A new mathematical model integrating the carbon tax and horizon planning to optimize the textile and clothing industry supply chain

Energy costs have surged significantly in recent years across various regions of the world. This inflation has a direct impact on households and businesses, by increasing production costs. It risks slowing the global economic recovery by reducing purchasing power and consumption. This study presents a new mixed-integer non-linear programming (MINLP) model with the objective of cost minimization within the direct supply chain of the textile and clothing industry. To consider different aspects in our study, the cost function is decomposed to the supply, production, energy, transportation, storage, and carbon tax emissions costs. It deals also with the management of multiple energy sources (specifically, electricity for production and fuel for transportation). This model simultaneously incorporates several critical factors, including life cycle assessment, carbon tax emissions, and planning horizon. To do this, a product's carbon emissions are quantified from raw material extraction through to the finished product, and three different planning horizons as long term t=infinity, medium term t=3 month, and short term t=1 month are considered to evaluate their impacts on the costs and emissions values. A shorter planning horizon leads to increased costs and reduced emissions reductions compared to a medium or long-term planning horizon. Additionally, the study introduces a new benchmark based on real -world data available in the literature, which serves as a valuable tool for evaluating strategic and tactical planning issues within textile supply chains. To evaluate the performance of our proposed model, we defined three different size of the problem by changing the number of factories, suppliers, production sites, warehouses and customers.The study's findings reveal that, over a medium and long-term planning horizon, there is an average cost increase of about 2% for different problem sizes, when considering a carbon tax ranging from 44.6euro to 86.2euro per tonne of emissions. When a higher carbon tax is applied, the total cost increases, while the carbone emissions and subcontracting activities will be decrease.