Time Window Violations in Cargo Delivery: Modeling the Impact on CO ₂ Emissions and Carbon Costs

Minimizing fuel consumption and carbon emissions through vehicle routing is a critical objective for logistics companies, especially in light of stringent greenhouse gas emission policies enforced by various countries. To address this challenge, numerous studies have proposed robust vehicle routing problem models. Many of these focus on heterogeneous vehicle routing with time window constraints, aiming to reduce fuel consumption and emission costs. However, most research treats delays in customer time windows merely as penalty costs, giving limited attention to the impact of these delays on CO 2 emissions and their associated costs. Such delays—often caused by traffic congestion and rerouting—are significant contributors to excess CO 2 emissions. This paper addresses this overlooked aspect by proposing a model that accounts for the additional fuel consumption and CO 2 emissions resulting from delayed deliveries. It explores uncertainty in delivery schedules by analyzing three critical traffic scenarios: (1) vehicles idling in standstill traffic, (2) vehicles moving in slow traffic, and (3) vehicles being rerouted because of traffic uncertainties—all of which exacerbate CO 2 emissions from late deliveries. We propose a heterogeneous vehicle routing problem with carbon penalty, which optimizes routing to minimize CO 2 emissions for both on-time and delayed deliveries. A mathematical model and a robust genetic algorithm are developed, with their effectiveness validated through practical scenarios. The results offer valuable insights for logistics providers seeking to enhance both sustainability and operational efficiency.