The main purpose of this paper is to present a comprehensive view of the application mathematical models in the designing and implementing SSCM beside to solving problems and making decision. The research questions are: what mathematical models are used for designing and implementing sustainable supply chain management, how to use them, which industries implemented in, what modules of SSCM depth in and finally finding the gaps of researches. The methodology of research is Systematic Literature review through peer review papers which are published in high ranking journals. In this paper, First, we search all papers through scientific data bases like Scopus, science direct, MDPI, Springer, Google Scholar, then, screening papers based on the criteria such as subject of paper, journals impact factor which is published in-should be peer review journal- and relative content of the papers. Finally, we selected 245 papers with three steps screening through 2806 papers that they have enough quality and relative to our research goals for context analysis. Through context analysis, first we categorized the information of the papers and drew the current situation of researches in the framework of our topic. Then, we evaluate and compare the goals of sustainability and current situation and found the gapes, then, offered new suggestions like implementing SSCMs models in pollutant industries like casting industry, Heavy industry, coal Industry and so on. On the other hand, there are gaps in researches in some modules of SSCM such as packaging, designing products, etc.

Previous research has shown that the effectiveness of selecting filter set from a large set of commercial broadband filters by vector analyzing method based on maximum linear independence (MLI). However, the traditional MLI is suboptimal due to predefining the first filter of the selected filter set being the maximum ℓ2 norm among all those of the filters. An exhaustive imaging simulation is conducted to investigate the features of the most competent filter set. In the simulation, every filter in a subset of all the filters is selected serving as the first filter in turn. From the results of the simulation, we found there are remarkable characteristics for the most competent filter set. Besides smaller condition number, the geometric features of the best-performed filter set comprise the distinct peak of the transmittance of the first filter, the generally uniform distributing of the peaks of the transmittance curve of the filters, the substantial overlapping of the transmittance curves with those of the adjacent filer sets. Therefore, the best-performed filter sets can be decided intuitively by simple vector analyzing and just a few experimental verifications. This work would be useful for optimizing spectral sensitivity of broadband multispectral imaging sensors or SFA sensors.