2 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. EM-16, NO. 1, FEBRUARY 1969 A Mathematical Basis for the Selection of Research Projects ANTHONY C. ATKINSON AND ARTHUR H. BOBIS Abstract—A method is presented for determining the money to be spent on product oriented research programs. The method is used by American Cyanamid's Organic Chemicals Division. INTRODUCTION D URING the past few years many articles have appeared describing mathematical models in- tended for use in evaluating research projects. These can be broadly separated into two categories: simple models that treat the process of research as if it- were static, and complex models that deal with research as a dynamic problem. In reviewing this literature, Baker and Pound [1] state that the simple models ignore what is perhaps the essential aspect of the prob- lem and are, therefore, of questionable utility, while the more complicated models require so much information that their usefulness can never truly be tested. With this paper, Ave are adding to the proliferation of methods and models. But we believe we have chosen a course that avoids the previous inadequacies and that, while dealing with the real problem, treats it in such a way as to en- courage use of the method. The justification for our belief is that the model has been developed in consul- tation with groups of researchers, and that management finds the results helpful in evaluating and planning re- search efforts. Our point of departure for this work was the paper by Hess [2]. The purpose of this paper is to describe the mathe- matics on which the model is based. By mathematics we mean both the algebra and the philosophy that led to the particular algebraic, formulation. The description is in five parts : 1) the probability model 2) commercial information 3) the rate of expenditure 4) optimization 5) simulation. An Appendix describes the distribution used to fit data. In building a mathematical model of the research process, we have had to make use of estimates of such quantities as the probability that a project will succeed. Although there is no means of checking such a number, and also no "frequentist" interpretation of such probabil- Manuscript received February, 1968; revised November, 1968. A. C. Atkinson was with the American Cyanamid Company, Bound Brook, N. J. He is now with Imperial College, London, S.W.7, England. A. H. Bobis is with the American Cyanamid Company, Bound Brook, N. J. ities, we have handled subjective probabilities as though they described recurring events. Also, no attention has been given to problems arising from optimistic or pessi- mistic estimations of such quantities as sales. We have worked on the assumption that decisions have to be made, usually on inadequate data, and that they will be made intuitively on the data, whatever its quality. Any- thing that can be done to quantify the bases for these decisions and to demonstrate the logical consequences of the assumptions is a step in the right direction. Twice a year the research managers in the American Cyanamid Company's Organic Chemicals Division col- lect data of the kind described in this paper and submit it for analysis. This is done at the time budgets are being prepared and again when we are reviewing the results of these expenditures. The computer evaluation, which is an allocation of research funds across the several projects, is used as a guide for the eventual budget. The analysis often points out shortcomings in the information. At this point the necessary modifications are made and the procedure repeated until there is general agreement that the analysis is based on the best possible information. Although the computer allocation and the eventual budget need not be identical, serious departures between the two must be examined. As will be shown, the model is general; there is nothing that is specific to the needs of the American Cyanamid's Organic Chemicals Division, nor is its use restricted to the chemical industry. It has been formulated so that it can be applied to those research projects whose objective is either the invention of new products or modification of existing products that are sufficiently well defined that sales and selling price are estimatable. The model as described limits the projects that are considered to those where technical success or failure will be determined within the ensuing five years. It has been our experience that in the product-oriented research projects that have been considered, few have been eliminated from the analysis on this basis. The analysis that is described is based on accumulated net profits over the next 11 years. This choice is arbitrary and some other basis could have been chosen. Another choice would have been to calculate the returns from each project over the product's expected life. The choice of 11 years has proven satisfactory. Returns beyond the eleventh year are subject to increasing variation, while discounting severely reduces the revenue. The choice of a shorter basis would, it is felt, unduly penalize the long- range project.