Time-Expanded Decision Networks: a Framework for Designing Evolvable Complex Systems*

Regular Paper Time-Expanded Decision Networks: A Framework for Designing Evolvable Complex Systems*

Matthew R. Silver and Olivier L. de Weck†

Department of Aeronautics & Astronautics, Engineering Systems Division, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139

TIME-EXPANDED DECISION NETWORKS

Received 10 October 2006; Accepted 13 February 2007, after one or more revisions Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/sys.20069

ABSTRACT

This paper describes the concept of Time-Expanded Decision Networks (TDNs), a new methodology to design and analyze flexibility in large-scale complex systems. This includes a preliminary application of the methodology to the design of Heavy Lift Launch Vehicles for NASA’s space exploration initiative. Synthesizing concepts from Decision Theory, Real Op- tions Analysis, Network Optimization, and Scenario Planning, TDN provides a holistic framework to quantify the value of system flexibility, analyze development and operational paths, and identify designs that can allow managers and systems engineers to react more easily to exogenous uncertainty. TDN consists of five principle steps, which can be implemented as a software tool: (1) Design a set of potential system configurations; (2) quantify switching costs to create a “static network” that captures the difficulty of switching among these configurations; (3) create a time-expanded decision network by expanding the static network in time, including chance and decision nodes; (4) evaluate minimum cost paths through the network under plausible operating scenarios; and (5) modify the set of initial design configurations to exploit high-leverage switches and repeat the process to convergence. Results can inform decisions about how and where to embed flexibility in order to enable system evolution along various development and operational paths. © 2007 Wiley Periodicals, Inc. Syst Eng 10: 167–186, 2007

* An earlier version of this paper was published and presented as follows: M. Silver and O. de Weck, Time-expanded decision network methodology for designing evolvable systems, AIAA-2006-6964, 11th AIAA/ISSMO Multidisciplinary Analysis Optim Conf, Portsmouth, VA, September 6–8, 2006. †Author to whom all correspondence should be addressed (e-mail: [email protected]).

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Key words: changeability; flexibility; real options; time-expanded networks; decision theory; system optimization; lock-in

NOMENCLATURE or for them to be changed by an external agent in the face of environmental change and uncertainty [Arthur, c = arc traversal cost, 1989; Simon, 1996; Cowan, 1990]. Lock-in and its cO = organizational premium for system relationship to technological evolution has been the change, subject of much research in various fields including CLCi = estimated lifecycle cost of the ith sys- engineering [Utterback, 1974; Silver 2005b], econom- tem configuration, ics [Arthur, 1989; Arrow, 2000; David, 2000], political CD = development cost (DDT&E), economy [Nelson and Winter 1982] and strategic inno- CF = fixed recurring cost per time period, vation management [Henderson et al., 1990; Christen- CV = variable cost as a function of demand son, 1997; Hax, Wilde, and Thurow, 2001]. The exact per time period, causes of lock-in are still debated [Liebowitz, 1985]. CSW(A, B) = cost of switching from A to B, They are generally acknowledged to be multidimen- ∆ ( ) CD B, A = incremental DDT&E of the new sys- sional, taking root in sociotechnical issues such as tem configuration B starting from A, network externalities [Katz, 1984; Witt, 1997], the cost CR(A) = cost of retiring system A, of learning new technologies [Utterback, 1974] and ∆ ( ) CR A, B = incremental retirement cost of system operating procedures, the risks associated with switch- A when switching to B, ing to new systems, the tradeoff between operating Dj = demand during time period j, slightly inefficient fielded technologies and developing i = number of system configurations con- new technologies [Sarsfield, 2001], and broader issues sidered, associated with political and organizational inertia m = number of arcs in the network, [Puffert, 2003]. The relative importance of these factors n = number of nodes in the network, in creating lock-in varies, depending upon the architec- N = number of people involved in operat- ture of the system and the nature of the system’s opera- ing the system, tions. N(n, m) = static network with a set of nodes, n, For large-scale technical systems, these factors can and set of arcs, m, be grouped into the general concept of switching costs, O(C) = “order of” computational cost for C which are weighed—whether formally or informally— configurations, against the benefits of switching to new systems, prod- O(Z) = “order of” computational cost for Z ucts or operating procedures. Switching costs can be time periods, real dollars, or quantifiable costs associated with per- Pi = point design, i, performance of the sys- sonnel considerations, political implications, or the tem when in the ith configuration, time it takes to switch to a new technology or system r = discount rate, configuration. They are further associated with what S = start node, might be called switching risk [Dixit, 1992]. t = arc traversal time, Increasing the adaptability or flexibility of a system T = number of steps considered, demands lowering future switching costs before the Ti = time period i, ∆ environmental changes which demand a switch arise. T = time step, Suh and de Weck have used the concept of switching Z = end node. costs to find where to embed flexibility in automotive platforms [de Weck and Suh, 2006]. Beyond cost, 1. INTRODUCTION adaptability is complicated by uncertainty in the operating environment. More specifically, a large variance There is increasing recognition that adaptability between time-scales of environmental fluctuations and [Ashby, 1966] and more recently changeability [Fricke those associated with switching times and total system and Schulz, 2005] are critical to the long-term effective- life-cycle times greatly hampers operators’ ability to ness and, in relevant cases, profitability of complex react strategically to exogenous change.1 We argue that, technical products and systems. Many complex systems in order to avoid architectural lock-in and by extension exhibit high degrees of architectural lock-in. This allow operators to react strategically in the face of makes it difficult for these systems to adapt themselves environmental fluctuations, the causes of switching

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costs and risks must be mitigated during the design using standard methods from time-expanded network stage, with explicit and rigorous consideration of uncer- theory [see Jarvis and Ratliff, 1982]. Once formulated, tainty in the future acquisition and operating environ- designers can use the time-expanded decision network ments. to conduct scenario planning and iteratively design Much recent research has addressed the need to more evolvable complex systems. design for flexibility and methods to design for it. Real As noted, while the sources of architectural lock-in Options Analysis, for example, is a method of valuing are multidimensional, from an economic perspective it system flexibility by framing system design in terms of stems from high capital expenses (capex), associated stock-option theory.2 Similarly, the concepts of Spiral with switching to new systems or system configura- or Evolutionary Development emphasize the need for tions. Framed this way, the problem becomes fairly continual development and improvement of large sys- simple: Lock-in will occur if the cost of switching from tems rather than all-at-once development and operation. one system configuration to another exceeds the ex- At their core, these methods seek either ways of system- pected benefits, discounted at some rate and assuming atically and strategically identifying the benefit of vari- a level of risk [Simon, 1996].4 In order to design for ous kinds of flexibility and introducing it at the design adaptability (changeability), we must lower switching stage, or delaying critical design decisions until exoge- costs. This insight leads directly to two important ques- nous uncertainties are resolved. The differences be- tions: (1) How can we quantify switching costs and (2) tween adaptability in the systems themselves versus once quantified, how can we design systems to diminish adaptability in the system development process have the appropriate elements of switching costs in order to recently been clarified by Haberfellner and de Weck improve life-cycle adaptability? The TDN methodol- [2005]. ogy described in the next section (Section 2) addresses Building on these studies, we introduce a new meth- these questions explicitly. Section 3 discusses how the odology and associated modeling tools to design method scales with problem size, and Section 4 then “evolvable” complex systems. Given their size and applies the method to the specific example of launch long-life cycles, complex technical systems are best vehicle development and operations under demand un- characterized as operational organizations evolving in certainty. The paper concludes with a summary, limita- the face of exogenous uncertainty, able to take various tions, and recommendations for future work in Section development paths when confronted with environ- 5. mental change, rather than fixed sets of technical components.3 In a nod to information theory, the determinant of a system’s “evolvability” is a function 2. TIME-EXPANDED DECISION NETWORK of the number of possible states that it might take, rather (TDN) than the state it is in, with the crucial caveat that changing between states incurs some kind of switching The TDN methodology involves identifying and quan- cost and associated switching risk. tifying switching costs, creating an optimization model Time-Expanded Decision Networks (TDNs) are a based on the concept of a time-expanded network, and method to clearly and rigorously represent feasible running this model under probabilistic or manually paths and, to the extent possible, quantify the expected generated demand scenarios to identify optimal de- switching costs along those paths. These paths and costs signs. TDN is, in effect, a method to run “quantitative can then be represented on a directed network with scenario planning” for system design, in which system arc-costs representing cost-elements incurred during responses are encoded through a time-expanded net- system operation, and expanded through a life-cycle work. The crux lies in identifying how and where switching costs are incurred and how these can be 1We employ here a classic distinction between strategic and tactical decisions. For example, see Shapiro [1989: 127]: “We should distin- lowered in order to maximize adaptability and, perhaps guish between strategic decisions, which involve long-lasting com- more importantly, determining exactly how much one mitments, from tactical decisions, which are short-term responses to the current environment. In the language of game theory, the strategic 4The simplified problem is complicated by uncertainty in the operat- decisions determine the evolution of state variables that provide a ing environment, which reduces incentives to switch even if the setting in which current tactics are played out.” benefit is equal or slightly above the cost of switching. This is due to 2For a good overview of Real Options Theory, see Trigeorgis [1996]. the fact the environment could change again, making the switch 3This touches upon concepts from the theory of Complex Adaptive unnecessary, so there is a “benefit of waiting.” This phenomenon has Systems (CAS). For example, see Olson [2001]. Another comparison been called “sunk cost hysteresis” by economists and has been studied with CAS is through the concept of real options [see Baldwin and and modeled extensively [Dixit 1992]. The phenomenon is outside Clark, 2000]. These studies, however, were not used explicitly in the scope of this paper, but could be included into the methodology developing the method. later.

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Table I. High-Level System Cost Elements

to road networks, to launch vehicles, and their associated cost models have been created in the past.5 Once a set of conceptual designs has been created, the basic elements of life-cycle cost for each point design i can be estimated (see Table I). Nonrecurring costs include initial development, CDi, and the cost of a Figure 1. Flow diagram of the 5-step TDN methodology. switch, Csw. The latter is described in more detail below. CDi is often described as DDT&E (design, development, testing, and evaluation), and includes nonrecur- should be willing to spend to lower these switching ring engineering and facilities costs such as design, costs at the development stage. analysis, testing of subsystems, system integration, sys- The TDN methodology consists of the five steps tem tests, and construction of any support equipment shown in Figure 1. These steps are described in more and facilities [Wertz and Larson, 1999]. Fixed recurring detail below, using a generic example of designing a costs CFi, are those incurred at every time period regard- system with three potential instantiations (configura- less of demand and/or expected changes in the operat- tions A, B, and C) and are then implemented in the ing environment, including labor, facilities, and following section (Section 4) in the context of launch overhead. For large, complex systems, labor is usually vehicle design and operations. a major driver for fixed recurring cost. Variable recurring cost CVi, is a function of the demand during a given year or time period. It includes operating costs, produc- 2.1. Designing an Initial Set of Feasible tion materials, and variable labor costs, among other System Configurations elements. Models of variable recurring cost often take into account benefits of learning, which reduces the cost The first step involves creating a family or set of inde- per unit as a function of cumulative production levels. pendent or point designs, and an associated high-level Regardless of how these three traditional cost-ele- cost model for their individual development and opera- ments are modeled, they are generally used to estimate tion. Such a family can consist of a core system or life cycle cost C of a given design or system configu- product platform with options to expand, or it can LCi ration i, as a function of the number of periods T, and include wholly unrelated point designs. Creating appro- the demand in each period, Dj: priate point designs is itself a complex process including initial requirements definitions and trade-studies. T ( ) = + × + ( ) (1) Important early stage questions include how best to CLCi D, T CDi CFi T ∑ CVi Dj . frame requirements, what metrics should measure sys- j=1 tem performance, how can one incorporate appropriate levels modularity into the system, and to what level of Discounting (time value of money) can also be in- detail should initial design descend? cluded when estimating lifecycle costs which leads to However, the TDN methodology explicitly recog- T + ( ) nizes that requirements, demand, and metrics are all CFi CVi Dj C (D, T, r) = C + ∑ . (2) subject to change as the systems evolves. Using the LCi Di (1 + r) j j=1 initial designs as inputs, it determines the “evolvability” of a set of designs in the face of environmental change. In this formulation the initial DDT&E costs, CDi,, are TDN thus shifts the emphasis from point designs to a not discounted. A large discount rate r will tend to set of system configurations and identifies specific subsystems and interfaces for redesign. Therefore, for the 5While inputs to TDN can be taken as given for the current paper, the need to develop better methods to represent the design space such that current purposes, we take point designs as inputs, not- a good set of initial designs can be created is an important area for ing that myriad complex systems from nuclear reactors, further development.

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( ) = ( ) × ∆ ( ) + ∆ ( ) reduce the impact of future expenditures on the lifecy- CSW A, B, N cO N [ CD B, A CR A, B ]. (4) cle cost relative to the initial expenditures. For commer- cial systems that generate revenue, Eq. (2) can also As a whole, adequately quantifying switching costs include the revenues (with positive sign) and the costs is a difficult problem which merits further study. Recent already discussed (with negative sign) in which case Eq. work on formal change propagation analysis [Eckert, (2) expresses the net present value (NPV) of the system Clarkson, and Zanker, 2004] provides guidance in this or project. area. One realistic example of how to quantify switching costs is presented below, in the context of launch 2.2. Quantifying Switching Costs and system design (Section 4). Creating a Static Network

2.2.1. Switching Costs 2.2.2. The Static Network Once an initial set of system configurations has been Once switching costs between system configurations designed along with an estimate of the three traditional have been estimated, they can be placed in a matrix, cost-elements (DDT&E, fixed, variable) established for with original system configurations (“from”) on the each point design, we must now identify the cost of rows and new system configurations (“to”) as the col- switching between these system configurations. As umns. To take a generic example, imagine three possi- noted, switching costs are difficult to quantify because ble point designs for a given system: A, B, C. The cost they combine direct production costs as well as indirect of switching from each to each, CSW(A, B), is placed in organizational and political costs associated with learn- a matrix (Table II.). Numbers at each cell in the matrix ing and changing established operating procedures. For represent the nondiscounted cost of switching from the our current purposes we assume that switching costs ith row (configuration) to the jth column (configura- comprehend two principal elements: tion). It should be clear that these can only represent estimated switching costs, as the actual switching costs 1. Technical cost associated with altering and pro- may turn out to be different once a switch is actually ducing a new configuration and/or technology executed in the future. The matrix is not necessarily 2. A premium for organizational change. symmetric. The entries on the main diagonal are zero, The first element includes the cost of designing, indicating that there is no direct switching cost associated with remaining in the same system configuration. building, and testing the new system (∆CD) and the cost This matrix is formally equivalent to what is called of retiring the old system (∆CR). Thus, the technical cost of switching from configuration A to B is the incre- a weighted node-node adjacency matrix in network mental cost of developing B, potentially reusing ele- flow theory and graph theory more generally [Ford and ments of A, plus the cost of retiring those parts of A that Fulkerson, 1962; Ahuja, Magnanti, and Orlin, 1993]. are no longer used when transitioning to B: That is, the matrix of switching costs defines a network whose nodes are the point-designs (configurations) and ( ) = ∆ ( ) + ∆ ( ) whose directed arc weights are the switching costs CSW A, B CD B, A CR A, B . (3) according to Eq. (3) or (4). The resulting graph is One key assumption is that while A and B will not represented in Figure 2. operate concurrently, there can be commonality be- We call this representation a “static network.” It tween A and B. If A and B share common subsystems covers all possible switches between the three systems or are based on common platforms, CD and CR must be at any given point in time. Because all n nodes in the estimated using more detailed analysis of which sub- graph are connected to all nodes as well as to them- systems are re-used and which must be changed. The selves, as a rule the number of arcs in this static network 2 premium for organizational change, cO, is optional, but will be n . It is important to note that here the cost of can be a function of the number of people (N) involved not switching, that is, staying at the same node in the in designing and operating the technology: static network, is zero. This is denoted by the fact that

Table II. Generic Switching Cost Matrix for System Configurations A, B, and C

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Figure 2. Graph representation of the switching cost matrix between A, B, and C, representing a partial static network. an arc from a node back to itself is zero. This does not mean that the cost for keeping the system operating in that configuration is zero—there are still fixed and variable recurring costs, as described below.

2.2.3. Completing the Static Network To frame the system’s life-cycle as a dynamic network flow problem we must add costs associated with developing and operating the system in the first place [see Eqs. (1) and (2)]. Then we must add the element of time Figure 3. Complete static network representing switching and staying costs, as well as development costs. Development to each link. The costs associated with operating each is represented by the dotted line from source S to all initial system configuration (CD, CF, CV) on the static network nodes. Retirement is represented by the dotted lines to the sink above can be coded into the network as follows. Z. Let N represent the static switching network defined above (Fig. 2) consisting of a set of nodes (point designs) P0, P1, P2, ...., Pn and directed arcs associated information relevant to the life-cycle cost, as a function with switching costs, CSW(X, Y). Let Pij represent the of demand, encoded in the arcs. directional arc from node Pi to node Pj. Associate the self-loops (that is, all arcs from a node to itself Pii) with 2.3. Creating the Time Expanded Network the sum of fixed recurring and variable recurring cost The goal of the TDN is to capture the cost of operating elements for that configuration, i, during one time pe- and switching system configurations through time, ∆ riod T: seeking least-cost paths through the network as a function of changing operational requirements such as de- P = C + C (D ) (undiscounted). (5) ii Fi Vi j mand. The network above captures all possible development paths during a system’s life-cycle assum- Now create a source node S and a sink node Z and ing the set of configurations represented in the initial connect them both to all nodes with appropriate direc- static network, but it is not dynamic—that is, it does not tional arcs. Associate all arcs Psi flowing from the include the element of time. The introduction of time source to the point designs with the initial development into a directed network transforms it into a dynamic cost of design i, PDi. This represents the DDT&E cost network flow problem. The generic problem involves of the initially chosen configuration. Associate all arcs finding min or max-cost flows from a source S to a sink flowing from point designs i with the sink Piz with the Z, in a directed network with transversal costs c. Dy- cost = 0.6 The result is a static network (Fig. 3) with all namic network flow problems further associate each arc with two variables: traversal cost c and a traversal time 6 Making all sink arcs = 0 makes the assumption that there are no t. Often the reformulated objective is to find the maxi- retirement costs associated with the system at the end of its lifecycle. Retirement costs could be encoded into the network at these arcs as mum flow that can be sent through the network in time future work. T, where costs represent maximum capacity. A solution

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to the maximal dynamic network flow problem was first presented by Ford and Fulkerson [1962] and sub- sequently elaborated upon in a host of different practical applications, e.g., time-varying traffic flow modeling [Köhler, Langkau, and Skutella, 2002]. Dynamic network flow problems can be solved by reformulating the dynamic network into a time-expanded static network, and then solving a traditional max or min cost flow problem on the resulting static network [Ahuja, Magnanti, and Orlin, 1993]. A time expanded network splits the problem into T time peri- Figure 4. Initial Time-expanded Decision Network (TDN) ods, with each node in the original network duplicated with three configurations and three time periods. at every time period. Arcs connect the nodes depending on traversal period, and the new network contains only cost information for each arc. Methods to reformulate static networks into time- decision nodes, and thereby decoupling operating pe- expanded networks are well established [see Ford and riod’s costs from switching decisions. This is done by Fulkerson, 1962, pp. 146]. We first divide the life-cycle splitting each time period with chance nodes (circles) into T time periods and associate each arc with a tra- at the beginning, and decision nodes (squares) at the versal time t. For simplicity and generality, let us as- end. Fixed and recurring costs are incorporated into the sume here that each arc in the network (switching or sub-arcs following the chance nodes at the beginning of ∆ 7 staying) takes exactly one time period T to traverse. each time period (let us call them chance arcs). Switch- Each node in the static network is duplicated in each ing costs on the other hand are incorporated into the arcs time period, and arcs between these nodes are expanded following the decision nodes at the end of each time through the new network-based traversal times t. period (let us call them decision arcs). The chance arcs Figure 4 expands the static network created by hy- represent the costs of operating the system at a level of pothetical system configurations A, B, C, into a time- demand, Dj, in time period Tj. The resulting time-ex- expanded network over 3 time periods, T1, T2, T3. It is panded network is shown in Figure 5. assumed for simplicity that the traversal time associated Initially, coming out of the start node S-19, a system ∆ with each arc is exactly one time period, T. Flow starts configuration (A, B, or C) must be chosen which causes at the start node S and ends at the end node Z. Figure 4 capital expenditures for DDT&E. If A is chosen, this represents the development alternatives and costs over amounts to CD(A). At the beginning of time period T1, a life-cycle, given three system configurations A, B, C the demand that will have to be satisfied during this and our four elements of cost (C , C , C , C ); how- D F V SW period, D1, is revealed at chance node 1. This allows ever, one critical element is still missing: If a path calculation of the operating costs during that time pe- through the network includes a switching arc, the “op- riod (both fixed and variable). Towards the end of the erating arc” during that time period will have been time period we encounter decision node 2. We have to avoided. In other words, a min-cost flow through the decide whether to remain in configuration A (with no above network can selectively chose to avoid costs switching costs incurred), or whether to switch to con- associated with periods of high-demand by switching figuration B or C, with the respective switching costs before them. In reality, an existing system will continue being incurred at that time. This process repeats itself to operate to meet existing demand while a new system until the last time period T3 at which time the system is configuration is being developed. retired as indicated by transition to the end node, Z-20. We therefore introduce a final distinction, taking a The sequence in which the nodes are numbered is cue from decision theory, between chance nodes and important and will be discussed below.

7Changes to this assumption can easily be made based on specific modeling needs. Sometimes, for example, switching to a new system 2.4. Create Scenarios and Run will take multiple time periods. These kinds of issues can be ad- Optimization dressed in different ways by, for example, changing the length of each time period or changing the cost of switching to take account of the 2.4.1. Operational Scenarios: Modeling Demand fact that it is really spread of multiple time periods (years). For our It is now possible to introduce operational scenarios modeling purposes in Section 4, we assume that 1 time period is 5 calendar years, and that it corresponds to making major development over time, by changing the cost of traversing the chance decisions in context of the budget reviews in the U.S. government. arcs as a function of operational demand and time-vary-

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Figure 5. Refined Time-expanded Decision Network. Chance nodes are circles, decision nodes are squares. Nodes are numbered in topological order. ing requirements on the system by creating various Geometric Brownian Motion (GBM) and applying demand scenarios. Demand scenarios can be determi- multiple combinations of demand scenarios (Fig. 6) nistic, involving known levels of demand at each pe- [see Haberfellner and de Weck, 2005]. In all cases the riod, or they may be probabilistic, in which case demand scenarios are time-discretized, and the infor- multiple instances of the TDN have to be solved, one mation is injected in the appropriate chance nodes. for each uncertain scenario. An important point with respect to the TDN meth- A simple way to examine the space of demand odology is that the four cost elements can be calculated possibilities is to create a number of discrete demand using separate and standard cost models and then used profiles that are likely to occur over time (i.e., steadily as inputs to the time-expanded network. That is, the rising demand, constant demand, falling demand, and a total cost of operating in each time period can be limited combination of the three) and applying these to computed as a function of the demand scenario and the the network. Another way involves modeling using particular present state (configuration) of the system,

Figure 6. Geometric Brownian Motion (GBM) model of uncertain demand, ∆T = 1 month, D0 = 50,000, µ = 8% p.a., σ = 40% p.a.—three scenarios are shown, based on de Weck, de Neufville, and Chaize [2004].

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and then these costs can be used as the cost of traversing point designs, increasing and decreasing commonality, the chance arcs and decision arcs in each time period. to see exactly how this affects least-cost operating and development paths through the network. As will be 2.4.2. Optimization: Finding the Shortest Paths illustrated in the example below (Section 4), this infor- The ultimate goal of the TDN methodology is to create mation can be used to exploit high-leverage switches a simulation of future states of the system to find the that in turn open vast new operating spaces that would set, or sets, of design configurations that minimize life never have been exploited had switching options not cycle cost (or maximize NPV) under various demand been considered and incorporated into previous de- scenarios. By extension, we want to identify exactly signs. where lowering switching costs may maximize adapt- The TDN method can be incorporating into a com- ability. The set may, or may not include more than one puter program that enables systems designers to frame point design, depending on the relevant ratios of the the problem of “design for evolvability” more rigor- four cost elements (CD, CF, CV, CSW) and the demand ously, to automate aspects of the analysis process, and at each time period. In other words, this may or may not to identify relationships between designs and the envi- involve switching from one design to another during the ronment that would be very difficult for humans dis- lifecycle. cover. This does not mean, however, that it automates Once the costs of operation are coded into the chance decision-making. The system designer’s knowledge is arcs of the time-expanded network, finding least-cost crucial and is primarily required in creating and select- paths involves implementing standard network optimi- ing interesting feasible system configurations, model- zation algorithms. If no loops exist in the network, as ing the four main elements of cost as well as in in Figure 5, nodes can be ordered topologically—that capturing the uncertain scenarios. A software program is, ordered in terms of how far they are from the source. based on this method should therefore be considered an When this is the case, a simple reaching algorithm can iterative design tool which frees system engineers to be used to find the shortest path. The so-called reaching creatively develop more evolvable (and thus profitable) algorithm [Ahuja, Magnanti, and Orlin, 1993, systems. Lauschke 2006] can solve the shortest path problem (i.e., the problem of finding the graph geodesic between 3. SCALING THE METHOD two given nodes) on an m-edge graph in m steps for an acyclic graph. The reaching algorithm is used in this An important question here arises: what is the compu- paper. For each operational scenario a different acyclic tational cost of conducting such quantitative scenario path through the TDN may be optimal. Even though one planning and how does it scale with number of configu- may chose to cycle between configurations, the graph rations and number of time periods? This section ad- will still be acyclic due to time expansion as discussed dresses this question. above. We are interested in identifying those configu- Of the five steps described above (Fig. 1), the first rations A, B, C, … that are most often chosen as initial two are conducted manually. That is, configurations and switching costs are inputs to a TDN program. The configurations and those switches i → j that are selected program then creates the static network at a computa- most often to switch among these configurations during tional cost, O(C2), where C is the number of configura- the lifecycle. tions. The next three steps involve creating the time-expanded network, applying demand scenarios to 2.5. Modifying System Configurations: the time-expanded network, and finding shortest paths Iterative Design for each scenario. Once formulated, the time-expanded decision network Creating the time expanded network is generally model is a powerful tool to help formulate and refine negligible from a computational (processing time) per- initial point designs as well as identify opportunities for spective—it involves creating a matrix with appropriate commonality and real options [Trigeorgis, 1996] numbering and enough spaces to account for every node among these configurations. A real option can be N in the network. Given T time periods and C system framed simply as a feature embedded “in” or “on” an configurations, the TDN will have the following num- initial design configuration to lower future switching ber of nodes, including the dummy start and end nodes: costs. The TDN can be used in many different ways to N = 2 × C × T + 2. (6) creatively identify point designs, and interfaces that may lower future operating costs. By combining myriad The factor of 2 comes from having split each node demand scenarios and network optimization algo- in Fig. 4 into a chance node and a decision node (see rithms, designers can selectively tweak elements of Fig. 5). Memory issues can potentially arise when there

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are many system configurations (C > 1000) and many Therefore, the computational cost of the TDN time periods (T > 1000). Generally, however, TDN is method, when implemented in conjunction with the intended for analyzing a limited number of configura- reaching algorithm, scales quadratically with the num- tions, C~O(10–100), for a few major time periods or ber of configurations C and linearly with the number of stages, T~O(10–20) from a strategic perspective, and in time periods T and scenarios S. The complexity of the this regime TDN performs reasonably well. method is The real computational costs are incurred during the 2 O(SC T). (11) process of iteratively applying scenarios and finding shortest paths. The two steps which contribute to the This appears to represent a significant improvement computational cost here are the computation of chance- over traditional multistage decision trees which are arc costs (operating costs) as a function of demand known to branch exponentially—similar to Eq. (7)—as scenario, and the running of the shortest path algorithm. a function of the number of decision states and decision Operating costs are calculated as a function of demand, stages. A more detailed comparison of the complexity Dj, in each time period and associated with chance-arcs of TDN with traditional decision trees is left for future on the time-expanded network (Fig. 5). Given T time work. periods and C system configurations, this is simply the × number of chance arcs, or C T calculations per sce- 4. APPLICATION OF TDN TO THE DESIGN nario. OF HEAVY LIFT LAUNCH VEHICLES The time expanded network defined above is acyclic, meaning that it contains no cycles. It is therefore The TDN method described above has been pro- possible to implement the reaching algorithm, to find grammed as a functional software tool8 and applied to shortest paths efficiently [Ahuja, Magnanti, and Orlin, the problem of designing an “evolvable” Heavy Lift 1993]. This is significant, since the number of all pos- Launch Vehicle (HLLV) system for NASA’s Vision for sible paths through the time expanded network is Space Exploration (VSE). This vision calls for the return of human explorers to the surface of the Moon # paths = CT. (7) by 2020, followed by crewed Mars missions. There is substantial uncertainty surrounding the number and Thus, the number of paths increases exponentially with timing of future missions, primarily due to budgetary the number of time periods if we were to attempt an fluctuations. exhaustive search of all paths. Like most large, complex systems, launch vehicle The reaching algorithm, on the other hand, finds a architectures and space system architectures generally shortest path in O(M) time, where M is the number of suffer from architectural lock-in [Shishko, 2001; Silver, arcs in the network. It has been proven that no other 2005b]. To apply the TDN method to this problem, four algorithm can have better complexity because any other different initial vehicle configurations were created— algorithm would have to at least examine every edge, one clean sheet design, one based on Evolved Expend- which would itself take M steps [Ahuja, Magnanti, and able Launch Vehicles (EELVs), and two based on Orlin, 1993]. In our case, Shuttle-Derived Vehicle (SDV) alternatives—and re- lated cost elements and switching costs were computed. M = (T − 1) × C2 + C × (T + 2), (8) The methodology was run using 10 plausible scenarios where the first term accounts for the switching arcs for Lunar and Mars exploration campaigns, and total (decision arcs) assuming that we can switch from any life-cycle costs were calculated. Initial results demon- configuration to any other configuration at any time strated preferred vehicle configurations, and iterative period, and the second term accounts for the chance arcs methods quantified the value of lowering switching as well as the initial development and final retirement costs under a uniform scenario probability distribution. arcs. Within each scenario, then, total complexity cost is 4.1. Step 1: Initial System Configurations O(Z), where The model was implemented using four point designs (Fig. 7) of interest to NASA during the heavy lift launch = ( − ) × 2 + × ( + ) + × (9) Z T 1 C C T 2 C T decision in support of the 2005 Exploration Systems For consideration of complexity, this reduces to Eq. Architecture Study. The four launch vehicle configura- (10) for each of S scenarios: tions considered are as follows: O(Z) = C2T + CT + C. (10) 8Using the Matlab V7.1/Simulink technical computing environment.

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4. P4 = D: Clean Sheet (CS) Heavy Lift Vehicle; Performance: 105 mt to low earth orbit. An N2 diagram showing the components of the launch vehicle models and implementation of the TDN method is shown in Figure 8. The N2 diagram references steps 1–5 shown in Figure 1. After performance and risk were estimated for each configuration, the first step of the TDN process involved estimating initial development costs for all four vehicles as well as fixed and recurring operating costs as a function of demand (“traffic model”). This was initially done by NASA and supplemented by the authors using traditional cost-estimating tools. For Figure 7. Four launch vehicle point designs used in the TDN more information on this process and the underlying application. From left to right: Shuttle Derived A (1); Shuttle assumptions, see Silver [2005a]. Derived B (2); EELV derived C (3); Clean Sheet design D (4). 4.2. Step 2: Calculating Switching Costs and Creating the Static Network 1. P1 = A: Shuttle Derived (SDV-A) Inline Heavy The next step involved calculating switching costs be- Lift; 3 Space Shuttle Main Engines; 2 four-seg- tween the vehicle configurations shown in Figure 7. As ment solid rocket boosters; Performance: 80 met- noted above, this depends crucially on the amount of ric tons to low earth orbit commonality between the systems and any real options 2. P2 = B: Shuttle Derived (SDV-B) Inline Heavy (reserved interfaces, extra margins, etc.) embedded in Lift; 3 Space Shuttle Main Engines; 4 four-seg- them. Systems can share subsystems at different levels. ment solid rocket boosters; Performance: 115 For example, Shuttle-derived vehicles and EELV de- metric tons to low earth orbit rived vehicles might be designed to use common large- 3. P3 = C: Evolved Expendable Launch Vehicle scale subsystems such as launch pads, with minor (EELV) derived rocket; Delta V core; 2 Zenith alterations. At a deeper level in the system decomposi- boosters; Performance: 62 metric tons to low tion, two shuttle derived vehicles might share almost all earth orbit first order subsystems—launch pads, manufacturing

Figure 8. N2 diagram of TDN implementation for the launch vehicle design problem.

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Figure 9. Estimating switching cost by decomposing subsystems between SDV configurations ($M).

facilities, rocket boosters, main engines—with altera- versus vertically stacked). These elements are not mu- tions only to specific second-order subsystems—i.e., tually exclusive and therefore the switching costs be- the external fuel tank. To calculate switching costs, tween each system must take into account what is then, we must break the system into its constituent already built and what has yet to be built. subsystems to identify commonality at the appropriate In the TDN path optimization, the resulting switch- level. ing costs between systems 1, 2, 3, and 4 (shown in Fig. To take one example of how point designs can in- 7) are needed. These are presented in Table III (in units volve commonality at a level deeper than the major of millions of dollars). subsystem level, imagine four shuttle-derived point designs (Fig. 9): a side-mount configuration with 4-seg- 4.3. Step 3: Create Time-Expanded ment solid rock boosters (SRBs); a side mount Network and Demand Scenarios configuration with 5-segment SRBs; an inline vehicle Once the four cost elements were determined, we cre- with 4-segment SRBs; and an inline launch vehicle with ated the time expanded decision network (Fig. 10). In 5-segment SRBs. Each of these system configuration this case we had four system configurations and divided pairs has commonality in a different way—some share the time horizon into four periods. Each time period was the same solid rocket boosters, others the layout of assumed to represent 5 years, so the total life-cycle is cargo to external tank. Calculating switching costs be- 20 years. This TDN has CT = 256 possible scenario-in- tween these systems demands examining how their dependent paths [Eq. (7)] and by plugging C = 4 and T common elements affect subsystem design. = 4 into Eq. (8), we obtain M = 72 arcs, some of which Figure 9 demonstrates how this can be done by are shown in Figure 10. decomposing major subsystems and examining how Next the demand scenarios were created. As noted, they affect subsystem design, in this case the subsystem modeling demand is complex and can be carried out in is the “facilities,” and the components are specific numerous ways depending on the application. For this buildings or parts of these buildings. As the highlights application, demand for the launch vehicles takes the demonstrate, different facilities must be altered depend- form of tons of payload needed to be shipped to low- ing on whether additional SRBs are added, or if the earth orbit (IMLEO) per time period9 and how many layout of the external tanks is modified (side mounted launches this would necessitate. NASA is principally

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Table III. Switching Costs ($M) between Four scenario. Two vehicle configurations (1 and 3) were Selected Launch Vehicle Configurations used, and no switches were employed. Figure 11 illustrates the two shortest paths, and Figure 12 shows the total life-cycle cost predicted for each scenario. Sce- nario 6 resulted in the highest total life cycle cost, because it contained the highest number of both Moon and Mars missions.

4.5. Step 5: Iterative Design The results demonstrate that two vehicles, namely con- concerned with returning to the Moon and possibly figuration 1 (SDV-A) and 3 (EELV-derived), respec- sending crewed missions to Mars; therefore, we had to tively, were optimal under different operating regimes. translate variations in kind and timing of Lunar and This raises the question: Would it be worthwhile to Mars missions to launch-vehicle demand [see Silver decrease the switching costs between these two vehicles 2005a]. Next, we created ten scenarios based on how and, if so, how much should we be willing to pay to do many Lunar and Mars missions might be launched this? This question can be easily answered using TDN. during each time period and translated this to different Specifically, we can systematically lower the switching numbers of launches for each vehicle and, by extension, costs between two vehicles in order to determine (a) at different patterns of operations costs along the chance what switching cost level switching between the con- arcs in the time-expanded network (Fig. 10). The 10 figurations would start to occur under each demand future demand scenarios are shown in Table IV. The scenario and (b) what the savings would be, if any, in underlying assumption of these scenarios is that the terms of total life-cycle cost. Moon will serve as a stepping stone to Mars. We carried out this numerical experiment, systematically lowered the cost of switching from the EELV- 4.4. Step 4: Path Optimization derived vehicle, configuration 3, to the shuttle-derived SRB vehicle, configuration 1, from $4 billion to $1 Once the demand scenarios we created and the resulting billion, in steps of $1 billion. The results are summa- operations costs coded into the network we ran the rized in Figure 13. network optimization (reaching) algorithm under each The results demonstrate that if the switching cost is scenario. The result was ten different shortest paths set to $4 billion, one switch is made in scenario 8 after through the life-cycle, as a function of each demand two time periods—this is a scenario where we encoun-

Figure 10. The time expanded decision network (TDN) for the launch vehicle case.

9Based on preliminary architectures, we estimated that a lunar mission required approximately 130 metric tons to lunar orbit, while a Mars mission requires on the order of 600 metric tons to be delivered to Low Earth orbit. Uncertainty in these numbers can be introduced by varying both the frequency of demand (number of missions) and the level of demand (mass of each mission). In our model we varied only frequency.

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Table IV. Ten Demand Scenarios for Future Launch Vehicle Usage across Four Time Periodsa

aThe total number of lunar missions (requiring 130 metric tons to LEO) is in light gray, the number of Mars missions (requiring 600 metric tons in LEO) is in dark gray.

Figure 11. Two resulting shortest paths through the life-cycle: vehicles 1 and 3 are chosen.

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Figure 12. Total life cycle costs ($ billion) for all ten scenarios. ter few lunar missions initially and many Mars missions 4.6. Calculating the Benefit later. As the switching cost is lowered further, switches What would be the benefit of lowering switching costs also occur in other scenarios (see Fig. 13). in this way? The answer depends on the exact scenario

Figure 13. Switches as a function of switching cost level between $1 billion and $4 billion.

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occurs, but that there are also LCC savings on average across all scenarios. Figure 15 makes this even more apparent. It shows the exact amount saved as switching costs are lowered between the two most-used vehicles (3 and 1). If we think all scenarios are equally likely, we can save up to $600 million on average by lowering the switching costs to $1 billion dollars. If we think that scenario 8 will probably occur, we can save as much as $2.8 billion by lowering the switching cost between configurations 3 and 1 to $1 billion. This therefore tells us specifically how much we should be willing to pay to lower the switching costs to those desired numbers. Switching costs can be lowered by embedding provisions in con- Figure 14. Total life cycle cost (LCC) as a function of figuration 3 that will make it easier to switch (make switching cost between EELV (3) and SDV vehicle (1). The changes) to configuration 1 at a later time. There are a lighter bars show average LCC across all 10 scenarios; the number of ways to accomplish this such as stand- darker bars show the LCC for scenario 8 specifically. ardization, extra margins, inclusion of interfaces for future expansion. This is an appropriate place to apply the principles of changeability enumerated by Fricke that ends up occurring in the future. The simulations and Schulz [2005]. demonstrated that if scenario 8 occurs, a switch be- The benefit obtained from lowering switching costs tween the vehicles occurs even at a relatively high in a way is the maximum price we would be willing to switching cost. In this case the savings of lowering pay on a real option that allows (but doesn’t require) switching costs between these vehicles would be high. switching from configuration 3 (EELV) to 1 (SDV) at Another way to present this, however, is to determine a later date. If it is cheaper to lower the switching costs how much is saved in terms of expected-cost if each than not to switch and incur future costs due to opera- scenario is equally likely. We created ten scenarios tional inefficiency, then the switching costs should be (Table IV), so each scenario would have a 10% chance lowered. If this is not the case, then it makes more sense of occurring. to keep the switching costs where they are in the initial Figure 14 illustrates the total life-cycle cost as a configuration and accept some amount of lock-in. Two function of the switching cost between the vehicles, final points should be noted. First, we can weight sce- both for scenario 8 in particular and for the case where narios as we please rather than resorting to averages. every scenario is equally likely. SC_Normal is thIe Second, lowering the switching cost might change the original case (with switching costs shown in Table III), performance characteristics of the system, and there- so it should be used as the baseline. The results demon- fore change the life-cycle costs. This should be taken strate that indeed, savings are greatest if scenario 8 into account during iterative design.

Figure 15. Total LCC savings as a function of switching cost: average for equally weighted 10 scenarios versus savings for scenario 8 alone.

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5. NOTES ON MODEL FORMULATION complete information about the future for each scenario. In an unfolding lifecycle scenario deci- The generic TDN modeling framework described in sion-makers will have to make the decision this paper can be implemented in different ways based whether to stay or switch based on incomplete on specific modeling demands, and applied to a variety information. TDN can be used to study the effec- of systems and industries. This section reviews some tiveness of various decision rules by comparing modeling issues raised in this paper including areas for them to the shortest path baseline. future work: • Transition Rules: As discussed above, at each transition point between time periods (stages) • Complete Information: Classic shortest path alone has to decide whether to remain in the current gorithms assume perfect information about fu- state or transition to one of the (C – 1) other states. ture operating costs. In reality operators do not This gives rise to the C2 switching arcs between know what operating scenarios will exist in the time periods and the CT total paths. One may future. This “limit to rationality” can be ac- reduce the number of paths a priori by introduc- counted for by revising the shortest path algo- ing so-called transition rules, which prohibit cer- rithm to limit the number of future time periods tain switches from occurring. This concept was considered at each point in time. However, while implemented in de Weck, de Neufville, and academically interesting, this may not be practi- Chaize [2004], where the staged deployment of cally useful. The goal for the model is to increase satellite constellations was optimized under de- system flexibility and enable practitioners to mand uncertainty. Instead of allowing switches change their behavior, not to model an operating between all 600 configurations, the number of environment per se. Designing systems that allowable paths was reduced by (i) forming 15 evolve optimally demands realism in potential families of 40 configurations each that shared operating scenarios and carefully considered common subsystems and only allowing switches probabilities of occurrence to identify and design within each family and (ii) by only allowing optimal switches, not necessarily realism in op- switches that would grow the system in terms of erator judgment. capacity. • Number of Time Periods: We can split the life-cy- • Operational Flexibility: When actual demand Dj cle into an arbitrary number of time units with is revealed at a chance node at the beginning of each time unit representing an arbitrary amount time period j, the fixed and variable cost at this of real-world time. Note, however, that the num- time period may not automatically be determined ber of potential paths increases exponentially according to Eq. (5). If capacity exceeds demand, with the number of time periods, T. This is miti- one may deliberately choose to shut down part of gated by the fact that the shortest path algorithm the system during period j, in order to temporarily scales linearly with the number of time periods. reduce fixed costs. When this is possible, we • Time to switch: Switching time can be modeled could potentially extend the TDN method to take in ways similar to classic “project cost curve” into account operational flexibility while being in problems. In these it is generally assumed that a the ith system configuration, not just switching project is an ordered set of jobs. Each job has an flexibility between configurations i and j. Con- associated normal completion time and a crash current consideration of operational and design completion time, and the cost of doing the job (in flexibility is left for future work. our case, making the switch) varies linearly be- • Impact on Design Cost: When lowering the tween these two times. Project cost curves have a switching costs from $4 billion to $1 billion in long history [Ford and Fulkerson, 1962: 151]. Section 4.5, we did not explicitly say how this • Mixed Strategies: We may want to operate more would be accomplished. Generally, lowering than one kind of a system configuration at the switching costs will require an increase in upfront same time. This can be done by sending more design cost. This relationship between switching than one unit of flow through the network. This cost and upfront development cost would be a is an area for future study. fruitful area of future research. In an extreme case • Decision Rules: There are a number of ways in we may decide to design a system that has zero which TDN can be used to study the effect of a switching costs to reversibly achieve any of the C variety of decision rules on lifecycle cost or NPV. system configurations under consideration. Such Specifically, the path chosen by the reaching al- systems are referred to as reconfigurable systems gorithm will always be optimal, since it assumes [Siddiqi, de Weck, and Iagnemma, 2006], since

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they can switch between configurations at no or volve networked structures providing services to very low cost. The ability to be reconfigurable, diverse populations over long life-cycles. These however, is often associated with significantly structures exhibit significant lock-in, with serious increased system complexity (more actuators, consequences if the nature and amount of demand sensors, etc.) and upfront effort. Given an explicit cannot be met. TDN can help design responses to relationship between switching costs and upfront critical scenarios and develop networks with bet- development effort, TDN could be used to find ter evolved reaction to match demand shifts. the optimal degree of system flexibility that bal- • Airline Expansion Decisions: Airlines create net- ances upfront expenditures with ease of down- works of transportation which are shaped by, but stream switching. can also shape, patterns of demand and operation. Decisions about both network structure and vehicle fleet selection are interdependent, and create 6. APPLICATIONS significant path dependence for airlines [Taylor and de Weck, 2007]. TDN can help create a mix TDN is a generic modeling methodology that can be of fleet selection, routing, and maintenance strat- applied to a host of system-design problems. In the vein egy, which allows for appropriate flexibility in of “real options thinking,” we can distinguish between the face of changing demand. designing for evolvability at the subsystem level or at • Factory Design Under Uncertainty: Companies the system (architectural) level. In the former case, the in multiple industries face the problem of capac- each design can be considered an instantiation of one ity planning under uncertainty. Once built, facto- system with modified subsystems, and the switching ries create a specific fixed and variable cost costs will involve the cost of changing those subsys- structure in the face of shifting demand, with tems. By contrast, the example of designing launch vehicles presented above involved more radical con- significant impact on a company’s bottom line. figuration changes at the level of the entire system Often, factors in the environment that indicated architecture. that a given factory in a given location would be More specifically, we envision that TDN could be favorable change rapidly, leaving companies with applied to the following kinds of systems: the decision to operate at lower margins or write off the sunken investment. TDN can be used to design both the factories themselves, and select • Complex Electromechanical Products: Systems factory locations, in a way that allows for greater in this category, from microchips to automobiles, flexibility and profitability over the life-cycle. must resolve a host of often conflicting design • Strategic Contracting Decisions: Design and ac- requirements in catering to one of many potential quisition decisions also depend on a host of con- target markets. Concepts developed to address these issues such as flexible platforming and ad- tracts and legal constraints among developers, aptation to dynamic market segments can be han- acquires, and operators. Whether for system de- dled more rigorously with the TDN methodology. sign, or even in purely business matters, contracts are designed to create lock-in using the legal • Real-Estate and Building Architecture: Tradi- tional building architecture used to define the system, in order to change the incentive structures “program” for a building as driven by its initial (cost of switching) among contracting parties use. This is true for residential construction but [Joskow, 1985]. Contracting decisions that affect also for many public buildings (museums, librar- the evolution of a system, or a business process, ies, etc.) and office buildings. Increasingly, how- can be made more rigorous by explicitly incorpo- ever, there is a realization that building use rating the costs of switching (even if the latter are changes over time and that—in order to reduce purely legal costs). The TDN methodology can future remodeling costs—buildings can be delib- thus be applied in the area of pure business strat- erately designed to be evolvable over time. An egy and contracting. example of this was provided by Kalligeros and de Weck [2004], where BPs new North Sea Ex- 7. CONCLUSIONS ploration Headquarters in Aberdeen, Scotland, was designed in a modular fashion. TDN represents an advance over similar methods to • Infrastructure Projects and Strategic Planning: design and analyze system flexibility. Many large-scale infrastructure projects, from First, it is formulated to enable designers to explic- electricity grids to water and gas pipelines, in- itly address the problem of high switching costs, a

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Systems Engineering DOI 10.1002/sys 186 SILVER AND DE WECK

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Matthew R. Silver is a doctoral student in the Engineering Systems Division at the Massachusetts Institute of Technology. He has a background in basic physical research, systems analysis and design, and management and is currently affiliated with the Strategic Engineering group at the Massachusetts Institute of Technology. Mr. Silver has been a research scientist at the MIT Space Systems Lab for 3 years, where he focused on the analysis and design of complex system architectures, and consulted on technology strategy and transfer for companies such as Payload Systems Inc. Prior to this he worked as a systems engineer at the Canadian Space Agency, where he developed and tested advanced concepts for space exploration. Matt has two masters’ degrees in Aerospace Engineering and Technology and Policy from the Massachusetts Institute of Technology and a bachelor’s degree with double major in Astrophysics and Art History from Williams College.

Olivier L. de Weck is currently an Associate Professor with a dual appointment between the Department of Aeronautics and Astronautics and the Engineering Systems Division (ESD) at MIT. His research interests are in Systems Engineering, Multidisciplinary Design Optimization and Space Systems. In 2001 he obtained a Ph.D. in Aerospace Systems from MIT. From 1987 to 1993 he attended the Swiss Federal Institute of Technology (ETH Zurich) in Switzerland, where he earned a Diplom Ingenieur degree (M.S. equivalent) in industrial engineering. From 1993 to 1997 he served as liaison engineer and later as engineering program manager for the Swiss F/A-18 program at McDonnell Douglas (now Boeing) in St. Louis, MO. He served as the General Chair for the 2nd AIAA Multidisciplinary Design Optimization (MDO) Specialist Conference in 2006 and obtained two best paper awards at the 2004 INCOSE Systems Engineering Conference. His research focus is on Strategic Engineering of complex systems.

Systems Engineering DOI 10.1002/sys