a Choose P(t)
Identify budget for concept generation to max u 6
Demand for flexible system q(a,P,t) 5
4
Corporate preferences
Input
S.O.
Project Utility u
Key Information
Figure 3.2. DBD Framework for Flexible Systems
The adapted framework utilized in this research and adaptations used by other researchers [31, 34, 35, 43] represent a first step to modeling engineering design in a business sense. Modeling design in a business sense requires an understanding of the customer needs and desires as well as an eye for the company’s bottom line. The beauty of the framework presented here is that these two things can be accounted for while providing decision support for the designers.
The following subsection details the
framework of Figure 3.2 and highlights these two important features.
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3.2.1 Details of the Flexible System Framework The framework shown in Figure 3.2 can be viewed as a flowchart for designing flexible systems. Here each component of the framework is discussed in detail before being applied to a simple case study. 1. Flexible system performance, M The flexible system performance M, represents the requirements of the system, i.e., how it should perform. For a flexible system, this is an extremely important step, since the decision maker will have to specify the multiple performance criteria that the system needs to be optimal for. In a Pareto sense this means identifying points on the Pareto frontier that represent the desired performance for the system. In most cases these points will be the extreme points of the Pareto frontier since they represent the optimal performance for the individual objective functions. This in mind, before the framework can be implemented, the Pareto set must be identified so that the decision makers know the potential for the system, i.e., how flexible the system could actually be if all the design variables were adaptable. Most likely, we would want to assume that all the variables are adaptable for the first iteration of the framework. 2. System design, x This represents the vector of design variables and their values for the performance specifications identified by M. For convenience, the individual design variables that make up x can be represented as, xi, for i = 1, 2,...,n, where n is the number of design
32
variables. In the case of a flexible system, the xi’s may be either adaptable or robust. If the individual design variables are adaptable, then they also have a vector of values that they may assume at any given time during operation of the system. In this case, the variables may be further indexed as xij, for j = 1, 2,...,m, where m is the number of unique values an adaptable variable can assume. The values for an adaptable variable may be continuous over a specified range (m is infinite) or discrete (m is finite). The nature of the design variable vector will be problem dependent and a consideration of the designer(s). •
Measure flexibility, fx This adaptation is directly linked to research question two, namely, how can
flexibility be measured. As stated in Chapter 1, having some metric for flexibility will be important to the designer as a means of comparing one design to the next within the framework. The approach to measuring flexibility is a simple one. The measure of flexibility will be a measure of “distance” between the extreme points of the Pareto set. As an example consider Figure 3.3. The straight line is the direct path between the extreme points of the Pareto set. The “length” of that line, represents the measure of flexibility in a system that can change attain the performance associated with those end points. This measure of flexibility is simply the measure of distance between two points in a plane given by the equation, d = (∆x2 + ∆y2)1/2 [48]. As variables are changed during system design, the new Pareto sets should be found and the flexibility measured.
The
expectation is that as the level of adaptability in a particular variable(s) decreases or as
33
variable(s) become robust, the amount of flexibility will decrease, i.e., the endpoints will be closer together. Performance Space
fx = ( ∆F12 + ∆F22)1/2
F1 fx
Pareto Set F2 Figure 3.3. Measuring Flexibility in Two Dimensions
The use of a “distance” measure between the extreme points on the Pareto set obviously must be amenable to more than two dimensions, as systems may have more than two objectives. It is in fact possible to measure in dimensions greater than two by simply measuring the “distance” from one extreme point to the next and adding all these “distances” together. The general form of the equation for measuring flexibility is given below. 1 m n 2 2 fx = ∑ ∑ ∆Fk i =1, j =i +1 k =1 i , j
(Equation 3.1)
The equation is a double summation, indexing first between the ith and jth extreme points, where m is the total number of extreme points and then indexing the number of objectives, where n is the total number of objectives (dimensions). It is noted here that when, i = m, the j = m + 1 point is simply the initial point, i.e., where i = 1. This
34
accounts for the “distance” between the mth extreme point and the first extreme point on the Pareto set.
•
Exogenous variables, y, These deal with the uncertainty of designing a system [19]. Exogenous variables
are factors that cannot be controlled by the designer(s) but none the less affect the design of the system at different stages. For instance, weather is an uncontrollable variable that may affect system performance. Another example is the future cost of labor or raw materials that may affect manufacturing costs. Dealing with the uncertainty in design has been addressed by some researchers recently. Monte Carlo simulation has been implemented by some researchers including Mistree [31], Azarm [44] and others as a means of modeling exogenous variables in the design process. In this work, modeling of the uncertainty of exogenous variables directly is not covered for simplicity. However, it is pointed out here that exogenous variables that may affect demand are dealt with indirectly, since the demand model is based on a probability of purchase equation (Equation 2.4). It is further pointed out here that Monte Carlo simulation or other uncertainty models could be easily incorporated into the framework presented here. 3. Identify system attributes and individual importance, a. These represent that about the system which a consumer is concerned with [19]. In this framework we want to identify those attributes which are most important to the potential consumers. The goal is to understand the attributes and their importance and generate concepts that represent the attributes appropriately.
35
Identifying attributes that are important to the consumer is a marketing phase in product design. Typically, potential customers are interviewed in order to generate all the possible attributes considered by consumers in the evaluation of a product. This list of attributes can be large and often, many of the attributes are similar or the same. It is possible to reduce the list of many attributes to a few “super” attributes through marketing techniques not covered here. In this research, it is assumed that the “super” attributes are known a priori, and are referred to simply as attributes throughout the rest of this work. To evaluate the individual importance of the attributes, consumer choice theory is applied. In this work, as mentioned in Chapter 2, conjoint analysis will be utilized to understand the importance of each attribute and determine the total utility for each product profile. In general, system attributes are not the same as design variables. That is, what the consumer considers in purchasing is not necessarily that which a designer considers in designing. As an example, consider Figure 3.4, and the design of a car. While the consumer is concerned with attributes like, smoothness of ride, the designer is concerned with suspension stiffness and damping, etc. This mapping between the design variables and the attributes is the process of identifying the relationship between the features/benefits of a product that a customer is interested in and the design variables that control these features/benefits.
36
Product
Consumers
Designers
Design Variables
Attributes 1) smoothness of ride
1) suspension stiffness, damping
2) comfort
2) interior head room, climate controls
etc….
etc….
Figure 3.4. Relationship of Attributes to Design Variables
•
Corporate preferences Knowledge of corporate preferences is necessary to determine the utility for profit
of the company. The main issues here are figuring out who represents these preferences and how can they be captured, since it is unlikely that a single person will represent the corporation. In this work, corporate preferences will be assumed for simplicity to accommodate the case studies. In general however, preferences can be assessed through utility functions, using approaches detailed by Keeney and Raiffa [30].
There are
difficulties associated with assessing aggregate preferences in general. Ways to deal with these are discussed to some extent in [30].
•
Project utility, u Based on the corporate preferences the next step is to asses the corporate utility
for a given project. For most companies, utility for any given project will be reflected through the amount of money that will be made from it, i.e., profit. That said, in this
37
research utility of Net Present Value, NPV, will be used. NPV takes into account the fact that a dollar today is worth less tomorrow due to inflation, etc [49]. Net present value is defined by the equation below [49], where, Co is the initial cost, (Pq – C) is profit at time t, rt is the discount rate at time t, and n is the number of years that a return is expected, i.e., product life cycle. n
NPV = −C o + ∑ t =1
( Pq − C ) t (1 + rt ) t
(Equation 3.2)
It might be asked, why not just maximize NPV?
To answer this question,
consider Figure 3.5, which shows hypothetical utility functions for two companies. From the figure it is obvious that the utility function of A approaches the maximum much faster than the utility function of B. This simply means that Company A is willing to take on projects that have a lower expected NPV than Company B. In terms of generating a budget, designers for company A will have a larger budget to work with than company B. Merely maximizing NPV will not provide this information and may result in companies rejecting projects prematurely. This point will become more evident in the case study.
Utility
max utility Company A Company B
Net Present Value Figure 3.5. Utility of NPV for Two Companies
38
4. Price, P(t) Simply put this is the cost the customer incurs in purchasing the product. However, price is more than that. From a marketing perspective, price represents an attribute that nearly, always exists. Price has a negative effect on a product's utility to a consumer, that is, as price increases, the consumers need for the product will decrease if all other attributes are held constant. However, if a product is deemed better on its other attributes, a consumer may be willing to pay more for it. Determining price can be a complicated issue and often depends on market conditions, corporate strategy, etc., i.e., it is a function of time. There is an entire body of research dedicated to pricing theory. In this work, the component utility of price will be determined through conjoint analysis and used to approximate the price for the system being developed. 5. Demand for the flexible system, q(a,P,t) Demand is a function of the attributes, price and due to competition, changing needs of consumers, time, etc.. In this work, demand is modeled as a probability of purchase (Equation 2.4), which is indirectly a function of a and P(t). It is pointed out here however, that the framework of Figure 3.2 is not limited to the demand model implemented in this research. In general there are multiple ways to model demand, including discrete choice analysis, discussed in Section 2.4.4.2. It is also possible to predict demand from pre-test marketing or test marketing. The approach to demand modeling is a decision to be left up to the marketing group within a given company.
39
6. Identify budget for concept generation to maximize utility From the demand, q(a, P, t) and the project utility, u, it is possible to calculate a budget for the total product development based on Equation 3.3. By using the cost for the non-flexible system as a starting point, it is possible to then estimate additional costs for adding flexibility. In this research it is assumed that the additional cost for a flexible system has two components, a one time initial cost for flexibility and a per-unit cost for adaptability [5].
This budget accounts for all costs for the entire product life cycle,
including costs for additional design, manufacture, labor, marketing, etc. Thus from the budget, it will be necessary to determine a design budget to be used in the concept generation phase. n
Budget = C o + ∑ t =1
•
Ct (1 + rt ) t
(Equation 3.3)
Sub-Optimization, S.O. Although steps 4, 5, and 6 are separated in the framework, the three steps together
represent a sub-optimization. The reason for this sub-optimization in the complicated relationship between demand, price, cost, and profit. The desired result in this research is to maximize the corporate utility of NPV, and from this recover the attribute levels and budget. 7. Compare utility of two most recent systems. This step simply evaluates the two most recent flexible designs and keeps the one that maximizes expected utility of NPV.
40
8. Choose x and levels of robustness/adaptability? At this point, a decision is to be made on whether to change the levels of adaptability/robustness and step through the framework again or to terminate iteration of the framework and enter the concept generation stage. In deciding whether or not to step through the framework again, it is important to monitor the relationship between the project utility, u, and system flexibility, fx. If it is noticed that decreasing fx, increases u, then the designer should choose to decrease the amount of flexibility in the system and step through the framework again. This means changing the amount of adaptability, ad, and/or robustness, rb, in the variables. In a mathematical sense, it can be shown that the change in utility is ultimately a result of changes to the design variables. This is shown by the chain rule relationship below, where n is the number of design variables.
du dfx du ∂ (ad ) ∂ (rb) × × × = dfx ∂ (ad )∂ (rb) ∂ ( xi ..x n ) ∂ ( xi ..x n ) ∂ ( xi ..x n ) This is not to say that the designer(s) should keep track of derivative information, per se. However, there should be awareness of the relationship between the project utility and the design variables. This relationship may prove a valuable tool in the research sense, in understanding the relationship between flexibility and adaptability/robustness, i.e., mapping between the performance space and design spaces. 9. Generate concepts based on budget and minimize cost, C.
At this point the designers generate concepts to deliver the flexible system and estimate the costs associated with each concept. The cost of the concepts generated should fall within the budget constraint of Step 6 and the attribute levels associated with the demand in Step 5. The costs associated with flexible system design are the same as
41
that of any typical system, namely, manufacturing costs, man hour costs, etc. However, there is one other important cost associated with the design and manufacture of a flexible system, namely, the cost of manufacturing the components and or controls that make the system flexible.
This cost is necessary in order to accommodate those variables
considered adaptable. The concept chosen should be the one that minimizes cost.
This stage is
important not only from the standpoint of finding a concept with minimum cost but also in that it may provide insight into which variables should be made robust within the system. As discussed, the starting point for a flexible system would assume that all the variables are adaptable. As concepts are created and reviewed, the designer(s) may realize that some of the variables cannot be made adaptable for a reasonable cost. This is the reason for the iterative nature between Step 8 and Step 9. In this case, it may be necessary to return to the framework and identify a new set of product attribute values.
The decision support framework presented here, though comprehensive, is intended to provide a flowchart for the design of flexible systems. In the next chapter, a case study is covered in order to aid in further comprehension of the framework details discussed here.
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CHAPTER 4 Case Study: Design of a Flexible Room
4.1 Introduction to the Flexible Room Problem The particular example used here was chosen for its simplicity from an engineering perspective, so that more focus can be given to the details of the framework. The case study is examined from the perspective of three different companies, all with different “risk profiles”, i.e., each of the risk attitudes of Figure 2.6 will be represented. In the next subsection, a brief background of the problem is presented. What follows is a step by step use of the Flexible System DBD Framework to arrive at a final design for each of the three companies.
4.1.1 Flexible Room Background To understand the motivation behind the case study presented here, consider the setup of a typical conference/banquet facility room.
Many of these facilities have
retractable walls so that several smaller rooms or one large room can be created. Although this gives some flexibility, there are still only a few, discrete configuration possibilities. Consider, however, the flexible room configuration of Figure 4.1. Not only are the walls retractable, they can also move from side to side for some specified range, represented by the shaded regions. This offers the facility many more configurations than one with just retractable walls.
43
L
Room 1
Room 2
X1
Room 3
W
X2
Figure 4.1. Flexible Room Banquet Facility
The objective of this case study is to utilize the flexible system design framework proposed in Section 3.2, to design a wall-system that will result in the flexible room discussed above. For this case study, the length, L, is set to 120 ft., and the width, W, is set to 60 ft. By utilizing the framework, it will be possible to determine whether such a system would be profitable enough for a company to produce. The details are covered in the next section.
4.2 Design of a Flexible Room Though this case study represents a potential product in reality, some of the information needed within the framework is best provided by the company making the decisions. Specifically, information of a marketing and cost estimation nature would rely on “experts” within the company. For the purposes of this research, some assumptions were made and are discussed here before the framework is applied.
44
The first assumption made is that a market for banquet facilities exists. The purpose of this assumption is to provide a hypothetical market growth model over the next ten years in the U.S.. In order to create the hypothetical model, statistical data for Accommodation and Food Services from the U.S. Census Bureau [50] was used and the following steps were taken: 1. Growth rate for the number of accommodation and food services from 1992 to 1997 is calculated to be 13.2%. 2. Based on this growth rate, the number of facilities for “Hotels with 25+ rooms”, “Casino hotels” and “Caterers” is calculated for the current year (2002). These three categories are assumed to be those that will contain banquet facilities. 3. It is further assumed that the number of these facilities that actually have banquet facilities is 40% for “Hotels with 25+ rooms”, 60% for “Casino hotels”, and 50% for “Caterers”.
The resulting total number of banquet
facilities for 2002 is found to be 11,440. This result is shown in Table 4.1. Establishments with banquet facilities: 1997 Hotels, 25+ rooms 16782 Casino Hotels 257 Caterers 6478 TOTAL 23517
2002 18997 291 7333 26621
w/ banquet facility 7599 (40%) 175 (60%) 3667 (50%) 11440
Table 4.1. Total Number of Banquet Facilities for 2002
4. In the next step, growth rates for the next ten years are assumed and plotted. A second order polynomial curve is fit to the data points in order to find an
45
equation to predict the number of new facilities each year. The plot and resulting “growth equation” are shown in Figure 4.2.
Percent growth
Market Growth Trend 3.5 3 2.5 2 1.5 1 0.5 0
y = -0.0311x 2 + 0.1538x + 2.65 R2 = 0.9348 0
2
4
6
8
10
12
Year
Figure 4.2. Assumed Growth Trend for Banquet Facilities
5. Based on the market growth model of Figure 4.2, it was possible to estimate the number of new banquet facilities expected to open each year for the next ten years. The resulting calculations are shown in Table 4.2 and the resulting market growth curve is shown in Figure 4.3. These numbers represent the potential customers looking to purchase a wall system for their banquet facility.
46
Market for banquet facilities: year year total potential market 2002 0 11440 0 2003 1 11757 317 2004 2 12090 333 2005 3 12433 342 2006 4 12777 344 2007 5 13114 337 2008 6 13436 322 2009 7 13732 296 2010 8 13991 260 2011 9 14203 212 2012 10 14357 153 Table 4.2. Banquet Facility Growth Calculations
No. of New Facilities
Banquet Facility Market Cycle 400 350 300 250 200 150 100 50 0 0
2
4
6
8
10
12
Year
Figure 4.3. Resulting Growth Trend for Banquet Facilities
The next assumption to be made is the utility for comparable non-flexible systems of four competitors. This assumption is necessary because without some type of competition, the demand for any flexible wall system configuration would be 100%. Of course, the reality is that there is nearly always some type of competition, so this assumption serves to capture that reality. It is pointed out here that the competition is
47
assumed to remain static over the ten year period. That is, none of the competitors create flexible systems of their own. In assuming utilities for the four competitors, the results of a hypothetical survey, to be discussed later, for the non-flexible wall system is used. Based on the survey, the utility for the non-flexible wall system is 28. From this, the four competitors were given arbitrary utilities of 24, 27, 29, and 31. Another necessary assumption is the corporate utility for NPV. As discussed in Section 4.1, utility functions that represent the three different risk attitudes (risk prone, risk neutral, and risk averse) are used in the framework. For future reference, Company A is risk averse, Company B is risk neutral, and Company C is risk prone. The assumed utility functions for the three cases are shown in Figure 4.4.
Figure 4.4. Utility Functions for Companies A, B, and C
48
Another important assumption is the discount rate, rt. Discount rate is “the return foregone by investing in the project rather than investing in securities [49].” This value is necessary for Equations 3.2 and 3.3. Typical values range from 1% to 30% [49]. Of course, the type of investing done by a company depends on their risk attitude. A risk prone company is likely to put money in riskier investment, expecting a higher rate of return, while a risk averse company is likely to put money in more secure investments. This means that a risk prone company will use a higher discount rate than a risk averse company when making a decision on a project.
For this work, it is assumed that
Company A (risk averse) has a discount rate of 7%, Company B (risk neutral) has a discount rate of 9%, and Company C (risk prone) has a discount rate of 12%. The final assumptions made deal with cost estimation. As discussed in Section 3.2.1, for a flexible system there is an additional one-time cost for adding flexibility and a per-unit cost for each based on the amount of adaptability for each variable. For this problem the cost assumptions are as follows: •
If the wall system is automated (motor driven side to side movement) the onetime cost of flexibility is an additional 20% of the cost of a static system.
•
If the wall system is manual the one-time cost of flexibility is an additional 18% of the cost of a static system.
•
For every foot of adaptability (side to side movement) the walls have the perunit cost is an additional 2% of the cost of a static system.
The assumptions made here are, for the most part, arbitrary. They serve only to mimic hypothetical possibilities normally provided by the company “experts”. With these assumptions in mind, it is now possible to step through the Flexible System DBD
49
Framework to arrive at a wall-system for Companies A, B, and C. In the next section, the first iteration of the flexible room problem is covered to demonstrate the framework, and final results are provided for all the iterations.
4.2.1 Single Iteration of the Framework for Flexible Room Problem As stated, the first iteration of the framework for the flexible room is covered in detail here. The problem is introduced in Figure 4.1 but is reproduced here with the appropriate numbers for convenience.
120 ft
Room 1
_ +
Room 2
X1
+ _
Room 3
60 ft
X2
Figure 4.5. Flexible Room Banquet Facility Design
1. Flexible System Performance, M For this problem, the flexible performance the designers are interested in is the area of rooms 1, 2, and 3 in Figure 4.5. Specifically, we are interested in maximizing the areas of the three rooms. Obviously, this is a case of multiple competing objectives. The formal problem statement is:
50
Find:
X1, X2
Objectives:
Maximize area of Room 1, A1 = 60’X1
Maximize area of Room 2, A2 = 60’(120’ – X1 – X2)
Maximize area of Room 3, A3 = 60’X2
Subject to:
30’ ≤ X1 ≤ 50’
30’ ≤ X2 ≤ 50’
It is assumed that complete adaptability in this case is one in which the variables X1 and X2 can move from 30’ to 50’ (+/- 10’ from the equal room position). This represents the ideal flexible system and as such is the starting point for identifying the optimal flexible system through the framework. Therefore, for this iteration of the framework, the wall-range is set to be +/- 10’.
2. System Design, x Given the problem statement above, it is possible to populate the Pareto frontier and identify the extreme points and the corresponding design variable values. These extreme points represent the performance (room areas) that the flexible room will achieve, and are listed in Table 4.3, where x = (X1, X2) and F = (A1, A2, A3). The resulting Pareto set is shown in Figure 4.6, with the extreme points corresponding to Table 4.3.
51
1 2 3 4
x (ft, ft) (30, 30) (30, 50) (50, 50) (50, 30)
2
2
2
F (ft , ft , ft ) (1800, 3600, 1800) (1800, 2400, 3000) (3000, 1200, 3000) (3000, 2400, 1800)
Table 4.3. Ideal Flexible Room Configuration Extremes
Figure 4.6. Pareto Set for Ideal Flexible Room
•
Measure Flexibility, fx Using Equation 3.1, the measure of flexibility for the current flexible room under
consideration can be calculated as: fx = [ {(1800-1800)2 + (3600-2400)2 + (1800-3000)2}1/2 1,2 + {(1800-3000)2 + (2400-1200)2 + (3000-3000)2}1/2 2,3 + {(3000-3000)2 + (1200-2400)2 + (3000-1800)2}1/2 3,4 + 52
{(3000-1800)2 + (2400-3600)2 + (1800-1800)2}1/2 4,1] fx = 6788.225 Since this configuration represents the ideal flexible room, the measure of flexibility found here is the maximum possible, denoted fxmax, and the normalized flexibility measure, fxnorm is equal to one, where generally fxnorm = fx / fxmax. It is pointed out here that, when calculating flexibility, order matters. That is, the designer must be careful that he/she moves along the performance space from one extreme point to another properly. Referring to Figure 4.6, if the designer starts from Point 1, then he/she must be careful to measure the flexibility in the order 1-2-3-4-1 or 14-3-2-1, i.e., the designer must make sure he doesn’t measure flexibility along a diagonal path through the Pareto set, but rather, measures the flexibility along a straight path around the Pareto set. This issue becomes difficult when there are more than three objectives and visualization of the Pareto set is not possible.
3. Identify system attributes and individual importance, a The attributes for the flexible room are room size, transition type (how the wall moves from side to side) and price.
These attributes are normally generated from
marketing research done within the company but are assumed in this work for simplicity. In order to determine how each of these attributes affects consumer preference for product, conjoint analysis is done to find the individual importance of the three attributes.
53
price wall range 0 +/- 5 ft +/- 8 ft +/- 10 ft
$45,700 8 11 16 20
manual $53,700 $57,700 5 2 8 6 14 10 17 12
$60,700 0 3 8 10
$45,700 8 13 18 20
automatic $53,700 $57,700 5 2 10 7 15 12 18 14
$60,700 0 5 9 11
~ Rate the above configurations on a scale of 0 to 20 with the following in mind: 0 ~> no value; would never purchase 10 ~> good value; would probably purchase 5 ~> little value; may consider purchase 15 ~> great value; would definitely purchase 20 ~> incredible value; would pay more to have
Figure 4.4. Survey of Possible Room Configurations
To assess the value of potential room profiles, a survey with a profile of 32 potential room configurations (4 wall ranges × 2 transition types × 4 prices = 32), is used to assess the consumer utility for a given configuration. The survey and hypothetical results are shown in Figure 4.4. This survey is not a full profile, because the wall range can assume any integer value between five feet and ten feet, and the price can assume any price between $45,700 and $60,700 in thousands of dollars. Conjoint analysis was done on the survey results to assess the component utilities of each attribute. The method of data analysis chosen is a simple averaging model, in which the component utilities are calculated as an average along each possible level. For example, to determine the component utility due to “manual” transmission the average of the survey results under the “manual” side of the survey was calculated. The choice of data analysis used here is not necessarily the best method, but is chosen instead for its simplicity. Again, these are just hypothetical possibilities. The validity of any particular methodology throughout this analysis is not an issue of interest in this work. For the “price” and “wall-range” attributes, second order polynomials were fit to the data, in order to recover the component utility functions. The resulting component utility graphs and equations are shown in Figure 4.5. With this data, to find the overall 54
utility of any configuration, the component utilities are found for each attribute and then added together. The results found here are the basis for the non-flexible system utilities discussed in the assumptions.
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Component Utility for Transition Type
Component Utility
11.00 10.50 10.00 9.50 9.00 8.50 manual
automatic Transition Type
Component Utility for Wall Range
Component Utility
20.00 y = -0.075x 2 + 2.6x - 3.25
15.00
R2 = 1
10.00 5.00 0.00 0
2
4
6
8
10
12
Wall Range
Component Utility
Component Utility for Price 16.00 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 $40,000
y = -3E-08x2 + 0.0026x - 41.296 R2 = 0.9967
$45,000
$50,000
$55,000
$60,000
$65,000
Price
Figure 4.5. Component Utility Graphs for Wall Attributes
56
•
Project Utility The utility for a project is found using the corporate utility functions of Figure
4.4.
By maximizing the project utility, the levels for the transition type and price
attributes are determined for the system with a wall-range of +/- 10’. It is noted here, that the maximum utility for any corporation approaches one but never actually reaches that value, as will be seen. This accounts for the fact that utility for money can never truly be maximized, i.e., more money is always good, but how good is determined by the “risk attitude” of the company.
4. Price, P(t) As mentioned in Chapter 3, setting the price is a complicated issue. In this work, price is treated as a product attribute and is set through maximization of corporate utility for NPV.
5. Demand, q(a,P,t) It is possible to calculate the probability of purchase for a given configuration of the flexible room by first finding the total utility and then using Equation 2.4. For example, consider a configuration in which the transition type is automatic, the wall range is ten feet and the price is $45,700. The resulting total utility for this can be calculated from the component utility graphs as: Utotal = Utransition + Uwall-range + Uprice Utotal = 10.44 + 15.25 + 14.25 Utotal = 39.9
57
Knowing the utilities of the non-flexible systems listed in the assumptions and the total utility calculated above, the resulting probability of purchase is for this example configuration is found from Equation 2.4 as: Pr = exp(39.9) / [exp(24) + exp(27) + exp(28) + exp(29) + exp(31) + exp(39.9)] Pr = .999 Simply multiplying the probability of purchase by the projected market size for any given year, results in the demand for the system.
6. Identify budget for concept generation by maximizing u Based on the cost of creating the non-flexible system, it is possible to estimate a budget for the flexible system. Referring to Equation 3.3, the assumption in this work is that the initial cost, Co, is zero, since the initial costs for this problem would be related to the design done by engineers whom are already accounted for within the company. The future costs, C, however, must be accounted for. These costs are due to the cost of manufacturing the system, installing it, and the additional cost of adding flexibility. The assumption used in calculating the cost for a single system is that the cost for the nonflexible system is $30,000. The additional costs associated with the flexible wall system are discussed in the list of assumptions above. Given this cost for each system, Equation 3.3 can be used to calculate a budget for an individual system in a given year over the ten year period. By multiplying the per unit budget for a given system configuration and the demand for that year, it is possible to find the total budget allowed for the ten year period.
58
•
Sub Optimization, S.O. The sub optimization approach used for this problem is a grid search that
combines steps 4, 5, and 6 in order to calculate the corporate utility for NPV at every possible point in the attribute space. The only variable that is held constant is the wall range (+/- 10’), since it is the adaptable variable value being investigated in this iteration of the framework. By maximizing the utility for NPV, a budget, price, and transition type are recovered for the current wall range. The result is shown in Table 4.4 for all three corporate utility function types. wall range = +/-10 U(NPV) Company A 0.998 Company B 0.818 Company C 0.559
Transition manual manual manual
Price $60,700 $60,700 $60,700
Budget $93,571,144 $87,750,216 $80,194,432
NPV $42,265,308 $39,636,048 $36,223,160
Table 4.4. First Iteration Results for Companies A, B and C
7. Compare utility of current and previous system Obviously, since there is no previous system, move to the next step.
8. Change levels of adaptability and robustness Looking at the results in Table 4.4, Company A has nearly maximized utility for NPV, and they may choose to stop iteration of the framework and move to Step 9. Company B and C, however, would change their level of adaptability for the wall range in order to see if they could raise the utility of NPV. For comparison purposes, iteration of the framework was continued for all three companies. discussion of these results is provided in the next section.
59
The results and general
9. Generate concepts based on budget Using the budget that was generated, it is now possible to generate concepts for the system. If it is found that the budget is not sufficient to create the system needed to achieve the predicted NPV, then it may be necessary to re-enter the framework. This time through, it might be a consideration to make one of the design variables robust, i.e., set one of the walls to a permanent position.
The problem presented here is a fairly simple one from an engineering standpoint. It serves to show how the design framework presented might be used to design a system and highlight some of the points discussed in previous chapters. revisited in Chapter 5.
These points are
In the following sections, the results of further framework
iteration are discussed and the evolution of the “effective” Pareto frontier and the changing measure of flexibility is also discussed.
4.2.2 General Results of the Flexible Room Problem Though for Company A, a single iteration of the framework may be sufficient for determining a design, Companies B and C need further iteration of the framework to arrive at a final wall-system design. The results of all iterations of the framework (for wall-range from 10’ to 5’) are shown in Figure 4.6. For reference, each table within Figure 4.6 is for a particular level of adaptability, i.e. a particular wall range. “U(NPV)” is the corporate utility for NPV, “Transition” is the resulting level for the transition attribute (manual or automatic), “Price” is the price attribute (cost to consumer),
60
“Budget” is the resulting budget for the ten year period of the project, and “NPV” is the estimated net present value of the project over the ten year period. wall range = +/- 10' U(NPV) Company A 0.998 Company B 0.818 Company C 0.559
Transition manual manual manual
Price $60,700 $60,700 $60,700
Budget $93,571,144 $87,750,216 $80,194,432
NPV $42,265,308 $39,636,048 $36,223,160
wall range = +/- 9' U(NPV) Company A 0.998 Company B 0.844 Company C 0.594
Transition manual manual manual
Price $60,700 $60,700 $60,700
Budget $92,215,040 $86,478,472 $79,032,184
NPV $43,621,416 $40,907,792 $37,385,404
wall range = +/- 8' U(NPV) Company A 0.998 Company B 0.869 Company C 0.631
Transition manual manual manual
Price $60,700 $60,700 $60,700
Budget $90,858,904 $85,206,704 $77,869,936
NPV $44,977,396 $42,179,432 $38,547,540
wall range = +/- 7' U(NPV) Company A 0.998 Company B 0.894 Company C 0.668
Transition manual manual manual
Price $60,700 $60,700 $60,700
Budget $89,494,704 $83,927,384 $76,700,760
NPV $46,332,168 $43,449,912 $39,708,636
wall range = +/- 6' U(NPV) Company A 0.999 Company B 0.917 Company C 0.702
Transition manual manual manual
Price $60,700 $60,700 $60,700
Budget $87,862,400 $82,396,600 $75,301,784
NPV $47,636,320 $44,672,936 $40,826,344
wall range = +/- 5' U(NPV) Company A 0.998 Company B 0.889 Company C 0.660
Transition automatic automatic automatic
Price $60,700 $60,700 $60,700
Budget $85,211,680 $79,910,792 $73,030,016
NPV $47,412,656 $44,463,180 $40,634,652
Figure 4.6. Results from all Iterations of the Framework
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From the results, several noteworthy points arise and are discussed here: 1. Previously it was noted that for a wall-range of +/- 10’, Company A may stop iteration of the framework since there utility for NPV is nearly maximized.
From the results in Figure 4.6 however, it is noted that
Companies B and C would not cease iteration of the framework until a design corresponding with a wall-range of +/- 6’. 2. The differentiation in final designs between Company A and Companies B and C can be attributed to their respective “risk attitudes”. In a sense, since Company A is risk averse, they are just as happy with an NPV of $42.2 million (wall-range of +/- 10’) as they are with $47.6 million (wallrange of +/- 7’). That is, once a certain level of NPV is reached, further increasing NPV does little to increase utility. Companies B and C on the other hand are more prone to risk than Company A, and thus they will have more significant increases in utility for slight increases of NPV. As an example, compare the results in Figure 4.6 for a wall-range of +/- 9’ to those for a wall-range of +/- 6’. Here, Company C only has an increase in NPV of $3.44 million with an increase in utility of 0.108, while Company A with an increase in NPV of $4.01 million only has an increase in utility of 0.001. 3. Further inspection of the results in Figure 4.6, shows significant differences in NPV and Budget for each company for any given wallrange. This result is again due to the “risk attitude” of each company. As
62
discussed in the assumptions, a risk prone company will make riskier investments, thus they discount the present value of money made in the future more than a risk averse company. The results of Figure 4.6 reflect this fact, since for any given wall-range, all the designs are the same, i.e., the attributes all have the same levels, yet Company C has a lower NPV and Budget than Company A. To further highlight this fact, consider the results in Figure 4.7 for a single iteration of the framework with a wallrange of 8’. For these results, the discount rates were changed to 4% for Company A, 9% for Company B and 18% for Company C. Notice for these more extreme discount rate results while Company A invests (budgets) about $34.4 million more than Company C, they only make about $17 million more over the ten year period. In the original results of Figure 4.6 however, for the same design, Company A invests about $13 million more than Company C, and only makes about $6.4 million over the ten year period. The key notion here is that “riskier” behavior lends itself to less investment with similar return, as would be expected. It should be noted however, that Company A’s return (NPV) is more certain than Company C’s. wall range = +/- 8' U(NPV) Company A 0.999 Company B 0.869 Company C 0.458
Transition manual manual manual
Price $60,700 $60,700 $60,700
Budget $100,734,992 $85,206,704 $66,367,080
Figure 4.7. Results for Extreme Discount Rates
63
NPV $49,866,304 $42,179,432 $32,853,340
4. A final note on the results is the fact that each company has the same design (levels on attributes) within each iteration (wall-range) of the framework. This simply results from the fact that all three companies use the same cost estimation model. Obviously, this does not occur often in reality but the interest in this work is to show how “risk attitude” affects design decisions, rather than the system models. The results discussed here, serve to show the value of the decision support framework and the importance of understanding the corporate position on risk. As shown, the final design decisions are highly dependent on the corporate “risk attitude”. In the next section, the affects of changing the level of adaptability in adaptable variables is discussed along with the importance of the flexibility metric.
4.2.3 Evolution of the Pareto Frontier It is expected that, as the level of adaptability within adaptable variables decreases, the system flexibility will decrease. In effect, the Pareto frontier of interest will shrink when the ideal flexible system (all variables fully adaptable) is reduced to a less than ideal system and consequently the measure of flexibility, fx, will also decrease. For the flexible room problem, this concept is shown in Figure 4.8.
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Figure 4.8. Changing Pareto Frontier for Flexible Room
The blue region represents the Pareto set for the ideal flexible room, i.e., X1 and X2 able to move from 30’– 50’ (wall-range of +/- 10’) and here fxnorm has a value of one. The red region shows the effective Pareto set for X1 and X2 in the range of 32’– 48’ (wall-range of +/- 8) and fxnorm has a value of 0.8. Finally, the green region shows the effective Pareto set for X1 and X2 in the range of 35’–45’ (wall-range of +/- 5’) and fxnorm has a value of 0.5. In concluding the case study, Figure 4.8 serves to show the value of having a flexibility measure. Though in this problem, it is easy to visualize the change in effective Pareto frontier, in a problem of higher dimensionality, this option won’t be available to the designer. In such cases, it will be useful in understanding how changes in the level of
65
adaptability affect system flexibility, i.e., how much flexibility is lost per unit of decreased adaptability. The case study covered here while technically simple, highlights the difficulty of designing engineering systems even within a decision support framework. In Chapter 5, the research questions proposed in Chapter 1 and the degree to which they have been answered is discussed. The future of this research and related topics are also discussed.
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CHAPTER 5 Conclusions and Future Work
The primary goals of this research are the introduction of a decision support framework to facilitate design of flexible systems and the introduction of a metric for the amount of flexibility within a flexible system. In Section 5.1, the primary research questions and the secondary research issues proposed in Chapter 1 are revisited and the degree to which they were answered is explored. In Section 5.2, future work related to this research is discussed.
5.1 Revisiting the Research Questions In Chapter 1, two main research questions are proposed as the focus of this thesis. The first of these questions is: 1) How can flexible systems be designed in a manner that provides decision support and accounts for all the stages in the creation of consumer driven products? To review, the motivation behind this question lies in the idea that engineers are decision makers and further, that design decisions rely on information beyond the engineering field, i.e., marketing and managerial input is an important aspect. Answering this question resulted in the DBD framework for flexible systems, detailed in Section 3.2. An adaptation of Hazelrigg’s original DBD Framework [19], the framework in Section 3.2 brings together the important components of the engineering and social sciences discussed in Section 2.4.
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As part of this first research question, two secondary research issues of interest are: 1.1)
Method/technique for changing the levels of adaptability/robustness.
1.2)
Incorporation of demand modeling to justify cost associated with a flexible system.
The first of these issues is dealt with in some manner through the maximization of corporate utility (Step 6 of framework) and the decision to re-enter the framework if a concept can not be generated that satisfies the budget constraint (Step 9 of framework). The second issue is dealt with more directly through the use of consumer choice theory. Specifically, conjoint analysis discussed Section 2.4.4.1 and Equation 2.4, allow for the calculation of a “probability of purchase” based on consumer utilities for a product profile. The second research question proposed in Chapter 1 was: 2) How can flexibility be measured? The motivation here is to provide a means for designers to compare the “amount” of flexibility from one system to another.
It could also potentially be a means of
comparison for customers. Answering this question resulted in Equation 3.1 and Step 2 within the framework. As part of this research question, two secondary issues addressed in this research are: 2.1)
Understanding the affects of varied flexibility on utility of product to consumer and corporation.
67
2.2)
Understanding the relationship between the measure of flexibility and the levels of adaptability and robustness.
The first of these issues is dealt with indirectly as part of the framework. That is, from one iteration of the framework to the next, the designers must be aware of how the changing level of flexibility is affecting the consumer utility and thus, the corporate utility. It should not be assumed that a decrease in consumer utility will lead to a decrease in corporate utility or vice-versa. Understanding the second issue is more complicated and is introduced in Section 4.2.3. As expected, decreasing the level of adaptability led to a decrease in flexibility. The ability to see how flexibility changes as levels of adaptability are changed within adaptable variables is an important consideration of designers as decision makers. Though the research issues raised in Chapter 1 have been dealt with to some degree in this work, as with all research, some questions still need further exploration and some new issues are raised. These issues are the focus in Section 5.2.
5.2 Future Work The future work associated with this research can be broken into two main categories, flexible system design and decision support frameworks in general. The issues are discussed here.
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5.2.1 Flexible System Design Flexible systems by themselves provide an interesting area of future research. Before such systems can become widely used, understanding the “mechanics” of their design is important. Understanding these “mechanics” means:
1. Formal
understanding
of
the
relationship
between
flexibility
and
adaptability/robustness. As discussed in Section 2.3, understanding this issue is closely related to understanding the issue of mapping between the performance and design spaces. A formal understanding means identifying a mathematical relationship between flexibility, which is measured in the performance space, and adaptability/robustness, which are design space characteristics.
2. Identifying the adaptable and robust design variables before the system design truly begins. The ability to identify variables as adaptable or robust at design start may lead to more efficient design processes by decreasing the number of iteration through the formal design process.
3. Improvement of the DBD framework for flexible systems, proposed in this research. Specifically, there is a need to overcome the difficulty of calculating flexibility, fx, encountered in Section 4.2.1, i.e., the designer must be sure to calculate the “distance” around the Pareto frontier and not across it. Further improvement could be made through the incorporation of more complex pricing models, demand models, etc.
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5.2.2 Decision Support Frameworks The desire to formally model the design process into a decision support framework is a growing trend in academia and to some extent in industry. However, making these academic based models useful will require:
1. Immersion in an industry setting, of the frameworks like the one proposed in this research is necessary. The insights of corporate decision makers will lead to improvements of these decision support models making them more useful tools. As a benefit to industry, use of these frameworks should improve the efficiency of the design process by bringing all the players that influence design decisions (not just engineers) under a more efficient infrastructure.
2. Decision support frameworks for different product types. According to Pahl and Beitz [51], product development can be classified as original design, adaptive design, and variant design. It may not be appropriate to use an adaptive design decision support framework when developing an original design.
5.3 Conclusion The work done in this thesis provides a preliminary decision support tool for the design of flexible systems. It also introduced a metric for measuring the amount of flexibility in a system. The hope is that this research lays further ground in making flexible systems a viable open engineering system. Further, it is hoped that this research strengthens the case for formalizing the design process in a decision support structure.
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References [1] Womack, J.P., D. Jones, and D. Roos, 1990, The Machine that Changed the World, HarperCollins Publishers, New York, NY. [2] Goldin, D.S., S.L. Venneri, and A.L. Noor, 1999, "Ready for the Future?" Mechanical Engineering, 121, No. 11, pp. 61-66. [3] Zeleny, M., 1997, “Towards the Tradeoffs-Free Optimality in MCDM,” Multicriteria Analysis, edited by J. Climaco, Springer-Verlag, Berlin, Heidleberg, pp. 596-601. [4] Kasprzak, E., and K. Lewis, 2000, “An Approach to Facilitate Decision Tradeoffs in Pareto Solution Sets,” Journal of Engineering Valuation and Cost Analysis, 3, No. 1, pp. 173-187. [5] Olewnik, A. et al., 2001, “A Framework for Flexible Systems and its Implementation in Multiattribute Decision Making”, ASME Design Theory And Methodology Conference, Pittsburgh, Pa., DETC2001/DTM-21703. [6] Phadke, M. S., 1989, Quality Engineering using Robust Design, Englewood Cliffs, New Jersey, Prentice Hall. [7] Lewis, L. and Parkinson, A., 1994, “Robust Optimal Design with a Second Order Tolerance Model,” Research in Engineering Design, 6, pp. 25-37. [8] Chen, W., J.K. Allen, K-L. Tsui, and F. Mistree, 1996, “A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors,” ASME Journal of Mechanical Design, 118, No. 4, pp. 478-485. [9] Chen, W. and K. Lewis, 1999, “A Robust Design Approach for Achieving Flexibility in Multidisciplinary Design,” AIAA Journal, 7, No. 8, pp. 982-990. [10] Chen. W., M. Wiecek, and J. Zhang, 1999, “Quality Utility: A Compromise Programming Approach to Robust Design,” ASME Journal of Mechanical Design, 121, 2, pp. 179-187. [11] Kalsi, N., K. Hacker, and K. Lewis, 2001, “A Comprehensive Robust Design Approach for Decision Trade-Offs in Complex Systems Design,” ASME Journal of Mechanical Design, 123, No. 1, pp.1-10. [12] Otto, K.N. and E.K. Antonsson, 1993, “Extensions to the Taguchi Method of Product Design,” Journal of Mechanical Design, 115, pp. 5-13. 71
[13] Parkinson, A., C. Sorensen, and N. Pourhassan, 1993, “A General Approach for Robust Optimal Design,” Journal of Mechanical Design, 115, pp. 74-80. [14] Sen, P., Z. Rao, and P. Wright, 1997, “Multicriteria Robust Optimization of Engineering Design Systems Under Uncertainty,” ICED ’97, Tampere. [15] Sundaresan, S., K. Ishii, and D.R. Houser, 1993, “A Robust Optimization Procedure with Variations on Design Variables and Constraints,” Advances in Design Automation, ASME DE 69-1, pp. 379-386. [16] Taguchi, G., 1987, System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs, UNIPUB/Kraus International Publications. [17] Tsui, K–L., 1992, “An Overview of Taguchi Method and Newly Developed Statistical Methods for Robust Design,” IIE Transactions, 24, No. 5, pp. 44-57. [18] Pindyck, R.S. and D.L. Rubinfeld, 2001, Microeconomics, Fifth Edition, PrenticeHall, Inc., Upper Saddle River, NJ. [19] Hazelrigg, G.A., 1998, “A Framework for Decision-Based Engineering Design,” Journal of Mechanical Design, 120, pp. 653-658. [20] Roser, C. and Kazmer, D., 1999, “Risk Effect Minimization Using Flexible Product and Process Design,” ASME Design for Manufacturing Conference, Las Vegas, NV, DETC99/DFM-8959. [21] Roser, C. and Kazmer, D., 2000, “Flexible Design Methodology,” ASME Design for Manufacturing Conference, Baltimore, MD, DETC00/DFM-14016. [22] Parkinson, A. and K. Chase, 2000, “An Introduction to Adaptive Robust Design for Mechanical Assemblies,” ASME Design Automation Conference, Baltimore, MD, DETC00/DTM-8761. [23] Simpson, T., J. Maier, F. Mistree, 1999, “A Product Platform Concept Exploration Method for Product Family Design,” ASME Design Theory and Methodology, Las Vegas, NV, DETC99/DTM-8761. [24] Finch, W., 1999, “Set-Based Models of Product Platform Design and Manufacturing Processes,” ASME Design Theory and Methodology Conference, Las Vegas, NV, DETC99/DTM-8761. [25] Ulrich, K. and S. Eppinger, 1995, Product Design and Development, McGraw-Hill, Inc., New York. 72
[26] Simpson, T.W., U. Lautenschlager, and F. Mistree, 1998, “Mass Customization in the Age of Information: The Case for Open Engineering Systems,” in The Information Revolution: Current and Future Consequences, W. Read and A. Porter, eds., Ablex Publications, Greenwich, Connecticut, pp. 49-71. [27] Sosa, M.E., S.D. Eppinger, and C.M. Rowles, 2000, “Designing Modular and Integrative Systems,” ASME Design Theory And Methodology Conference, Baltimore, Maryland, DETC2000/DTM-14571. [28] Smith, M., K. Grigoriadis and R. Skelton, 1992, “Optimal Mix of Passive and Active Control in Structures,” Journal of Guidance, Control and Dynamics, 15, No. 4, pp. 912-919. [29] Pareto, V., 1906, Manuale di Econòmica Polìttica, Società Editrice Libràia, Milan, Italy; translated into English by A. S. Schwier, as Manual of Political Economy, Macmillan, New York, 1971. [30] Keeney, R. and Raiffa, H., 1993, Decisions With Multiple Objectives: Preferences and Value Tradeoffs, Cambridge University Press, United Kingdom. [31] Marston, Matthew and Mistree, Farrokh, 1998, “An Implementation of Expected Utility Theory in Decision Based Design”, ASME Design Theory and Methodology, Atlanta, GA, DETC98/DTM-5670. [32] Thurston, D., 1999, “Real and Perceived Limitations to Decision Based Design,” ASME Design Theory and Methodology Conference, Las Vegas, NV, DETC99/DTM-8750. [33] Callaghan, A.R. and Lewis, K. E., 2000, “A 2-Phase Aspiration-Level and Utility Theory Approach to Large Scale Design,” ASME Design Theory and Methodology, Baltimore, MD, DETC2000/DTM-14569. [34] Gu, Xiaoyu et al., 2000, “Decision-Based Collaborative Optimization under Uncertainty,” ASME Design Automation Conference, Baltimore, MD, DETC2000/DAC-14297. [35] Chen, W., and Wassenaar, H. J., 2001, “An Approach to Decision-Based Design,” ASME Design Theory and Methodology, Pittsburgh, PA, DETC2001/DTM-21683. [36] von Neumann, J. and Morgenstern, O., 1953, The Theory of Games and Economic Behavior, Third Edition, Princeton University Press, Princeton, NJ.
73
[37] Thurston, D., 1989, “Multiattribute Utility Analysis in Design Management,” IEEE Transactions on Engineering Management, Vol. 37, pp. 296-301. [38] Thurston, D., 1991, “A Formal Method for Subjective Design Evaluation with Multiple Attributes,” Research in Engineering Design, Vol. 3, pp. 105-122. [39] Ben-Akiva, M. and Lerman, S., 1985, Discrete Choice Analysis Theory and Application to Travel Demand, The MIT Press, Cambridge, MA. [40] Dolan, R., 1990, “Conjoint Analysis: A Manager’s Guide,” Harvard Business School Publishing, Boston, MA. [41] Green, P., and Srinivasan, V., 1978, “Conjoint Analysis in Consumer Research: Issue and Oulook,” Journal of Consumer Research, Vol. 5, pp. 103-123. [42] Arrow, K.J., 1963, Social Choice and Individual Values, 2nd ed., Yale University Press, New Haven, CT. [43] Gupta, Satyandra and Samuel, Anoop, 2001, “Integrating Market Research with the Product Development Process: A Step Towards Design for Profit,” ASME Design for Manufacturing Conference, Pittsburgh, PA, DETC2001/DFM-21202. [44] Li, H. and Azarm, S., 2000, “Product Design Selection Under Uncertainty and with Competitive Advantage,” Journal of Mechanical Design, Vol. 122, pp. 411 – 418. [45] Green, Paul E. and Rao, Vithala R., 1971, “Conjoint Measurement for Quantifying Judgemental Data,” Journal of Marketing Research, Vol. 8, pp. 355 – 363. [46] Luce, R., 1959, Individual Choice Behavior: A Theoretical Analysis, Wiley, New York. [47] McFadden, D., 1970, “Conditional Logit Analysis of Qualitative Choice Behavior,” Frontiers in Econometrics, ed. P. Zarembka, Academic Press, New York, pp. 105142. [48] Thomas, G. and Finney, R., 1996, Calculus and Analytic Geometry, 9th ed., Addison-Wesley Publishing, Reading MA. [49] Brealey and Myers, 2000, Principles of Corporate Finance, 6th ed., McGraw-Hill, Boston, MA. [50] US Census Bureau, 2000, Economic Census Reports Accommodation and Food Services, http://www.census.gov/epcd/www/97EC72.HTM. 74
[51] Pahl, G., and W. Beitz, Engineering Design: A Systematic Approach, New York: Springer, 1996.
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