One of the key issues in contemporary economics and inventory management is the determination of the economic production quantity for perishable products. This problem holds particular significance due to challenges such as product deterioration, imperfect production, stochastic demand, and its dependency on price, which complicate optimal decision-making in real-world supply chains.
In this research, the economic production quantity problem for perishable items under stochastic demand is examined, incorporating realistic assumptions including a constant deterioration rate for products, rework of defective items, full backordering of shortages, demand dependency on selling price under Brownian motion behavior, and an exponentially declining production rate to simulate the progressive deterioration of production equipment over time.
In this problem, the production system manufactures perishable products, a portion of which are defective due to imperfect processes. The system performs rework on defective items to convert them back to perfect-quality products, while also accounting for the gradual decline in production rate resulting from equipment aging. To maximize long-run average profit and prevent excessive costs associated with holding, shortages, and deterioration, the production lot size, backorder level, cycle parameters, and dynamic pricing policy must be optimally determined through joint optimization.
For this purpose, a comprehensive nonlinear stochastic mathematical model is developed with an infinite planning horizon to capture long-term behavior. The model is solved using a hybrid approach combining Monte Carlo simulation for handling stochastic elements and gradient descent for efficient optimization and is executed with a numerical example to demonstrate its applicability. Numerical results indicate that the production decline rate and non-reworkable defective items exert the most significant negative impact on profitability, whereas demand price elasticity dominates the deterioration rate in influencing optimal policies, and gradual price reduction in price-sensitive markets substantially increases profit by stimulating demand and mitigating losses from deterioration.