Analysis of Production Inventory Model with Time- and Price-Dependent Demand Under Multiple Prepayments and Preservation Technology

This study presents a production-inventory model for non-instantaneous deteriorating items that follows a two-parameter Weibull distribution deterioration. The deterioration rate is mitigated using preservation technology investment. The customer demand rate is modeled as a product of a power-form time function and an exponential price function, while the production rate is constant. Shortages are allowed and fully backlogged. The manufacturer employs a multiple prepayment policy for the customer as an advance payment and delivers the product on the final due. Furthermore, carbon is emitted during all inventory activities, including production, holding, and deterioration. Two carbon policies are analyzed to mitigate emissions, including (i) carbon tax and (ii) carbon cap-and-trade. The primary objective of the proposed model is to maximize total profit per unit time by determining the optimal selling price, preservation technology investment, the stock depletion time, and cycle length. A numerical example is presented to validate the proposed model, and the solution is obtained using the proposed algorithm implemented in MATLAB. A sensitivity analysis is performed, and the insights from this analysis are discussed in detail. The comparative analysis demonstrates that integration of preservation technology investment, an advanced payment method, and complete backlogged shortages increase the manufacturer’s average total profit by 10.56%. Furthermore, the implementation of a carbon tax and a cap-and-trade policy reduces total carbon emissions by 4.25% and 5.97%, respectively.