Fuzzy sets to model master production effectively in Make to Stock companies with Lack of Homogeneity in the Product

Supply chains (SCs) with Lack of Homogeneity in the Product (LHP) present inherent sources of uncertainty due to the heterogeneity of raw materials and uncontrollable productive factors. LHP SCs are characterized by producing units of the same finished goods that are not homogeneous. However, the exact quantity of each one in a production lot will only be known when it is produced. These SCs must classify finished goods into subtypes according to customer requirements. In this paper, a fuzzy mathematical programming model is proposed. To match homogeneity customer requirements with the sizing of production lots, the proposed master plan considers two main aspects: 1) forecast demand is expressed in terms of number of orders with a similar order size; 2) LHP is modeled by considering that each production lot is split into several homogeneous sub-lots. Then uncertainty is considered by means of fuzzy sets in order sizes and homogeneous sub-lots quantities. The fuzzy model is evaluated by emulating real conditions and is compared with the equivalent deterministic one to assess its robustness. The results demonstrate that the fuzzy approach outperforms the deterministic one and that it is more effective for handling real situations when LHP is present.