Sustainable two and three rates of imperfect production systems for defective items with price-advertisement demand

Sustainable production involves the creation of products and the delivery of services in a way that protects the environment, ensures economic viability, and promotes the health and safety of employees, communities, and customers. This paper focuses on sustainable production models for an imperfect production system that produces defective items, with demand influenced by price and advertisement, where the optimal production quantity is the primary decision variable. Two models are developed: one incorporating three production rates, and the other considering two production rates. The price break-even point is calculated, and the demand law is validated. This study introduces a sustainable production strategy for managing defective and damaged items, addressing the following points: (1) A small percentage of manufactured goods may be defective, but their quality can be improved through investments in quality enhancement; (2) Carbon emissions from manufacturing processes and product stock can be reduced by investing in carbon reduction efforts; (3) Advertisement and price-dependent demand are effective methods to increase product popularity across all customer segments; (4) Setting the product price, which can be determined using the price break-even point, is a crucial aspect for manufacturers; and (5) By employing two and three rates of production, initial investments can be minimized, and holding costs can be reduced. The objective of this paper is to maximize profit in an imperfect production system. A mathematical model is developed for both scenarios, and a numerical experiment is conducted to validate the mathematical formulation. Sensitivity analysis is performed to assess the impact of inventory factors on total profit and derive management implications. The model results have been implemented using Microsoft Visual Basic 6.0.