An optimal production model for non-instantaneous decaying goods with two-stage production period, power demand pattern, linear holding cost and partial backorder

Abstract

Many existing economic production quantity (EPQ) models are based on the assumption of an exponential demand rate. However, this assumption does not accurately reflect the demand pattern of most real-life items, as product demand rarely changes at an exponential rate. In practice, demand often varies throughout the inventory cycle; it may start slow, increase gradually, and decline toward the end, making the power demand rate a more realistic representation. This research proposes an optimal production model for non-instantaneous processes of decaying goods with a two-stage production period, power demand pattern, linear holding cost, and partial backorder. Shortages are allowed and partially backlogged. The necessary and sufficient conditions for the existence of an optimal solution are established. The model determines the optimal time with a positive inventory, duration of shortages, total production cost, and economic production quantity. We demonstrate the models validity   through a numerical example and then conduct a comparative analysis with an existing model. Results show that the proposed model produces a lower average total production cost, indicating better performance. Furthermore, a sensitivity analysis is conducted on selected parameters to evaluate their impact on total cost and EPQ, with recommendations provided to help manufacturers minimize costs.