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

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.

OPTIMAL ONLINE ALGORITHMS ON TWO HIERARCHICAL MACHINES WITH RESOURCE AUGMENTATION

This paper investigates an online hierarchical scheduling problem with resource augmentation, i.e., the resources of the online algorithms are different from those of the offline algorithms. The machines are provided with different capacity according to their hierarchies. One with the hierarchy 1 has a speed of s(q) in the online (offline) algorithms and can process all the jobs. The other with hierarchy 2 has a speed of 1 in the online/offline algorithms and can only process partial jobs. The objective is to minimize makespan. For any 0 < q, s < ∞, we present optimal online algorithms with parametric competitive ratios.