Optimal replenishment policy for fuzzy inventory model with deteriorating items and allowable shortages under inflationary conditions

Abstract

This study develops an inventory model to determine ordering policy for deteriorating items with constant demand rate under inflationary condition over a fixed planning horizon. Shortages are allowed and are partially backlogged. In today’s wobbling economy, especially for long term investment, the effects of inflation cannot be disregarded as uncertainty about future inflation may influence the ordering policy. Therefore, in this paper a fuzzy model is developed that fuzzify the inflation rate, discount rate, deterioration rate, and backlogging parameter by using triangular fuzzy numbers to represent the uncertainty. For Defuzzification, the well known signed distance method is employed to find the total profit over the planning horizon. The objective of the study is to derive the optimal number of cycles and their optimal length so to maximize the net present value of the total profit over a fixed planning horizon. The necessary and sufficient conditions for an optimal solution are characterized. An algorithm is proposed to find the optimal solution. Finally, the proposed model has been validated with numerical example. Sensitivity analysis has been performed to study the impact of various parameters on the optimal solution, and some important managerial implications are presented.

Keywords

• inventory
• deterioration
• partial backlogging
• inflation
• triangular fuzzy number and signed distance method