| Summary: | Clinical trial planning of candidate drugs is an important task for pharmaceutical companies. In this paper, we propose two new multistage stochastic programming formulations (CM1 and CM2) to determine the optimal clinical trial plan under uncertainty. Decisions of a clinical trial plan include which clinical trials to start and their start times. Its objective is to maximize expected net present value of the entire clinical trial plan. Outcome of a clinical trial is uncertain, i.e., whether a potential drug successfully completes a clinical trial is not known until the clinical trial is completed. This uncertainty is modeled using an endogenous uncertain parameter in CM1 and CM2. The main difference between CM1 and CM2 is an additional binary variable, which tracks both start and end time points of clinical trials in CM2. We compare the sizes and solution times of CM1 and CM2 with each other and with a previously developed formulation (CM3) using different instances of clinical trial planning problem. The results reveal that the solution times of CM1 and CM2 are similar to each other and are up to two orders of magnitude shorter compared to CM3 for all instances considered. In general, the root relaxation problems of CM1 and CM2 took shorter to solve, CM1 and CM2 yielded tight initial gaps, and the solver required fewer branches for convergence to the optimum for CM1 and CM2.
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