A Retailer’s Deteriorating Inventory Model with Amelioration and Permissible Backlogging Under Power Pattern Demand

There are many ways to handle an inventory problem, starting with mathematical and simulation strategies that include trial and error techniques. Mathematical techniques are consistently effective strategies for reducing total inventory costs. In this article, we deal with a retailer’s inventory system in order to determine an optimal strategy that minimizes the total inventory cost under several constraints. These constraints include power-pattern demand, constant deterioration, Weibull amelioration, permissible partial backlog shortages, different inventory costs, and inherent imprecision of various expenses concerning the current scenario. Subsequently, we develop the mathematical model of the problem and its solving policy in both crisp and fuzzy circumstances. Furthermore, to validate our findings we consider numerical examples followed by the convexity graphs of the total cost function via Mathematica 11.1.1 software. Finally, we study the sensitivity analysis and accordingly present several managerial insights for the benefit of the inventory managers.