Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand

- Defective rate of items is production rate dependent in an imperfect production model.
- Production rate and screening rate are different.
- Demand of perfect items is advertisement dependent.
- Advertisement rate is increasing with time at a decreasing rate.
- Some demand of perfect items is lost due to depreciation and long run of the business.

In this article, an economic production quantity (EPQ) model with imperfect production system and advertisement dependent demand has been presented. The advertisement rate has been assumed to be a function of time which has been increased with respect to time at a decreasing rate i.e., it has grown exponentially with respect to time but rate of growth gradually has decreased. Here, the rate of producing defective units has been followed to be a function of production rate. Also, the produced units have been inspected in order to screen the defective units but the screening rate is less than or equal to the production rate and greater than the demand rate. For the developed EPQ model, the total profit has been maximized to obtain the optimum production rate and production run time in the system. Here, algorithms have been developed for finding the optimal profit of the imperfect production inventory model. Finally, different numerical examples have been considered to illustrate the feasibility of the model taking different special cases in the system and then some sensitivity analyses have been carried out to get the impact of some parameters on the objective function of the model.