A Fuzzy Inventory Model for a Deteriorating Item with Variable Demand, Permissible Delay in Payments and Partial Backlogging with Shortage Follows Inventory (SFI) Policy

This research studies a fuzzy inventory model for a deteriorating item with permissible delay in payments. For this paper, the demand depends on selling price and the frequency of the advertisement. In order to make a more realistic inventory model, it is considered the case of stock-out which is partial backlogged. In this work, it is taken account the shortage follows inventory (SFI) policy. Several scenarios and sub-scenarios have been provided, and each corresponding problem has been defined as a constrained optimization problem in the fuzzy environment. Further, these problems have converted into a new problem using the nearest interval approximation technique of fuzzy numbers. Quantum-behaved particle swarm optimization (QPSO) algorithm with the help of interval mathematics has been used to solve the optimization problems. Numerical examples have been solved in order to illustrate the proposed inventory model. Finally, with the aim to analyse the significant influence of different factors on the optimal policies, a sensitivity analysis is done.