Optimal inventory management system for deteriorating items with linear demand, shortages and partial backlogging in a triangular fuzzy setup

In the present communication, we have proposed an optimal inventory management system for deteriorating items with linear demand, shortages, variable rate of deterioration and partial backlogging in the fuzzy environment. In real life situations, we certainly face the uncertainty component associated with the different parameters such as demand, raw materials supply, various other inventory costs, rate of deterioration, etc. Uncertainty theory in fuzzy terms has been found to be a useful methodology to describe the inherent subjective indeterminacy. The objective of the present work is to optimise the total average cost function by taking triangular fuzzy numbers into account. The defuzzification methods viz. graded mean, signed distance and centroid have been applied to obtain the results of the proposed model. For a detailed illustration of the proposed model, an example of inventory model has been considered and solved in view of the parameters involved. Further, the sensitivity analysis with respect to the various influencing parameters have been presented with the help of some graphical representations. The paper is finally concluded with a scope for the possible future work.