Although important for production industries to reach fully sustainable manufacturing processes, those implementing production systems face challenges in reaching this reliability goal. In this direction, a production system is modelled through a basic economic-production paradigm under carbon emissions with a storage constraint and demand-dependent unit production cost. More reliable production houses produce fewer defective products than the unreliable production system. As the model contains a power-function, a geometric programming procedure is employed to obtain a quasi-closed form of the optimal solution. A numerical example based on data from the literature and a case study based on industry data, are provided to demonstrate geometric programming as a valuable analytical tool to resolve this type of problem for a production system under carbon emissions. Finally, a sensitivity analysis and graphical illustration are provided to illustrate the model. Numerical results show that the production system becomes completely reliable when the recommended model is used. [Submitted: 18 May 2019; Accepted: 8 March 2021]
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