2009 Mathematical Modeling B Problem

The reasonable arrangement of the eye beds in question B

Hospital queuing is very familiar with the phenomenon, it in such or that form in front of us, for example, patients to outpatient visits, to the charge of the pricing, to the pharmacy to take medicine, to the injection room injections, waiting for hospitalization, etc., often need to wait in line to accept some kind of service.

We consider the mathematical modeling problem of the reasonable arrangement of ophthalmic beds in a hospital.

The hospital's ophthalmic clinic is open every day and there are 79 beds in the inpatient department. There are four main categories of ophthalmic surgery in the hospital: cataract, retinal disease, glaucoma and trauma. The appendix gives information on the various types of patients during the period from July 13, 2008 to September 11, 2008.

Cataract surgery is simpler and there is no emergency. At present, the hospital is every Monday to do cataract surgery, such patients before the preoperative preparation time of only 1, 2 days. Patients who do two eyes are more than one eye, accounting for about 60%. If you want to do the eyes is a Monday first, Wednesday to do another one.

Traumatic illness is usually an emergency, the hospital is arranged immediately when the bed is empty, and the surgery is arranged the next day after hospitalization.

Other ophthalmic diseases are more complex, there are different conditions, but the general hospitalization within 2-3 days after the operation can be accepted, mainly after the observation time is longer. This type of disease surgery time can be arranged according to the needs, generally not scheduled in Monday, Wednesday. Due to the low number of emergencies, these eye diseases can be modeled without emergency.

The hospital eye surgery conditions are relatively adequate, in considering the hospital bed arrangement may not consider the surgical conditions limit, but taking into account the surgeon's arrangements, usually cataract surgery and other eye surgery (except for emergencies) do not schedule on the same day. At present, the inpatient Department for all non-urgent patients are in accordance with the FCFS (first come, first serve) rules of hospitalization, but waiting for the patient queue is getting longer, the hospital hope you can use mathematical modelling to help solve the hospital bed reasonable arrangement problem, To improve the effective use of hospital resources.

Problem one: Try to analyze and determine a reasonable evaluation index system to evaluate the problem of the hospital bed arrangement model.

Question two: Try to establish a reasonable hospital bed arrangement model for the current situation of the inpatient department to determine which patients should be hospitalized on the second day according to the number of patients to be discharged on the next days. and evaluate your model using the index system in question one.

Question three: As a patient, nature wants to know early about when he will be hospitalized. Whether it is possible to inform the patient at the time of their approximate check-in interval based on the statistics of the hospitalized patients and the patients awaiting hospitalization.

Question four: If the inpatient department does not arrange surgery in Saturday and Sunday, would you please re-answer question two, should the hospital's operation schedule be adjusted accordingly?

Question five: It is proposed from a manageable point of view that, under normal circumstances, hospital bed arrangements may take the form of a roughly fixed proportion of the number of patients occupying beds, and try to establish a model for the shortest proportion of beds for all patients within the system, including the waiting time for admission and hospitalization, in this scheme.