Volume 34, Issue 1, 2025
DOI: 10.53555/03276716.2025.13
Complementary and Substitute Products for Imperfect Production, Defective items with Advertisement-Sales Return-Cournot’s Linear Inverse Demand Decision on: Optimal Demand and Green Production Replacement Policy
Abstract
The mathematical relationship that describes price as a function of quantity required is known as an inverse demand function, or price function, in the field of economics. In consumer decision theory, this function also reflects psychological responses to price, product perception, and purchasing intentions. A substitute product is one that can be used to meet the same needs of the customer in place of another product. Complementary products, like gasoline, SIM cards, and baking powder, are items that are purchased in addition to the main product and frequently offer little value or are not used separately. This paper explores optimal demand and green production replacement models for complementary and substitute products within an imperfect production system, integrating both economic and psychological drivers of consumer demand. It examines defective items considering advertisement-influenced sales returns and Cournot’s inverse linear dependent demand. Additionally, it focuses on determining the optimal demand and green production lot size using a third-order equation. Two models are developed. In model-1, complementary products for imperfect production system, defective items with advertisement-sales return-Cournot’s inverse linear dependent demand and in the model-2, substitute products for imperfect production system, defective items with advertisement-sales return-Cournot’s inverse linear dependent demand. Price break even point is determined, law of demand is verified, and highest possible profit was calculated from 3 different product demands in both the models. A carbon cost and green investment technology cost are used to reduce carbon emissions in both the models. This study aims to ascertain ideal pricing & production lot size in order to maximize overall profit. Applicability of this concept is illustrated by numerical examples. The overall profit is shown to be dependent on the degree of complementarity and substitutability. To evaluate the stability of the suggested model, a sensitivity analysis of the best options is provided. Visual Basic 6.0 is used to generate the data.
Keywords
Substitute products, Complementary products, Defective items, Optimal demand, Production lot size, Price break even point, and Law of demand.