A two-phase simple model to determine the timing and duration of R and D project tasks

The problem of determining the timing of risky R and D tasks (activities) and non-routine tasks is analysed through a simple non-linear mathematical programming model. The model ignores issues related to the flow of information gathered at each time point as a function of the amount of resources invested to this time point (see Lucas 1971, Management Science , 17 , 679-697, including his followers, and the literature on managerial economics for alternative approaches). The typical non-convex or non-concave structure of the objective function, which maximizes the expected discounted net value of the project, implies the possibility of multiple local optimal solutions. Forpracticalpurposes, theglobalsolution canbeidentified either by employing global optimization methods satisfying the K - T necessary conditions, i.e. Z (the gradient function of the objective function) 0, or by enumerating the objective value function for, at most, four basic solutions. An illustrative example indicates that solutions establishing overlapping and non-overlapping tasks can be candidates for optimality.