Effect of price-advertisement-sales return dependent demand for imperfect production, reworking, scrap and shortages – in third order equation

¹ R.M.K. Engineering College, Kavaraipetti 601206, India
² Sri Ranganthar Institute of Engineering and Technology, Coimbatore 641110, India

^* Corresponding author: sankariooty@gmail.com

Received: 13 September 2024
Accepted: 8 July 2025

Abstract

In this paper, an imperfect production system with price-advertisement-sales return-dependent demand, for head and wagger shortages, reworking, and scrap is considered in a third-order equation. In the literature, only two decisions variables that is optimum shortages and optimum quantity were considered. But in this paper, three decision variables are considered which are optimal pricing, production lot size, and shortages. Here, achieving the best price, manufacturing lot size, and shortages for overall maximum profitability in an imperfect production system is the goal. The breakeven point of price is considered and the law of demand is verified. The maximum profit is determined based on three alternative prices of the product. To evaluate the best values for the three decision variables – price, quantity, and shortages – a mathematical model is put forth. The validity of the mathematical formulation is demonstrated through a numerical experiment, and the effects of inventory factors on overall profit and management insights have been examined using sensitivity analysis. The price break even point is 2509.8728 in which neither profit nor loss and the maximum profit is 28 6278.88 with the corresponding price of 3586.96. To the best of my knowledge, however, no authors have created models for head and wagger shortages in terms of ideal pricing, production lot size, and shortage policies that take demand, reworking, and scrap in third order equation into account along with price-advertisement-sales return dependence. The model result validation was programmed in MS Visual Basic 6.