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Quick diagnosis is critical for neurovascular patients. Diagnosis of these patients needs the assistance of expensive and heavily used imaging equipment. This results in long waiting time which potentially threats patient's life. It is clearly very important for the neurovascular department to improve the service level by reducing the waiting time. To deal with this problem, this paper proposes a new reservation process between the neurovascular department and the imaging department. The neurovascular department reserves a certain number of time slots in advance for the imaging techniques, i.e., magnetic resonance imaging (MRI). This ensures that the stroke patients can receive the examination more quickly. This problem is formulated as a stochastic programming model in order to reach the best comprise between patient waiting time and unused time slots. To solve this problem, a two-step Monte Carlo approach is proposed. The problem is first approximated by a deterministic Monte Carlo optimization problem. It is further simplified to determine the contract. Given the contract, we then propose a feasible control policy. Numerical results show that the contract and the control policy proposed in this paper are quite efficient.