A production-inventory model under stock-dependent demand, Weibull distribution deterioration and shortage

In the present article, we establish two production inventory models (Model I and Model II) for deteriorating items when the demand rate depends on the instantaneous inventory level. The production rate depends not only on the stock level but also on the demand. In both the models, we consider the Weibull distribution deterioration. Model I is developed and solved without allowing shortages whereas Model II is developed and solved allowing shortages that are backlogged. Three numerical examples are given to illustrate the solution procedure of the two models. Sensitivity analysis is also carried out.