<![CDATA[To advance the circular economy, refurbishing activities are essential to mitigate industrial waste. While cap-and-trade policies regulate greenhouse emissions, their mathematical interactions with refurbishing distribution strategies remain under-researched. This study assesses the implications of distribution structures on profitability under environmental constraints. Two multivariable optimization models were developed: Model C (direct distribution) and Model M (indirect distribution via a retailer). Objective functions were optimized for price and production volume under cap-and-trade constraints. A sensitivity analysis of 15 parameters employed partial derivatives to determine the profit function's rate of change relative to market potential (Q), price elasticity (λ), cannibalization (β), and carbon costs. Model C yielded a higher optimum value ($165,796) than Model M ($124,341). Sensitivity analysis identified Q as having the highest positive gradient. Conversely, profits exhibited high sensitivity to λ and β, where incremental coefficient increases led to non-linear margin deterioration. Mathematically, optimal pricing proved nearly inelastic to carbon price fluctuations, suggesting that production costs and demand coefficients dominate the profit function's Hessian matrix. Model C maintained lower pricing for new ($370,219) and refurbished items ($220,163) compared to Model M ($555,109 and $330,081). This study demonstrates that direct distribution mitigates “double marginalization” in multi-tier chains. Mathematically, firms should prioritize optimizing market parameters (λ, β) over carbon-cost mitigation. Furthermore, policymakers must recognize that cap-and-trade programs may drive industries toward vertical integration to achieve mathematical optimality.]]>
