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The incorporation of reverse logistics into production routing problems can promote and coordinate the implementation of sustainable development for supply chains. This study aims to incorporate reverse logistics into production routing problems and investigate the reduction of carbon emissions under carbon cap-and-trade. Mixed-integer programming models are proposed for the production routing problem with reverse logistics by considering simultaneous pickups and deliveries in vehicle routing subproblems. To solve this problem, we propose a solution method of a branch-and-cut guided search algorithm based on adaptation of known valid inequalities. Computational results highlight the trade-offs among various performance indicators, including emission levels and operational costs of production, inventory holding, fuel consumption, and drivers

Reducing Carbon Emissions in a Closed-Loop Production Routing Problem with Simultaneous Pickups and Deliveries under Carbon Cap-and-Trade