An inventory model under uncertain inflationary conditions, finite production rate and inflation-dependent demand rate for deteriorating items with shortages

In the existing literature, inventory models under inflationary conditions are usually developed under the assumption of certain inflation rates and constant, time-varying or stock-dependent demand rate. In many real-life situations, the practical experiences reveal that the inflation is non-deterministic and a variable. Meanwhile, the demand rate can be related to the inflation rates. The theoretical contribution of this article is to consider stochastic inflationary conditions with variable probability density functions (pdfs) over the time horizon, and the demand rate is dependent to the inflation rates (any arbitrary pdfs can be used). The developed model, also, implicates to finite replenishment rate, finite time horizon and deteriorating items with shortages. The objective is minimisation of the expected present value of costs over the time horizon. The numerical example and case study have been provided for evaluation and validation of the theoretical results and some special cases of the model are discussed.