A bi-level multi-follower optimization model for R&D project portfolio: an application to a pharmaceutical holding company

Ann Oper Res. 2023;323(1-2):331-360. doi: 10.1007/s10479-022-05052-0. Epub 2022 Nov 8.


The need for a study of project portfolio optimization in pharmaceutical R&D has become all the more urgent with the outbreak of COVID-19. This study examines a new model for optimizing R&D project portfolios under a decentralized decision-making structure in a pharmaceutical holding company. Specifically, two levels of decision makers hierarchically decide on budget allocation and project portfolio selection-scheduling to maximize their profit, and we formulate the problem as a bi-level multi-follower mixed-integer optimization model. At the upper level, the investment company has complete knowledge of the subsidiaries' response, acts first, and decides on the best budget allocation. At the lower level, each subsidiary responds to the allocated budget and decides on its portfolio scheduling. Since the lower level represents several mixed-integer programming problems, solving the resulting bi-level model is challenging. Therefore, we propose an efficient hybrid solution approach based on parametric optimization and convert the bi-level model into a single-level mixed-integer model. To validate it, we solve a case and discuss the optimal strategy of each actor. The experimental results show that the planned project portfolio for each subsidiary of the holding company is drastically affected by the allocated budget and its decisions.

Supplementary information: The online version contains supplementary material available at 10.1007/s10479-022-05052-0.

Keywords: Bi-level multi-follower modeling; Budget allocation; New product development; Pharmaceutical holding company; R&D project portfolio.