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Carbon emissions are receiving greater scrutiny in many countries due to international forces to reduce anthropogenic global climate change. Carbon taxation is one of the most common carbon emission regulation policies, and companies must incorporate it into their production and pricing decisions. Activity-based costing (ABC) and the theory of constraints (TOC) have been applied to solve product mix problems; however, a challenging aspect of the product mix problem involves evaluating joint manufactured products, while reducing carbon emissions and environmental pollution to fulfill social responsibility. The aim of this paper is to apply ABC and TOC to analyze green product mix decision-making for joint products using a mathematical programming model and the joint production data of pharmaceutical industry companies for the processing of active pharmaceutical ingredients (APIs) in drugs for medical use. This paper illustrates that the time-driven ABC model leads to optimal joint product mix decisions and performs sensitivity analysis to study how the optimal solution will change with the carbon tax. Our findings provide insight into 'sustainability decisions' and are beneficial in terms of environmental management in a competitive pharmaceutical industry.

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Using mathematical programming with activity-based costing (ABC) and based on the theory of constraints (TOC), this study proposed a green production model for the traditional paper industry to achieve the purpose of energy saving and carbon emission reduction. The mathematical programming model presented in this paper considers (1) revenue of main products and byproducts, (2) unit-level, batch-level, and product-level activity costs in ABC, (3) labor cost with overtime available, (4) machine cost with capacity expansion, (5) saved electric power and steam costs by using the coal as the main fuel in conjunction with Refuse Derived Fuel (RDF). This model also considers the constraint of the quantity of carbon equivalent of various gases that are allowed to be emitted from the mill paper-making process to conform to the environmental protection policy. A numerical example is used to demonstrate how to apply the model presented in this paper. In addition, sensitivity analysis on the key parameters of the model are used to provide further insights for this research.