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This article introduces a mathematical model for optimizing total profit by considering various complex factors, including time-dependent shortages, split demand, Gompertz distribution degradation, a linear holding cost function, and partial backlog issues. The two stages of demand, which are time-dependent linear demand and price-dependent exponential demand, occur when there are no shortages. A comprehensive approach to inventory management decision-making is illustrated through a sensitivity analysis and numerical example, highlighting the influence of system limitations on the optimization outcomes. This model is an effective tool for improving inventory management practices and assessing concavity while maximizing profitability. With MATLAB, relationships between model parameters are graphically represented.
Thirumalaisamy Vanjikkodi (Mon,) studied this question.