Research on Real-Time Scheduling Strategy for Multi-Level Medical Examinations Based on Stochastic Dynamic Programming Method
There is a significant difference between real-time scheduling and appointment scheduling for medical examinations.The demand for examiners in real-time scheduling is based on the release time(readiness time)on the day of service.Due to the uncertainty of the service time required by examiners,the production capacity of e-quipment and the needs of examiners in the real-time scheduling process are both uncertain.This paper establishes a discrete Markov decision model using stochastic dynamic programming method,determines the optimal strategy for real-time scheduling of medical examinations,and further searches for the upper and lower bounds of the sto-chastic dynamic programming model.For stochastic dynamic programming models,the so-called"upper bound"refers to the optimal decision made by hospital managers when the arrival time and required service time of differ-ent types of examiners are clear.The problem can be reduced to a deterministic 0-1 integer programming problem.The construction of the lower bound is not unique.Two strategies can be considered:"Device 2 only serves Type 2 inspectors"and"Device 2 serves Type 1 inspectors when idle".Finally,numerical examples are used to compare the upper and lower bounds with the optimal results of the stochastic dynamic programming model.In the case where the arrival of inspectors and the required service time are both uncertain,the stochastic dynamic program-ming model fully considers the priority of type 2 inspectors and the order in which each inspector arrives.The 0-1 integer programming model is the determined offline optimal model,which has sufficient understanding of the inspector's demand information and naturally obtains greater benefits.However,the 0-1 integer programming model,from the perspective of increasing profits,does not overly consider the priority of Type 2 inspectors over Type 1 inspectors,and does not necessarily refer to the order in which inspectors arrive when arranging inspec-tions.The total waiting time of the examiners that can be served and the total revenue of the devices under the strategy of"Device 2 serving Type 1 examiners when idle"are relatively close to the results of the stochastic dy-namic programming model,and this strategy is easy to execute.
Markov processstochastic dynamic programmingupper and lower bounds
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