Organic photovoltaic (OPV) technology promises a relatively inexpensive option for the solar energy conversion, provided its efficiency increases beyond the current level (similar to 7-8%) along with significant improvement in operational lifetime. To achieve this high efficiency/reliability, a systematic theoretical approach is required to optimize the underlying device fabrication process. In this article, we use an anneal-time dependent process-device co-simulation framework (the phase-field model for phase separation coupled with the self-consistent drift-diffusion transport for free carriers) to explore the effects of the process conditions (e.g., annealing temperature, anneal duration) on the performance of organic solar cells. Our results explain experimentally observed annealing effects on the solar cell performance, namely, (i) peak of the short circuit current, (ii) insensitivity of the open circuit voltage, (iii) low fill factor, etc., that would otherwise be deemed anomalous from the perspective of conventional solar cells. As such, this work offers a detailed analysis of the effects of annealing on OPV morphology and its electrical performance. This work also provides a theoretical framework for the optimization of process conditions, which might eventually lead to higher efficiency/reliability of the organic photovoltaic technology. Published by Elsevier B.V.