Descriptions of parameters and symbols (t = 1,2).

This paper investigates optimal ordering strategies in supply chains under two-level price fluctuations and initial profit allocation. By utilizing Copula functions to model the complex relationship between fluctuating prices and uncertain demand, the study develops both continuous and discrete decision models for practical applications. A discrete algorithm is proposed to approximate the optimal solution, with its convergence rigorously proven. Numerical experiments demonstrate that profit allocation ratios significantly impact optimal order quantities and overall supply chain profit. Price fluctuations, particularly at the discount level, present critical challenges, necessitating flexible and adaptive ordering strategies. The study also investigates the influence of different Copula relationships on optimal ordering decisions, revealing how varying market conditions—from moderate price sensitivity to high volatility—affect optimal order quantities. By examining ordering strategies in the context of profit allocation contracts, this research offers a new perspective on how supply chain members can collaboratively navigate uncertain markets. The findings provide actionable insights for managers to mitigate risks, improve coordination, and seize new opportunities. Extending traditional models to incorporate price fluctuations and profit allocation, this study makes theoretical and practical contributions to supply chain management, offering robust strategies to strengthen supply chain resilience.