Bubble Planning and the Mathematics of Consortia Jonathan Bard University of Texas at Austin, USA
Boaz Golany Technion, Haifa, ISRAEL
Fred Phillips* Management in Science and Technology Dept. Oregon Graduate Institute of Science & Technology Mailing: P.O. Box 91000 Portland, Oregon 97291-1000 USA Shipping: 20000 N.W. Walker Rd., Beaverton, Oregon 97006 USA Phone 503/690-1335 FAX 503/690-1268 Internet:
[email protected] World Wide Web http://www.ogi.edu
October, 1998 for Third International Conference On Technology Policy and Innovation Austin, Texas, September, 1999
Abstract The paper formalizes the simple idea of “bubble planning” in order to develop it as a key tool for designing consortia. Following some definitions and examples of consortia and their purposes, optimization models are set forth for the purposes of selecting consortium members and budgeting the consortium in a way that satisfies all members. A final optimization model addresses the special problems of overhead costs in university-based consortia. The results, which include a numerical illustration from Oregon Graduate Institute’s Center for Entrepreneurial Growth, are especially applicable to cross-sectoral consortia. We remark also on the applicability of these ideas to cross-functional teams within a single organization. KEY WORDS:
CONSORTIA; ALLIANCES; BUDGETING; PUBLIC-PRIVATE PARTNERSHIPS; TEAMS.
* corresponding author
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Bubble Planning and the Mathematics of Consortia Jonathan Bard, Boaz Golany, and Fred Phillips
Introduction The paper begins by briefly formalizing the simple idea of “bubble planning” in order to develop it as a key tool for designing consortia. Following some definitions and examples of consortia and their purposes, optimization models are set forth for the purposes of selecting consortium members and budgeting the consortium in a way that satisfies all members. A final optimization model addresses the special problems of overhead costs in university-based consortia. The results, which include a numerical illustration from Oregon Graduate Institute’s Center for Entrepreneurial Growth, are especially applicable to crosssectoral consortia. We remark also on the applicability of these ideas to cross-functional teams within a single organization.
Bubble Planning A bubble plan1 depicts the constituencies, suppliers, partners, and other entities comprising the business environment of an organization. A bubbles-within-bubbles picture (see Figure 1) shows the natural groupings of these entities. It is a “plan” in the sense of a map, not in the sense of a sequence of future actions, though it is used to generate action plans. It is an obvious and straightforward picture of an organization’s multiple stakeholders and potential stakeholders. From the point of view of this paper, a bubble plan is useful for an organization that engages in many consortial projects. Such an organization will use the bubble plan to choose, from its list of stakeholders and potential stakeholders, a subset that is best suited to participate in a given consortium.
Purpose and Organization of Consortia We characterize a consortium as a special-purpose alliance of different organizations. • The member organizations may be competitors. • There are generally more than two members. Bubble planning, a tradition at the IC2 Institute of the University of Texas at Austin, has been promulgated by the Institute’s founding director, George Kozmetsky. An early published example of bubble planning is in Phillips (1978), the first IC2 research monograph. At Kozmetsky’s urging, this publication contained a matrix representation of the flows of resources and interests among the participants in an international, public-private arrangement for the financing and distribution of energy. 1
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• The totality of what the members bring to and take from the consortium is multidimensional, i.e. more than just the exchange of goods for money. Items of exchange may include knowledge, access to markets, entre to political circles, conference facilities, staff resources, etc. (See Table 1.) • The member organizations may cross traditional sectoral (government, industry, university, press) lines, and indeed the consortium may be necessary because the task at hand arises from recent changes in the business/social/political environment and cannot be dealt with by a single sector. • The consortium is expected to last for a period probably measured in years, and thus depends on good relationships among members, favorable public opinion, and/or favorable political climate.
Table 1. Possible “Items of Exchange” in a Consortium knowledge conference facilities equipment prestige/name recognition
access to markets staff resources lab space favorable location
entre to political circles graduate students customers/qualified leads investment capital
Well-known examples of industrial consortia are CAM-I, the non-profit computeraided manufacturing consortium; MCC, the for-profit, private microelectronics R&D consortium (Gibson and Rogers, 1994); and SEMATECH, the government-supported semiconductor manufacturing consortium (Young, 1994). Public-private consortia include HUD’s enterprise zones, and NIST’s Advanced Technology Program (ATP) support for high-cost, high-risk technology development by groups of industrial companies. Universities become participants in, or instigators of, consortia as exemplified by the IC2 Institute’s JIMT program at the University of Texas at Austin, the University of Texas-NASA Technology Commercialization Centers, and Oregon Graduate Institute’s Center for Entrepreneurial Growth. In each of the cases just cited, the consortium represented an innovative organizational response to changing business and technological conditions. There are many other reasons for organizations, even competing organizations, to ally. These are explained admirably in Lynch (1993), and we will not go into further detail about them here.
Selecting Consortium Participants A well-networked consortium designer will have a good sense of the pressing business needs of all stakeholders in his/her bubble plan, and also an idea of the surplus resources and special expertise of each stakeholder. The business needs, resources and areas of expertise are the “items of exchange” listed in Table 1 (which of course is not exhaustive). The designer’s organization has a mission and needs of its own, which are the impetus for the launch of a consortium. The designer believes that his/her organization’s needs can be 3
provided by a combination of the entities in the bubble chart.
The first part of the design task, then, is to identify a subset of these entities (stakeholders) that (i) can provide, collectively, what the designer’s organization needs; and (ii) are motivated to do so, by reason of having their own needs satisfied in exchange. (The 4
obvious additional requirement, that it be done in a way that leads to a financially viable consortium, is dealt with in the next section of the paper.) This first part of the design task, expressed as a mathematical optimization, leads to a modified set covering problem. This optimization identifies a possible exchange economy2, without quantifying the amounts of the exchange items that will change hands. To establish notation, call each potential consortium member a “node.” The index (node) o represents the consortium. As it is the needs of the designer’s organization that spurs the formation of the consortium, then the node o also represents the designer’s organization. “Resources” are items of exchange, exemplified by the list in Table 1. Let xj = 1 if node j is to be included in the consortium; otherwise xj = 0. The xj are to be determined by the optimization. Input data are: aij = 1 if node j has resource i; 0 otherwise. bij = 1 if node j requires resource i; 0 otherwise. wj = difficulty, distance, or communication “cost” of including node j in the consortium. wj might represent how receptive to a proposal node j is perceived to be, the weight of favors to be called in in order to recruit node j, or any other measure of difficulty. All wj will be set equal to one unless there is notable a priori ease or difficulty in recruiting a particular node j. To select consortium members, minimize
Σj wjxj
subject to
Σj aijxj > bio
and
Σj∈k Σi bikaijxj > 1 for every k xj = 0 or 1 for every j.
Note that this optimization allows for exchanges that are not directly between recruited members and the original organization. For example, node 1 might have something that node 2 needs while node 2 has an item node o needs and node o can fulfill a need of node 1. Figure 2 shows the results of this process for the Center for Entrepreneurial Growth at Oregon Graduate Institute of Science and Technology. The formal optimization just adduced was implicit in the Center’s design; however, the Center was designed heuristically before the mathematical model was devised.
2
Some of these ideas were foreshadowed in Charnes and Cooper (1974), and also, in an empirical study of a
single-sector (multiple government agencies) problem, in Danziger (1978). 5
Setting Objectives and Budgeting the Consortium Organizations are motivated to join the consortium, which from their point of view is a new and unfamiliar way of doing business, by anticipating a greater-than-ordinary return on their investment. For this reason, the consortium designer must set objectives that provide the required return. The designer must be familiar with potential members’ business models, and be in a position to set an objective that each member j will receive a multiple nj of its usual return on its several kinds of resource investments. Experience indicates that nj should be between two and ten. For example, suppose a candidate member needs exposure to potential customers and to new technologies. This same candidate has a high-profile chief executive and a corporate jet that makes frequent trips to Washington, D.C. The consortium plans to hold conferences and deal with funding agencies in Washington. Based on an estimate that the company usually gains ten qualified leads to customers and technology suppliers each time the CEO gives a speech or each time he/she flies to Washington, the consortium must be able to offer 20-100 qualified leads each time the company’s CEO speaks at a consortium event or allows a consortium staffer to occupy an seat on the company’s airplane. We move toward a finished consortium budget by distinguishing resources (“items of exchange”), goals, programs, and budget lines (expenditure categories). A three-stage process of allocations and optimizations leads to the final budget. 1. Set goals for the consortium. Each member j will contribute cij units of resource i to the consortium. The designer intends for each unit of resource i coming from member j to be transformed into resource k at a rate specified by an “objectives” matrix Rjik. This matrix has nonzero elements only where member j has resource i and other members need resource k. The quantities nj are implicit in the Rjik matrix, although the latter matrix is not a one-toone transformation of input resources into output resources. Rather, the R matrix is a multivariate production function transforming the full set of inputs to a set of outputs.3 The total input resource i available to the consortium is Ii = Σj cij and the consortium’s output of resource k, denoted by Ok, is Ok = ΣjΣi cijRjik The cij must respect the (perceived) budgets of members j, yet be sufficient to meet output goals. The consortium designer must be satisfied both with the total set of Ok as they 3
This raises the possibility of using productivity measurement tools like Data Envelopment Analysis to
evaluate the performance of consortia, or the performance of multiple programs within a single consortium.
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relate to the designer’s mission, and with member o’s own ROI, represented by Σi cioRoik . 2. Allocate input resources to programs. The next step in this multi-stage objective/budget setting process is to link resources to programs. Programs are consortium activities such as publications, conferences, etc. Table 2 shows by example how cash, lab space, staff and student resources are transformed into conference, publication, and internship programs. Let the programs be indexed by r, and let yir be the amount of (input) resource i allocated to program r. A matrix Prik transforms inputs i into outputs k for each program r. Table 2. Linking resources to programs. Resources students Programs conferences publications internships TOTAL
money
laboratories
staff time
y11 y12 y13 I1
y21 y22 y23 I2
y31 y32 y33 I3
y41 y42 y43 I4
As input levels cij are already fixed, we wish to find any solution of ΣrΣi yirPrik > Ok and ΣrΣk yir = Ii for every i and k. If the program productivity coefficients Prik are known to be fixed, then they may be regarded as constants in the above simultaneous equations. It is also possible to allow the Prik to vary, making these nonlinear equations. In that case, one might stipulate ranges for the Prik, Lrik < Prik < Hrik with the upper range constituting a “stretch goal” for the consortium. The goal in solving these equations is to ensure consortium programs can produce the needed outputs. 3. Linking programs to budget lines. Now that resources have been linked to programs, it remains to make the result look like a conventional budget by tying activities to conventional institutional budget lines. Table 3 shows how this amounts to “budgeting” each program.
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Table 3. Linking programs to budget lines. Programs TOTAL Budget Lines
conferences
publications
internships
Salaries/benefits ΣrΣizri1 Rent Equipment Supplies Utilities Travel Outside services Overhead/G&A TOTAL
Σiz1i1
Σiz2i1
Σiz3i1
... ... ... ... ... ... ... Σiyi1
... ... ... ... ... ... ... Σiyi2
... ... ... ... ... ... ... Σiyi3
... ... ... ... ... ... ...
To effect this transformation, we need an additional quantity ρil which takes on a value of one if resource i can be used in budget line l, and zero otherwise. For example, students and paid staff (as well as cash) can be used to put on a conference, but laboratory space is generally not a useful resource for a conference activity. We then introduce zril , the fraction of resource i allocated to line l for/from program r. Values of zril must be set so that Σl ρilyirzril < yir for every i and every r. It is likely that certain minimums are known for particular budget lines, e.g., that a program manager must be hired at a certain salary, that a minimum square footage must be rented, or that a certain number of trips must be taken, and that all these expenditures serve all the consortium’s programs jointly. These constraints are of the form ΣrΣi ρilyirzril > Bl A final step is to clarify cash requirements. The set of resources may be partitioned into cash and non-cash (“in-kind”) resources. If it is necessary to represent the total “dollar size” of the consortial project, or to document matching contributions to a grant, one must then estimate the dollar values of in-kind contributions. Note that the quantities in Table 3 and the constraints noted just above, sum over the index i and so are not meaningful until this partitioning and/or “dollarizing” has been done. In an actual consortium the link between, say (to revisit the example that opened this section), speeches, plane seats and customer leads may be very approximate, or even (in some cases) implicit and unspoken. But it is important to remember that a convincing case 8
must be made to prospective members about the return on their resources. The new consortium must announce ambitious goals to the press, and some of these must be quantitative. And of course by the time a financial budget is set, all relevant considerations must be reduced to numbers.
Overhead Costs and University-Based Consortia What we referred to above as “budget lines” are called “Expenditure Categories” in Table 4, in order to clarify issues of overhead accounting. The organization hosting the consortium may demand reimbursement for the indirect costs (utilities, janitorial, landscaping, other institutional G&A) of locating the consortium activity within the institution. While the nominal rate for indirect cost recovery varies according to the source and according to the disposition of the funds, indirect costs are not actually assessed until the associated direct costs are expended. Thus, overhead (indirect cost) rates must be defined in matrix form as in Table 4.
Table 4: Overhead Rates Applied Income Categories / Kind
Expenditure Categories Salaries & Benefits - On-campus - Off-campus Scholarships Equipment Other Direct Expenses - On-campus - Off-campus
Donations
Service Fees
in Dollars Donations
& Memberships
Grants
In-
0% 0% 0% 0%
20% 20% 0% 0%
61% 35% 0% 0%
0% 0% 0% 0%
0% 0%
20% 20%
61% 35%
0% 0%
These rates depend on: • for federal government grants, a standing agreement between the government and the institution; • the principal investigator’s skill or “clout” in negotiating lower rates with institutional administration; • non-governmental granting bodies’ policies about use of their funds for overhead recovery; • widespread university policies that scholarship expenditure and gift and unrestricted donation income are exempt from overhead recovery; and • other considerations such as the reduced actual indirect costs of off-site 9
activities. As allowable overhead recovery rates often do not allow the institution to recover its actual overhead costs, it is in the institutional administration’s interest to recover the maximum allowable overhead recovery from each project (in this case, each consortium). While the administration is also interested in advancing the institution’s mission, the consortium designer (“principal investigator,” in grant language) has a more immediate need to advance the mission by devoting the maximum allowable consortium funds to the direct costs of consortium activities. Different consortium members (which may include government agencies) contribute different kinds of income to the consortium. Represent the overhead recovery rates of Table 4 as Ωlm , where m indexes the “flavor” of the income, as shown by the column headings of the Table. Let Mlm be the amount of money of “flavor” m that is allocated to budget line l. The marginal sums ΣlMlm are fixed. Then, administration wishes to Maximize ΣlΣmMlmΩlm subject to ΣlMlmΩlm < ΣlMlm and all Mlm > 0 and the consortium designer wishes to Minimize ΣlΣmMlmΩlm subject to ΣlMlmΩlm < ΣlMlm and all Mlm > 0 This resembles the transportation/distribution problem of operations research with the exception that row sums are not fixed. However, additional constraints of the row-sum and other kinds may be appended to acknowledge mutual concessions of the two parties, as this is not a strictly adversarial situation.
Conclusion and Further Applications A modified set covering optimization has been set forth as a way of designing consortia. Following the solution of this problem, a budgeting process occurs. In this paper, we have prefaced a standard and familiar two-stage budgeting process with a “zeroth” stage which sets “return on resource” objectives for every consortium member. The resulting three-stage budgeting process produces a budget that satisfies the mission and resource needs of the consortium designer; provides a superior ROI to the selected consortium members and opens doors for new ways for the members to do business; and may result in a social good such as more efficient use of tax dollars or more rapid commercialization of technology. A final, optional optimization formalizes the game between principal scientist and central administration which, in a university consortium, balances the need for mission-related expenditure against indirect cost recovery. 10
In practice it is found that the most useful features of consortia - flexibility, initiative, thinking outside the box, and dealing with new conditions and new organizational structures are not appealing to all the employees of all potential consortium members. The best participants are people who are competent and devoted to their home organizations, yet capable of stretching themselves to respond to a larger vision. Employees with narrower orientations are best left in place within member organizations, and out of contact with the consortium. The consortium design process described here places a heavy burden on the designer, as he/she must show insight into the business situations of all potential consortium members, understanding their incentives, personalities, and motivations. Yet, designers of several successful consortia have risen to this challenge. It seems to us that this skill, and the design process set forth in this paper, are also applicable to multi-function teams within a single organization. Such multi-function teams (matrix organizations) often fail due to the primary loyalty of team members to their line department affiliation. Team leaders fruitlessly attempt to change the attitudes of team members, or load them with conflicting incentives. Our experience with consortia, reflected in the models of this paper, shows that in cooperative endeavors, we should not try to change people. We can only design a cooperative organization (consortium, cross-functional team, etc.) that respects people’s existing incentives and motives. We can only choose people with aptitude, then introduce them to a superordinate consortial vision that encompasses (rather than opposes) their current motives and stretches (rather than changes) them. This is the management philosophy underlying the mathematical models of this paper.
References Charnes, A., and W.W. Cooper, “An Extremal Principle of Accounting Balance of a Resource-Value Transfer Economy: Existence, Uniqueness, and Computation.” Center for Cybernetic Studies report #185, and Rendiconti di Accademia Nazionale dei Lincei, April, 1974. Danziger, James N., Making Budgets: Public Resource Allocation. Sage, Beverly Hills CA, 1978. Gibson, David V. & Rogers, Everett M. (1994). R & D Collaboration on Trial. Boston: Harvard Business School Press. Lynch, Robert Porter, Business Alliances Guide. John Wiley & Sons, New York, 1993. Ochs, Lyle, Center for Entrepreneurial Growth at Oregon Graduate Institute: Business Plan. Oregon Graduate Institute of Science and Technology, Portland, OR, 1998. Phillips Fred, A Model for Public-Private Sector Distribution Planning for the U.S. Coal Industry. IC2 Institute, Technical Series #1, Austin, 1978. Young, Ross. (1994). Silicon Sumo: U.S.-Japan Competition and Industrial Policy in the Semiconductor Equipment Industry. Austin: The IC2 Institute of the University of Texas at Austin.
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