An imperfect production-inventory model for reworked items with advertisement, time and price dependent demand for non-instantaneous deteriorating item using genetic algorithm

This article deals with an imperfect production inventory system with advertisement, price, and time-dependent demand for a non-instantaneous deteriorating item. Every manufacturing company aims to produce only perfect quality items, but this is not possible in reality. Firstly, the manufacturing system starts producing perfect items, but after some time, it starts producing imperfect items also, because of the manufacturing machine's long run. Perfect products are ready to sell, and some percentages of imperfect products are reworked to become perfect, and the remaining defective products are sold at a cheaper price. An efficiency cost is included to maintain the system efficiency. Considering these conditions, we developed a profit function. This profit function is highly nonlinear. Therefore, we employed a real coded genetic algorithm to obtain the optimum values of production rate, selling price of the perfect quality item, selling price of imperfect item, and inverse efficiency factor to maximise the profit. The model is demonstrated by using numerical example followed by sensitivity analysis.