Continuous-time planning and scheduling of internal closed-loop systems in multi-stage supply chain networks with recycling trade-offs

The article considers supply chain networks of process industries within several days or months. Continuous-time production, distribution, and recycling of goods and their subsequent reintegration into closed loops is analyzed. The aim of the study is to quantify trade-offs resulting from decisions on the usage of recyclable quantities. A mixed-integer linear programming model based on a new network structure with third-party contractors is developed. A numerical study consists of thirty scenarios with randomly generated data. The model allows for generating compromise solutions in acceptable computation times, if limiting the transfer of recyclable goods to disposal results in decreasing network profits.