In this study, the coordination problem of a dairy supply chain under stochastic demand is investigated. To enhance efficiency and improve the level of coordination among supply chain members, a two-echelon mathematical programming model is developed in which a combination of an option contract and a revenue-sharing mechanism is employed. Within this framework, shortages are classified into two types, namely lost-sales shortages and backorder shortages, and the decision-makers' behavior in response to both types of shortages is modeled simultaneously. The primary objective of the model is to determine the optimal order quantity and option contract price in such a way that the profits of both supply chain members are increased while the overall system performance approaches that of the centralized system. The main contributions of this research include the explicit differentiation of shortage types, the simultaneous integration of the option contract with a revenue-sharing structure, and the use of the revenue-sharing mechanism to incentivize the retailer to improve responsiveness to shortages. The results of the numerical analysis demonstrate that the proposed coordination mechanism improves the profitability of supply chain members compared with the decentralized model, leading to an 11.59% increase in the total profit of the supply chain. Furthermore, the sensitivity analysis indicates that an increase in the backorder rate enhances the retailer's profit, whereas a higher option price has a positive impact on the manufacturer's profit.