(614f) Management of the Pharmaceutical R&D Using Stochastic Programming

Due to the changing circumstances in the managed-health-care environment, the productivity of pharmaceutical research and development (R&D) pipelines in terms of new drugs have started to decline, while the cost of developing a new product has increased. Therefore, systematic methods that aid the management of the pharmaceutical R&D can have substantial impact. The development of such methods, however, is a challenging task due to the stochastic nature and the large number of decisions involved in the R&D pipeline. Specifically:

a) Sources of uncertainty include the cost, duration, resource requirements and outcome of clinical trials (technical uncertainty) as well as the revenues from sales (market uncertainty). While market uncertainty is clearly very important, the uncertainty in the outcome of clinical trials is the most significant source in the development process.

b) Decisions include the selection and prioritization of potential drugs; the timing and resource allocation; resource planning related decisions (hiring, outsourcing, etc.); the out-licensing of drugs.

In this work, we develop a stochastic programming (SP) approach that simultaneously accounts for the selection of drugs, the scheduling of clinical trials, and the resource planning and out-licensing decisions. Given are a) a portfolio of drugs with the corresponding clinical trials and the associated data (duration, cost, resource requirements, probability of success), b) the available resources and associated costs, and c) financial data for the revenues from sales, out-licensing deals, etc. The goal is to determine the decisions that maximize the expected net present value of the R&D pipeline over a fixed time horizon.

The uncertainty in the outcome of clinical trials is modeled via a reduced set of outcomes that leads to a smaller set of scenarios. The planning horizon is divided into a number of periods (stages) resulting into a multi-stage SP mixed-integer programming (MIP) formulation, where decisions are made for each scenario and each time period (stage). The endogenous uncertainty of the R&D process is modeled via non-anticipativity inequalities. To reduce the number of these constraints we develop a number of properties by exploiting the characteristics of the problem at hand (i.e. gradual realization of clinical trial uncertainty). We also develop results that allow us to replace some of the these inequalities with equalities. These results serve the dual purpose of reducing the model and tightening the linear programming formulation. For example, for a three-drug instance, the number of variables was reduced from 19,281 to 4,512 and the number of constraints was reduced from 50,238 to 17,850, with larger improvements for larger problems.

Finally, we develop a branch-and-cut algorithm where we start our search based on a reduced formulation and add only the non-anticipativity constraints that are violated at each node of the search tree. Thus, non-anticipativity constraints do not impede problem generation, allowing larger problems to be solved. Note that unlike conventional branch-and-cut algorithms, we start with a subset of the necessary constraints but we add non-redundant constraints. To correctly find incumbents and upper bounds, we modify the procedure for the pruning of nodes. A number of different implementations were examined. The least computationally intensive approach turned out to be the one where we start from a formulation with no non-anticipativity inequalities and all equalities, while we check for violations at every node. Using the proposed methods, we are able to solve realistic instances with up to seven potential drugs.