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From the on-line point, we consider the hospital’s medical examination appointment problem with hierarchical machines. This approach eliminates the need for both demand forecasts and a risk-neutrality assumption. Due to different unit revenue, uncertain demand, and arrival of patients, we design on-line booking policies for two kinds of different situations from the perspective of on-line policy and competitive analysis. After that, we prove the optimal competitive ratios. Through numerical examples, we compare advantages and disadvantages between on-line policies and traditional policies, finding that there is different superiority for these two policies under different arrival sequences

On-Line Booking Policies and Competitive Analysis of Medical Examination in Hospital