Vendor-Buyers relationship model for deteriorating items with shortages, fuzzy trapezoidal costs and inflation

In this paper, an integrated inventory model is developed from the perspective of a single vendor and multi-buyers for deteriorating items under fuzzy environment and inflation. In the development of the model, it is assumed that all costs parameters, demand and the production rates are imprecise in nature; they are represented by the trapezoidal fuzzy numbers, as these parameters are not constant and can be disturbed due to daily market changes. We use function principle as arithmetic operations to find the total inventory cost in fuzzy sense and Graded Mean - Integration Representation Method to defuzzify the fuzzy total inventory cost. Inflation is used to find the present worth of total cost. Since the optimal policy of buyers may not be the most economical for a vendor, thus to deal with this situation, integrated cost policy is used to reach the optimal policy. Finally, a numerical example is given to illustrate the model.