Cellular manufacturing system (CMS) is a manufacturing concept where aims to group products to part families
according to their similarities is manufacturing processing and also, machines are grouped to machine cells based on
parts manufactured by them. CMS framework is a major application of group technology (GT) philosophy. Group
technology is a management theory that aims to group products with similar process or manufacturing characteristics,
or both (Mitrofanov, [1]). Some real-world limitations in cell formation (CF) are: available capacity of machines must
not be exceeded, safety and technological necessities must be met, the number of machines in a cell and the number
of cells have not be exceeded an upper bound, intercellular and intracellular costs of handling material between
machines must be minimized, machines must be utilized in effect (Heragu, [2]).
There exists many considerations in designing and planning of CMS in different areas such as cell formation
problem (Uddin et al. [3]; Logendran et al. [4]; Cabrera-Rios et al., Cabrera-Rios et al. [5]), considering layout
problem in CMS problem (Bazargan-Lari, [6]), production planning concurrently in CMS (Riezebos et al., [7]), in
addition, simultaneously scheduling in CMS (Wemmerlov and Vakharia, Wemmerlov and Vakharia [8], Solimanpur
et al. [9], Aneja and Kamoun [10]), etc. Of these issues, the cell formation problem is an area that has been more
researched in literature (Soleymanpour et al. [11], Onwobolu and Mutingi [12]). Exceptional elements are defined as
parts which must be processed in different cells and therefore they have intercellular movements. Shafer et al. [13]
developed a model which introduces different states for exceptional elements considering inter-cell and intra-cell
movement, machines duplication and subcontracting costs. Saad [14] proposed an integrated approach to redesign
CMS considering emphasis on redesign aspects. His approach used simulation based on scheduling module.
In practice, costs, demands, processing times, set-up times and other inputs to classical CMS problems may be
highly uncertain so that it can have impact on results sensitively. Thus, development models for cell formation
problem under uncertainty can be suitable area for researchers and belongs to a relatively new class of CMS problems
that not researched well in the literature. In addition, parameter estimates may be mistaken due to inaccurate
measurement in the modeling process such as aggregated demands. Knowing this, researchers must develop models
for CMS under uncertainty. In this way, random parameters can be either continues or described by discrete scenarios.