Effects of variable setup cost, reliability, and production costs under controlled carbon emissions in a reliable production system

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.