Construction scheduling, in practice, commonly relies on the usage of commercial project management tools (PMT) without specific optimization features. To obtain optimal schedules, planners often need to develop separate optimization models with special tools, which, however, demand further processing and editing of optimization results by PMT into forms expected for project management. In this regard, separation of optimization and PMT also requires considerable additional work for complete and harmonized updating of schedules during construction execution. Mentioned drawbacks and lack of available time may take to deficient construction scheduling during the implementation phase resulting in poor or even insufficient realization of project goals. Therefore, this paper presents an achievements survey on the integration of optimization and PMT that allow sustainable construction scheduling, particularly in terms of continuous optimal time and resource allocation throughout the project life cycle. Such work has not yet been comprehensively done up to now and the present contribution intends to fill a literature gap in the aforesaid area. Following a brief introduction, the optimization platform for construction scheduling is given in the article. Focusing on construction scheduling, an in-depth achievements survey on the integration of heuristics methods, mathematical programming and special solving methods with conventional PMT as well as optimization-based building information modeling (BIM) tools is then performed and findings are reported. The paper ends with conclusions and recommendations for further research.