Background Refurbishing encompasses the process of collecting used products, refurbishing them into new ones, and offering them to consumers. Within this framework, manufacturers can opt for either in-house refurbishing, managed internally, or outsource these operations to third parties and retailers. Methods Our study also takes into account the limited supply of remanufacturable products and incorporates customer behavior distinctions, differentiating between high-end and low-end customers in our models. The primary aim of this research is to formulate and analyze models for in-house refurbishing, refurbishing outsourcing to third parties, and refurbishing outsourcing to retailers. We seek to identify optimal solutions, conduct a comprehensive analysis, and implement strategies to maximize benefits. Additionally, we compare the in-house refurbishing model with the outsourcing refurbishing model. Leveraging multivariable function optimization techniques alongside the Karush-Kuhn-Tucker method, we endeavor to ascertain the optimal strategy, thereby facilitating a nuanced and methodical examination of the intricate dynamics governing profitability and sustainability within the refurbishing sector. Results Our study has applied rigorous mathematical modeling and optimization methodologies to identify optimal configurations for each model, aiming to enhance profitability across diverse parameters, including product quantities, quality selections, and pricing strategies. Conclusions Our analysis underscores that the in-house refurbishing approach tends to yield superior profits for profit-oriented enterprises, whereas outsourcing refurbishing to retailers is conducive to meeting environmental sustainability goals. Furthermore, our investigation has considered pivotal factors such as the constrained availability of remanufacturable products and consumer behavior, with a particular emphasis on discerning preferences among high-end and low-end clientele. We also perform sensitivity analyses to assess the impact of parameter variations on optimal outcomes. Our findings yield three distinct refurbishing models: the in-house refurbishing model, suitable for profit-driven companies under specific production cost parameters, and the outsourcing refurbishing to retailers model, tailored for environmentally-conscious companies, contingent upon particular production cost parameters.