<p>Recent advancements in technology have driven digital transformation within manufacturing organizations, leading to modernization efforts. This has not only increased throughput and quality metrics but also facilitated the creation of new digital platforms. These platforms serve as foundational layers for analytical professionals to build value-adding solutions. One key area experiencing significant advancement is shop-floor scheduling. The digital transformation, accelerated by COVID-19 pandemic, has spurred the development of more advanced and resilient solutions to real-world problems. While scheduling problems with regular performance measures are well-researched, allowing for the development of exact algorithms, more complex shop-floor environments with non-regular measures require further investigation. This work addresses the problem of scheduling the jobs on available identical-parallel machines to minimize the job completion time variance (CTV). We focus on solving a restricted version of this parallel machine scheduling problem, proposing three QIP (Quadratic Integer Programming) mathematical models and a heuristic method. The development of these mathematical models, exploiting dominance properties of completion time variance (CTV) minimization problems, constitutes a major novel contribution. The proposed heuristic addresses a special case (when all machines are not required to be used) of the parallel-machine problem. Computational analyses of these models and the heuristic, compared with existing methods, demonstrate the superiority of the proposed solution approaches for this restricted problem.</p>