A sustainable inventory model for stochastic demand using innovative multi-item production system with reduced failure rate

Any smart product needs to be advertised to generate more consumer demand and lower sale prices. Naturally, any smart product's demand rises when its price falls. This research proposes a multi-product production method that considers advertising and price-dependent stochastic demand for products and where the production system's failure rate is reduced while consuming the least amount of energy. This paper also investigates issues like unusual carbon emissions, energy consumption and machine breakdowns common in long-run production systems. To guarantee product quality, the current model adopts an inspection cost method. An autonomation policy is also discussed to have an error-free inspection. Hence, we construct a model where items that are not perfect are easily detected from the production process. This makes the production process smarter. The machine's production rate and failure rate determine the unit production cost. Further, the optimum energy costs of the model contain all expenditures associated with the manufacturing process. This study aims to identify the ideal combination of advertising expenses and selling price that will result in the highest possible profit with the fewest failed attempts. The model's total profit is a complex, non-linear function, which is solved numerically using an iterative process. Furthermore, the hessian matrix also provided for the optimality of the numerical validation. In order to determine the solution that works best for the developed model, the Mathematica software has been utilized.