Optimal pricing and cycle–length decisions in an EOQ model with polynomial–price dependent Demand and Rayleigh deterioration of items

This paper develops an Economic Order Quantity (EOQ) inventory model for perishable items with price–dependent polynomial demand and Rayleigh–type deterioration of items. The proposed framework extends classical EOQ models by capturing nonlinear demand behavior and time–dependent deterioration effects, providing a more realistic representation of inventory systems for perishable goods. Explicit expressions for the total profit function are derived, and analytical optimality conditions for both the selling price and the replenishment cycle length are established. A comprehensive sensitivity analysis is conducted to examine the influence of key parameters, including deterioration intensity, demand elasticity, and polynomial demand coefficients, on optimal pricing and ordering decisions. Numerical examples illustrate the practical implications of the model and highlight the importance of accounting for higher–degree demand functions in determining optimal inventory policies. The results demonstrate that the model exhibits stable quasi–concave behavior and offers valuable insights for managers seeking to maximize profitability while effectively controlling inventory costs. The proposed approach provides a flexible, analytically tractable framework suitable for a wide range of real–world inventory management problems.