Oskar Morgenstern, R. W. Shephard, and H. Grabowski, A Graph Oriented Model for Research Management (1965)

Prepared for the Office of Naval Research, this final technical report develops a conceptual framework for allocating research support when discoveries are uncertain and their consequences extend beyond the projects that produce them. Its four parts move from the organizational conditions of research, through a graphical representation of scientific interdependence, to a matrix formulation and a programme of further investigation. An appendix examines estimation errors. The authors’ aim is preliminary but substantive: to establish that research can be modelled as an interconnected system before claiming that such a model can guide allocations empirically.

The central difficulty is not simply predicting whether a project will succeed. Even retrospective evaluation cannot disclose what an unsupported alternative would have produced. Opportunity cost therefore remains partly inaccessible, while the value of a realized discovery depends on its subsequent uses elsewhere. Basic research intensifies these problems because its anticipated outcomes are least specifiable and its indirect consequences potentially broadest. Nevertheless, the authors resist an absolute division between basic science and engineering: a practical measurement device can enable experiments that transform theory.

It is therefore clear that the worth of any given research support should be determined from both derived and immediate effects.

“Derived effects” supply the report’s organizing concept. Research outputs are ideas, theories, experiments, devices, and materials, not merely printed pages or commodities with observable market prices. Their importance lies partly in making other research possible. Evaluating projects separately against immediate governmental objectives misses these pathways and can undervalue work whose relevance becomes visible only through intermediate activities.

Part I gives this systemic argument an institutional counterpart. Supporting agencies require scientifically competent staff who can challenge researchers without imposing narrow control. Conferences, personal contacts, laboratory visits, and proposed “working sabbaticals” should strengthen exchanges between government laboratories and universities. The authors also advocate mobility for younger scientists, attention to organizational stagnation, and opportunities for scientists engaged in classified work to re-enter open scientific discussion. Their endorsement of occasional cancellation as a managerial instrument is qualified by the need for alternative funding sources.

This brings a certain competition into being among agencies, which is just as necessary as the competition among research workers.

Funding plurality protects inquiry against a single authority’s rejection of an entire direction of research. It matters especially near basic science, where the authors favour keeping several avenues of support open. For large engineering efforts, by contrast, duplication may be less defensible. Management must thus accommodate different scientific purposes rather than apply one administrative rule throughout the research hierarchy.

Part II translates interdependence into a directed graph. Nodes aggregate research activities; arcs indicate influences between them. Pure, applied, and direct research form a broad progression toward governmental uses, but these distinctions depend partly on motivation and on the chosen level of aggregation. Connections can run in both directions, and the denser relationships of basic science resemble a web more than a tree. The classification is consequently a modelling decision, not a uniquely given taxonomy.

The test for relevance is whether there exist connected paths between the given research activity and the particular government problem studied.

This criterion replaces a demand for immediate applicability with an inquiry into mediated influence. The report distinguishes three representations: the Fundamental tree describes scientific and engineering relationships independently of funding; the Navy tree selects connections relevant to naval objectives; and the ONR tree superimposes activities actually supported and influences the agency hopes to strengthen. Their separation prevents an agency’s current portfolio from defining the limits of relevant knowledge. ONR must attend to the wider Navy tree, including research financed elsewhere, when judging its own contribution.

Part III assigns transfer coefficients to the graph’s arcs. These express how effort in one activity can have an effect equivalent to direct effort in another. Successive transfers yield the series (X=Y(I+C+C^2+\cdots)), which, when convergent, becomes (X=Y(I-C)^{-1}). The formal resemblance to Leontief input-output analysis enables the calculation of cumulative interdependence. The interpretation differs, however: research transfers amplify the effective consequences of an initial allocation rather than describe the gross production needed for a final bill of goods. A seven-node numerical example shows how substantial indirect effects can arise despite relatively few direct connections.

The calculation depends on strong simplifying assumptions: outputs are proportional to inputs, transfers are linear, and a stable coefficient matrix adequately represents relationships. Manhours and expenditure are considered as possible measures, but neither resolves differences in scientific ability, equipment requirements, or institutional costs. The model also initially neglects the effort needed to discover and assimilate relevant results. Later extensions introduce time lags, discounting, budget limits, and personnel constraints; the appendix discusses how coefficient errors propagate through cumulative effects.

However, before doing so, we should try to implement our basic model and empirically ascertain whether our underlying model actually describes the real process of research.

This qualification governs the proposed optimization framework. A utility function and resource constraints could support allocation decisions, but the report has not established either reliable measurements or an adequate expression of social objectives. Its concluding agenda therefore prioritizes aggregation rules, transfer indices, empirical network construction, and investigation of nonlinear relationships. The report’s lasting conceptual contribution is to make scientific interdependence central to research management while distinguishing a possible formal model from a validated decision instrument. Its institutional recommendations complement that restraint: productive support depends on communication and scientific judgment as well as calculation.