<p>Extensive research has been performed on determining the optimal order quantity by minimizing operations costs in production-delivery systems. Most of them focused on cost efficiency, overlooking the environmental effects of production processes, transportation, and holding inventories. Recent studies have highlighted the necessity of adjusting traditional inventory models to incorporate social-environmental concerns to meet the growing sustainability needs. Motivated by this notion, we develop a mathematical model that integrates operations and carbon emission costs to determine the optimal order quantity in the production-delivery supply chain. The order quantity is set equal to the positive multiple of the demand. A formula via the calculus method of differentiation is derived to determine the optimal multiplier value for the optimal order quantity and it is illustrated with a numerical example problem. A comparative study of the optimal results found for increased carbon prices shows the minimum total carbon emission cost as 35.60% of the minimum total cost. Sensitivity analyses are conducted to see the effects of changes in parameter values upon the minimum total operations and carbon emission costs. Besides, the variance-based sensitivity and cross-parameter interaction analyses confirm that demand is the key factor in affecting the minimum total cost while carbon price is the dominant driver of the minimum total carbon emission cost. Finally, a comparative analysis on total carbon emission with and without integrating the operations cost is performed. These research findings enhance theoretical understanding of sustainable supply chain flow optimization, emphasizing the potential significance of integrating environmental attention with operational efficiency.</p>