Forecasting through dynamic modeling

TECHNOLOGICAL F O R E C A S T I N G A N D S O C I A L C H A N G E 3, 291-307 (1972)

291

Forecasting Through Dynamic Modeling* A. W A D E B L A C K M A N

Abstract The techniques of industrial (system) dynamics were applied to simulate a representative industrial research laboratory and to forecast the effect on future laboratory operations of matching an exploratory forecast of the laboratory's output to an exogenous goal schedule set by normative forecasts of future requirements. The laboratory operating policies which were found to produce stable growth patterns in response to normative growth goals were found to be different from those which would have been intuitively expected to produce stable growth. This finding is in agreement with the work of other investigators which has pointed out the unreliability of intuition when applied to multiloop, high-order, nonlinear feedback patterns characteristic of most management and social systems. The simulation outputs forecast (1) the future balance between government and internal support required to achieve the normative goals, (2) future personnel and facility requirements, (3) capital expenditures, and (4) the decision criteria required to achieve the goals and to assure orderly growth of the laboratory. The simulation also produces data which determine the long-term costs of achieving the normative goals and thereby allows benefit-cost comparisons of internally produced R/D with R/D obtained through acquisition and merger or licensing opportunities. Introduction Technological forecasting work to date has been focused on two distinct classes of methodologies: those having to do with exploratory or capability-oriented forecasts and those having to do with normative or needs-oriented forecasts. These methodologies have been critically appraised by Roberts[l] where the contrasts between the rather crude methodologies of exploratory forecasts and the relatively sophisticated methodologies of normative forecasts have been pointed out and where the desirability of the use of dynamic modeling techniques which would combine exploratory and normative forecasts in a dynamic feedback system has been recognized. The need for the development of dynamic modeling techniques has also been pointed out by Jantsch[2] who has stated that "the full potential of technological forecasting is realized only where exploratory and normative components are joined in an iterative or ultimately in a feedback cycle." The application of dynamic modeling to the problem of research and development (R/D) project selection and budget allocation was first accomplished by Roberts[3]. Other past work related to the application of dynamic modeling to technological forecasting is summarized in [1]. Although the work published to date has provided much insight into the dynamics of the R/D process, there has been no application of dynamic modeling using "real" data to examine managerial policies which are required to close the loop between normative and exploratory technological forecasts related to the operation of a representative R/D laboratory. Such a model would be extremely useful for planning laboratory operations and determining the desirability of undertaking proposed future R/D programs. For example, suppose normative forecasts indicate the desirability of A. WADEBLACKMANis with United Aircraft Research Laboratories, East Hartford, Conn. * This paper was originally presented at a conference on Technology Forecasting sponsored by the Industrial Management Center and held at Hilton Head, South Carolina, May 2 to 7, 1971. Copyright © 1972 by American Elsevier Publishing Company, Inc.

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A. WADE BLACKMAN

maintaining an annual growth rate in R/D output at a Specified amount over the next decade. To meet these goals the management of the R/D laboratory is then faced with the problems of planning resource allocations for facilities acquisition, the acquisition of personnel, planning proposal and sales efforts to obtain external support, developing new organizational structures, etc. The processes involved in the operation of an R/D laboratory are highly complex and involve many feedback loops and nonlinearities. It has been shown by Forrester[4, 5] that intuition is unreliable when applied to highorder, multiloop, nonlinear feedback systems. Therefore, the only available alternative for planning future operations which will ensure smooth growth is to develop a dynamic model which sufficiently replicates laboratory operations and then use this model to forecast the future policies which will be required to achieve a normative-oriented goal schedule. The full implications of the normative forecast of future R/D needs can only be evaluated after the dynamic model indicates what is actually required (in terms of costs, manpower, disruption of the existing organizational structure, etc.) to produce a future technological capability schedule (i.e., an exploratory forecast) which responds to the normative forecast. Once these implications are fully set forth, it may then be desirable to modify the normative forecasts or to achieve the normative requirements by alternative means more attractive in a benefit-cost sense (e.g., the acquisition and/or licensing route for supplying a future technological need might be preferred to internal development). The objective of the work described herein was to construct a dynamic model of a representative R/D laboratory and apply this model to determine operating policies required to produce a future technological capability in response to a normative forecast of future technological requirements.

Methodology To achieve the objectives of this study, an approach was necessary that allowed evaluation of the effect of a normative goal schedule on a number of different policies and strategies evaluated over a period of a number of years. The required approach would realistically evaluate the complex interactions between various segments of the R/D laboratory, allow for realistic time variations, and yet not be too complex or costly to preclude solution. A mathematical modeling approach based on the techniques of industrial dynamics I developed by Professor Jay W. Forrester and his associates at M.I.T.[6] appeared to possess the characteristics required for this investigation. System dynamics is based on servomechanism theory and other techniques of system analysis and is predicated on the ability of high-speed digital computers to solve large numbers (hundreds) of equations in short periods of time. The equations are mathematical descriptions of the operation of the system being simulated and are in the form of expressions for levels of various types which change at rates controlled by decision functions. The level equations represent accumulations within the system of such variables as dollars, personnel, facilities, etc., and the rate equations govern the change of the levels with time. The decision functions represent either implicit or explicit policies established for the system operation. Mathematical simulation of a system can only represent a real system to the extent that the equations describing the operation of the components of the system accurately ' As pointed out in [4], system dynamics is a more appropriate name for the industrial dynamics methodology, because it applies to complex systems in a wide variety of fields. This nomenclature will be adopted in the discussions which follow.

FORECASTING THROUGH DYNAMIC MODELING

293

describe the operations of the real system components. It is usually impossible to include equations for all of the myriad components of a real system because the simulation rapidly becomes too complex. It is, therefore, necessary to obtain an abstraction of the real system based on judgment and assumptions regarding which components of the real system are those which control overall system operation. The model construction involved the iterative procedure illustrated in Fig. 1. A model was initially constructed based on a perceived mechanism of system operation. This model was then tested against the historical performance of the system. If disagreement existed, sensitivity analyses were conducted to indicate the controlling variables in the model and revisions were made in the model formulation until acceptable agreement was obtained between past system performance and model predictions. The model was then used to determine improved policies and to forecast future system performance with existing or revised operating policies.

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Fig.1.Dynamimodel-building c procedure. The data and assumptions upon which this study is based were obtained from the records of a selected industrial R/D laboratory and from interviews with its management. The data presented herein, however, do not represent the actual operations of the laboratory but have been arbitrarily scaled to represent operation of a hypothetical research laboratory employing approximately 700 people and operating on an annual budget of approximately 12 million dollars. Most of the data obtained from the "real" laboratory were from one operating section representing approximately one-fourth of the entire laboratory's research engineering effort. The dynamic relationships between normative forecasts of desired future R/D requirements, the operating policies of the laboratory required to meet these requirements, and exploratory forecasts of the laboratory's future output with a set of operating policies are illustrated in Fig. 2. In this illustration, the normative forecast is considered to have been established exogenously. With a given set of operating policies, exploratory forecasts are then made to determine the laboratory's future output capabilities. If the output capabilities do not agree with the normative requirements, revisions must be effected in the laboratory's operations in order to achieve the normative goal schedule. The major focus of the study described herein was to determine the operating policy

294

A. W A D E B L A C K M A N

revisions (as a function of time) which were required to respond to an exogenous normative output schedule. The annual expenditure rate of the laboratory was adopted as a measure of the laboratory's output on the basis of historical relationships which were found to exist between this variable and the laboratory's output of papers and presentations as well as the number of patents produced. These relationships are shown in Figs. 3 and 4, NORMATIVE FORECAST OF FUTURE R/D REQUIREMENTS

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Fig. 2. Dynamic relationships between normative forecasts, operating policies, and exploratory forecasts.

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FORECASTING THROUGH DYNAMIC MODELING

295

respectively. The exogenous normative forecast was expressed in terms of a desired annual growth in expenditure rate which corresponded to an annual growth rate in the output of papers and presentations and patents.

Analysis The primary feedback loops assumed to affect the growth of the laboratory are shown in Fig. 5. The backlog of unallocated funds of the laboratory (i.e., the funds available for expenditure at the beginning of a time period) is assumed to control the number of engineers and scientists employed which in turn controls the overall employment level. The number of engineers and scientists employed have an influence (Loop 1) on the efforts of management to attract new business 2 (in the form of government contracts)--the larger the number of engineers and scientists employed, the greater will be management's efforts to attract new business to keep them productively employed. Also, the number of engineers and scientists employed will affect the rate of expenditure of funds which affects the output of the laboratory which will in turn affect new business (Loop 2). Similarly, the greater the number of engineers and scientists, the greater must be the inventory of facilities for their use. A larger facilities inventory (Loop 3) would be expected to have a favorable effect on attracting new business. The rate of expenditure will also affect the level of the backlog of unallocated funds of the laboratory which will in turn affect the level of the work force which can be supported (Loop 4). It can be seen that Loops 1-3 are positive feedback loops because an increase in the variables in the loop causes the other variables to increase in time; e.g., increasing the backlog in Loop 1 generates new business which further increases the backlog. Conversely, Loop 4 can be seen to be a negative feedback loop; i.e., an increase in the backlog increases the rate of expenditure which tends to decrease the backlog.

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Fig. 5. Feedback loops affecting growth. 2 In the sense used herein "new business" refers to the dollar volume of new business obtained. It is assumed that relationships between the expenditure of funds and laboratory output which have prevailed historically (see Figs. 3 and 4) will continue to prevail in the future.

296

A. WADE BLACKMAN

Because the extent of new business was a key variable in the study, it was necessary to investigate those factors that influenced this variable. It was hypothesized that the management effort to attract new business is related to the level of the engineer/scientist work force. Therefore, new business should be related to the professional work force available. It was also expected that the extent of new business attracted should depend on the general reputation of the laboratory for doing good work. This reputation was hypothesized to be related to the laboratory's output which in turn should depend on the rate of expenditure of funds. The facilities inventory was also expected to attract new business, because the greater the extent of facilities, the greater the probability of the laboratory having the special equipment required for a requested research job. Hence, it was hypothesized that the key variables affecting new business are: (I) the engineer/scientist work force, (2) the rate of expenditure of funds, and (3) the facilities inventory. The dollars per year received from new government contracts was used as a measure of the extent of new business. To reduce fluctuations with time, values for the dollars received per year from government contracts were smoothed utilizing a two-year moving average. A line was fitted through the smoothed points by the method of least squares. Multiple regression analysis was then employed to derive an equation which related the least square, smoothed values of the extent of new business to the three key variables discussed previously. The equation obtained was y = 0.635xl + 0.363Xz - 0.010x 3 - 0.189

(1)

where S/year received from new contracts Y = four-year average of S/year received' $ spent/year x~ = four-year average of $ spent/year' number of engineers and scientists and x2 = four-year average of engineers and scientists' net fixed assets x3 = four-year average of net fixed assets A multiple correlation coefficient of 0.988 was determined for the equation, and the agreement between the data and Eq. (1) is shown in Fig. 6. The agreement between the computed values and the smoothed data is excellent (the standard error of estimate was determined to be 3.16 percent) which gives justification to the assumption that the three key variables utilized are the controlling ones. An examination of the relation between output and rate of expenditure of funds gives further justification. It was believed initially that output should be related to the number of engineers and scientists on the work force. To test this belief, it was decided to use the number of papers and presentations made and the number of patents produced as measures of output. When these variables were plotted vs. the number of engineers/scientists in the work force relatively poor correlations (variations of greater than 40 percent from a straight line through the data) were obtained. However, when these variables were plotted vs. the expenditure rate, the obviously good correlations (variations of less than 5 percent from a straight line through the data) of Figs. 3 and 4 resulted.

FORECASTING THROUGH DYNAMIC MODELING - - 0

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Fig. 6. Agreement between smoothed values and values calculated from Eq. I. In summary, the key variables affecting the extent of new business appear to be (1) the rate of expenditure of funds, (2) the engineer/scientist work force, and (3) the facilities inventory. The output ofthe laboratories appears to be related to the rate of expenditure of funds to a much greater degree than to the engineer/scientist work force. The facilities inventory has a very small effect within the range of the data. Further analysis of the assumptions made will be discussed in relation to the feedback loops shown in Fig. 5.

Loop 1 Figure 7 presents a correlation (maximum variation approximately 25 percent from a straight line through the data) between the laboratory budget and the number of 1.6

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A. WADE BLACKMAN 1.6

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Fig. 8. Effect of professional work force on attracting new business calculated from Eq. 1. engineers and scientists in the work force. The curve appears to justify the assumption made in Loop 1 that the level of the professional work force depends on the backlog of unallocated funds. It has been assumed that the management effort to attract new business is related to the level of the professional work force. The effect of the extent of new business with variations in the professional work force was calculated from Eq. (1) with xt and x 3 held equal to 1.0 and the results are presented in Fig. 8.

Loop 2 The effect of the number of engineers and scientists in the work force on the rate of expenditure is shown in Fig. 9 (maximum variation approximately 25 percent) and the 1.6

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FORECASTING THROUGH DYNAMIC MODELING 16

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Fig. 10. Effect of rate of expenditure on attracting new business calculated from Eq. 1. relationship between the expenditure rate and the laboratories output has been discussed previously. The effect of the rate of expenditures (and hence output) on attracting new business was calculated from Eq. (1) with x2 and x 3 held equal to 1.0 and is presented in Fig. 10.

Loop 3 The effect of the number of engineers and scientists in the work force on the facilities inventory is shown in Fig. 1 1 (maximum variation approximately 8 percent from a straight line through the data.) On the basis of this correlation the facilities desired by the engineers and scientists were assumed to vary linearly with the number of engineers and scientists in the work force. The facilities inventory can be seen from Eq. (l) to have a negligible effect on new business in the range for which data were available. However, at lower values of the 1.6

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300

A. WADE BLACKMAN

facilities inventory some effect would be expected, because facilities limitations might then become a constraint on work output. Loop 4 Because the level of the backlog of unallocated funds is a function of the rate of expenditure of funds, this last assumption is simply justified by definition. The detailed system dynamics model shown in Fig. 12 was developed from the assumed key feedback patterns. It contains about fifty equations which are developed and discussed in detail in [7]. The level of aggregation considered in the model is such that resource allocations are on the basis of total budgets or capital outlays and are not carried down to the level of detailed project funding. The model shown in Fig. 12 contains six sectors: I. The funds backlog sector [Eqs. (1,L) through (7.4,C)] 3 describes how the funds backlog responds to the organization's activities and desired growth rate. 2. The management sector [Eqs. (8,A) through (14,C)] represents the effects of management's efforts on attracting new government business and describes the flow of contractual support from the government. 3. The funds-rate sector [Eqs. (14.5,L) through (20,C)] describes the exogenous flow of funds from nongovernment sources, the flow of funds from government sources, and the effects of the rate of expenditure on the inflow of government funds. 4. The personnel sector [Eqs. (21,A) through (31,C)] represents the hiring and firing decisions and their influence on the professional work force. ...........................

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FORECASTING THROUGH DYNAMIC MODELING

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5. The facilities sector [Eqs. (32,A) through (43,A)] represents the inventory of facilities, its change due to fluctuations in the professional work force, and its influence on the receipt of government contractual support. 6. The contracts sector [Eqs. (44,R) through (46,N)] describes the rate of receipt of government contractual support and the contractual support backlog. Results and Discussion

The system dynamics model as initially formulated was run on an IBM 7094 computer utilizing the DYNAMO compiler simulator program[8]. Figure 13 presents the results of these calculations in the form of plots of the data obtained from the DYNAMO output. The several variables that are plotted against time are: the average backlog of unallocated funds, ARB; the contract backlog, COBL; the average managerial effort toward attracting additional government business, AMEG; the engineer/scientist work force, ESWF; and the total facilities inventory, FAIT. 4 These plots represent the operation of the laboratories for a period of ten years for a normative growth rate of 5 percent per year. Conditions are assumed to be initially in a steady-state and operation of the model begins at time equal to zero. During the first months of operation the backlog of unallocated funds and the professional work force begins to expand slightly, but the contract backlog decreases because of a paucity of new contracts. This reduced contract backlog causes the unallocated funds backlog to begin to decrease. At about the same time the facilities inventory begins to increase as a result of the earlier increase in professional work force. The reduced funds backlog causes a greater management effort toward attracting new government business which works with the increase in facilities to cause an increase in the contract backlog which causes the funds backlog to go up again around the 20th month. This overall pattern repeats itself and oscillations of increasing amplitude (almost 50 percent increase in the funds backlog in the first cycle) characterize the growth pattern over the ten-year period. The period of the oscillations in the funds backlog increases with time. The first cycle has a period of approximately 40 months and the second, approximately 72 months. The oscillations result from the negative feedback loop (Loop 4, Fig. 5) and the increasing amplitude results from the positive feedback loops (Loops 1 through 3, Fig. 5). Such oscillations although highly undesirable are nevertheless characteristic of the growth patterns of many organizations as discussed in [9]. It is instructive to observe that oscillating growth behavior can be produced by a set of operating policies which appear to be logically consistent and which on the basis of intuition would have been predicted to produce stable growth. Stability can only be determined a posteriori from the simulation results, which makes obvious the usefulness of simulation techniques as a management tool and which emphasizes the unreliability of intuition (as discussed in [4]) when applied to the multiloop, high order, nonlinear feedback patterns which are generally characteristic of most management and social systems. The inital formulation of the model failed to produce acceptable agreement when tested against actual historical performance of the "real" laboratory. As indicated in Fig. 1, it was then necessary to conduct sensitivity analyses, identify the controlling 4 The relationship between these variables and the symbols used in the plot is indicated on the ordinate of Figs. 13 and 14.

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14. Ten-year simulation of laboratory operations, growth rate = 10~o per year.

304

A. WADE BLACKMAN

variables in the model, and modify the model to obtain acceptable agreement between the model predictions and historical data. The results of these sensitivity calculations and the model modifications are discussed in detail in [7]. The salient features of the revisions required to obtain satisfactory agreement between model predictions and historical data are summarized below. It was decided that a hiring policy for engineers and scientists which depended in large measure on the desired funds backlog and to a lesser extent on an average of the actual funds backlog would be desirable. Such a policy would insulate the hiring decisions from the short-range fluctuations in the funds backlog and make them depend to a greater extent on the longer range considerations of the normative growth rate. This would be consistent with the efforts to attract additional government business which also depend on the normative growth rate. In other words, a hiring policy based to some degree on the desired future growth would tend to compensate for the lag times which are inevitable in hiring competent professional personnel. The assumption made earlier that the laboratory expenditure rate depended only on the level of the professional work force was reexamined. It was decided that it would be more realistic to assume that the expenditure rate depends both on the level of the professional work force and on the overall management policy concerning expenditures. For example, if in a given period few contracts were received and the addition of government funds to the unallocated funds backlog was at a reduced rate, management might exercise caution and expend funds at a reduced rate to maintain the desired funds backlog. This could be accomplished by reducing the support personnel used on the project, revising scheduling, deferring material and computational expenditures, tighter cost control, etc. Of course, the variation which could be achieved would have proscribed limits; i.e., a lower limit would be imposed by the minimum costs of the existing personnel. An additional revision was a change in the policy assumed concerning management efforts to attract additional government business. Instead of basing the efforts to attract new business solely on the difference between the desired contract backlog (i.e., that 1.4

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Fig. 15. Comparison of predicted and actual funds expenditure rates, standard deviation +7.4yo, model predictions for 20%/year growth rate, [] data.

FORECASTING THROUGH DYNAMIC MODELING

305

required for a given growth rate) and the actual contract backlog, it appeared desirable to also have these efforts depend on the difference between the desired and actual funds' backlog levels. The results of the sensitivity runs were incorporated into a final set of revised policies which appeared to be the best compromise between the variables to produce the most stable growth patterns. The final set of equations are discussed in detail in [7]. The results of simulation runs for these policies for a normative growth rate of 10 percent per year are presented in Fig. 14. 4 Acceptable agreement was obtained between the normative (desired), R/D output of the laboratory and the exploratory forecast of the laboratory's output capabilities (as indicated by the Average Research Budget, ARB). The agreement between the simulated results for a growth rate of 20 percent per year and the actual data obtained from the operation of the "real" laboratory used as a basis for this investigation is presented in Figs. 15-17. The first four years of the simu1.4

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Fig. 16. Comparison of predicted and actual professional work force, standard deviation +9.7 70, -model predictions for 20 %/year growth rate, [] data.

lated results are compared with historical data for: the funds expenditure rate, FE; the engineer/scientist work force, ESWF; and the facilities inventory, FAIT. The results agreed within standard deviations of + 7 . 4 ~ for FE; +9.7°//o for ESWF; and ± 1 0 . 2 ~ for FAIT. This agreement is thought to be very good considering the scatter which exists characteristically in data of this type and provides ex post facto support for the assumptions upon which the model was based. Several conclusions can be derived from these results which have useful implications for the management of R/D laboratories. If a high normative rate of growth is desired or required from competitive pressures and this rate of growth cannot be attained internally from the supporting organization or from external commercial sources, then the rate of government support is the most important single factor in achieving the normative (desired) growth rate. Management must seek this support aggressively. It is necessary to increase the effort devoted to attracting government business as the laboratory grows in size. The effort exerted in attracting new business can be expected

306

A. W A D E B L A C K M A N 1.4

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Fig. 17. Comparison of predicted and actual facilities inventories, standard deviation +I0.2~., ---model predictionsfor 20%/yeargrowthrate, [] data. to exhibit short-term fluctuations which will be subject to random variations in the incidence of government requirements for additional research. It will, therefore, be necessary to have a technical sales force which is flexible or can be easily expanded to respond to these varying requirements. It is desirable to base personnel policies and facilities acquisition policies on the long-term desired rate of growth rather than short-term backlogs in funds. A consequence of this result is the necessity of assuming the risk of not having sufficient future support for the personnel hired. This, however, must be faced and planned for or smooth growth patterns cannot be achieved. It is also necessary to assume the risk involved for the commitment of funds for facilities as the professional work force increases. It is essential to have these funds available without too much delay because the effectiveness of the newly hired personnel will be limited if sufficient facilities are not available, their output will decrease, and it will be more difficult for the laboratories to attain the level of new government business necessary for their support. Therefore, the most essential ingredient for growth would appear to be a management policy fully committed to long-term growth. Concomitant with such a growth commitment must be the willingness to assume the risk involved in the commitment of funds for the personnel and facilities required to achieve the desired long-term growth. Although such a policy may involve risk, such risks may be the price which must be paid to achieve stable long-term growth. The model outputs which are considered most useful in indicating the effect on laboratory operations of closing the loop between normative and exploratory forecasts are summarized below: 1. The balance between government and internal support required to achieve a growth objective can be forecast for future time periods. 2. Personnel and facilities acquisition strategies can be investigated and requirements forecast.

FORECASTING THROUGH DYNAMIC MODELING

307

3. Future capital requirements can be predicted. 4. Management information system parameters and decision criteria required for smooth growth patterns can be identified. 5. The long-term cost of various normative forecasts of R / D requirements can be determined to allow benefit-cost comparisons of internally produced R / D with R / D obtained through possible licensing and/or acquisition and merger opportunities. References 1 E.B. Roberts, Technol. Forecasting 1, (1969) 113. 2 E. Jantsch, Technological Forecasting in Perspective, Organisation for Economic Co-operation and Development, Paris (1967), pp. 15-17. 3 E. B. Roberts, The Dynamics of Research and Development, Harper and Row, New York (1964). 4 J. W. Forrester, Technology Review 73, No. 3, 52 (January 1971). 5 J. W. Forrester, Principles of Systems, Wright-Allen Press, Cambridge, Mass. (1968), Ch. 3. 6 J. W. Forrester, Industrial Dynamics, M.I.T. Press, Cambridge, Mass. 0961). 7 A. W. Blackman, Thesis, M.I.T. Sloan School of Management (1966, unpublished). 8 A. L. Pugh, III, Dynamo User's Manual, Second Edition, M.I.T. Press, Cambridge, Mass. (1963). 9 D. W. Packer, Resource Acquisition in Corporate Growth, M.I.T. Press, Cambridge, Mass. (1964). Received May 24, 1971