Abstract
Two distinct inventory models are investigated for a deteriorating item under the frequency of advertisement and market price-sensitive aggregate demand where the deterioration percentage complies with Weibull distribution. In one model, the stock-out environment is not studied, while another one handles the stock-out situation by moderately backordering based upon the waiting time duration for the products. Advance payment, another realistic feature, is implemented by paying off a fraction of the acquisition cost amid single or many equal segments from the order placing moment to receiving moment whereas the remaining fraction is accomplished at the order delivery instant by the practitioner to the supplier. The utmost aim is computing the inventory policy along with the market price and marketing strategy to reach the highest total profit for both models. The models formulated here extend several inventory studies previously developed in the literature and suggest several important outcomes. This makes two exceedingly nonlinear and mixed-integer optimization problems, which are elucidated by constructing two efficacious algorithms. Two numerical illustrations are accomplished to perceive the working competence of the algorithms and the consequences of the parameters on the practitioner's optimal policy are highlighted in a tabular form executing a sensitivity examination. Based on the performed analyses, finally, some decision-making salient findings are obtained.