A two warehouse supply-chain model under possibility/ necessity/credibility measures

This article presents a joint performance of a supply chain (SC) with two warehouse facilities. A realistic two warehouse multi-collection–production-inventory model with constant/stock dependent demand, defective production system and fuzzy budget constraint has been formulated in an SC context. Here rate of defectiveness follows a probability distribution and fuzzy constraint is imposed in a necessity/possibility/credibility sense and defuzzied following fuzzy relations. The rates of collection for each raw material and production are assumed as control variables. Also the defective units are screened along with production and reworked with a known rework rate. The model is reduced to the equivalent deterministic one of minimizing the expected total cost with imprecise demand through possibility, necessity or convex combination of them (credibility). All these formulations are solved using Generalized Reduced Gradient (GRG) technique. The model is illustrated numerically for different types of demands and with respect to those demands, the optimal production and stock level are presented in both tabular and graphical forms. The sensitivity of the total operating cost on the variation of capacity of the market warehouse is also presented to illustrate the advantage of a two warehouse system in SC.