Stochastic optimization: pharmaceutical portfolios decision-making under uncertainty

Abstract

The process of developing pharmaceutical drugs is long and costly, with a low probability of an approved drug in the final stage. Given a portfolio of several different pharmaceutical projects, it is therefore highly important to select the ones that maximize the expected profit. This paper presents a mathematical optimization model given the rules of a pharmaceutical project. The model is initially fully deterministic but is later expanded to include stochastic constraints. A recourse view of the problem is also discussed, meaning optimization under the assumption that choices can be made based on the realization of stochastic variables. The deterministic model is linear and thus straightforward to solve, while the stochastic constraints introduce non-linearities that greatly increase the complexity of the problem. Possible approaches to reduce this complexity are discussed, such as approximations and linearizations, along with the best use of the models. The deterministic model is also applied to a test portfolio and the results, such as the revenue, cost, solution time and others are discussed in the light of combinatorial complexities and decisions under risk.