The nature of construction and formulation of the multi-objective functions in the flexible job shop (FJS) provides great insights about the study of the technique and the mechanism in scheduling helping to prioritize efforts for optimizing the manufacturing execution performance, which draw the focus of the researchers at home and abroad. From the perspective of the model, the solution method and the objective function, this paper reviews and analyzes the related academic papers and conferences articles during past few years. As a result, the construction forms of the multi-objective function and the scheduling scenarios show strongly positive correlation with the Makespan, the delivery tardiness, the energy consumption or the cost. Consequently, facing with the characteristic in a general way, the detailed construction analysis on the function for the flexible job shop scheduling problem (FJSP) is critical reviewed, and a total 6 types with 49 kinds classification are discussed. Obviously, the main goals are to summarize, analyze, discuss, and synthesize the existing achievements, the current research status, and the ongoing studies on the FJSP functions construction, and additionally to give useful insight into future research. Combined with the development trend of the intelligent manufacturing and the operations research, arguing for the formulation of the multi-obj. function, this review is expected to contribute to the future research of FJSP.

With the development of international cooperation, South Africa (SA) has been China’s largest trading partner in Africa for several consecutive years. China and SA can build the digital “Belt and Road” to modernize the manufacturing system locally and optimize process control by benchmarking with the best-in-class manufacturers in each country. In this research, an evaluation technology of manufacturer intelligence regarding the selection of decision support system (DSS) of smart manufacturing technologies, analyzing China–South Africa relations, is described. Firstly, the three keys aspects that enable the technologies of DSS are discussed in detail. Then, one key technology, the manufacturers’ intelligent evaluation system with 15 indexes, was built. The indexes and their measurements are also proposed. Finally, a fusion method based on boosting with multi-kernel function (online sequential extreme learning machine based on boosting, Boosting-OSELM) is introduced. The purpose of Boosting-OSKELM is to combine several weak learners into a strong learner (lower mean square error, MSE) through an acceptable time delay. Finally, the case study is presented to demonstrate the improvement on the MSE and process time, showing a relative MSE improvement of 96.19% and a relative time delay ratio of 31.46%. Totally, the largest contribution of the proposed evaluation method in this study is the conversion of the history data saved by the manual scoring method into knowledge in accessible MES and resealable time delay, which will free up the expert workforce in the entire process. We expect this paper will help future research in this field.