Online scheduling in hospital theatre scheduling

Abstract

Increasing population across all age groups has contributed to the increasing demand for health care especially those that require surgeries, thus putting more pressure on hospitals. The inability to provide adequate and efficient treatment as a result of resource constraints causes patients to wait longer for treatment. Waiting for treatment due to unavailability of an operating theatre can result in both deteriorating health and inconvenience. It is even more frustrating when the scheduled operation is cancelled because some slots is used for emergency patients or the scheduled operations are longer that planned. When such situation occurs, some patients need to be rescheduled.

To resolve this problem, an operating theatre scheduling for emergency and regular patients is considered. We consider the single operating theatre problem across multiple days together with the multiple operating theatres problem on a single day. The aim is to minimise the cost incurred when patients need to be rescheduled as well as ensure minimal delay and rescheduling. We develop a model and design an algorithm to schedule operations for patients, taking into account their urgency. Patients’ urgency depends on their respective situation and changes depend on several factors.

Tackling the problem of scheduling single operating theatre, we use a heuristic method to provide a starting solution before applying local search and simulating annealing. The schedule is updated daily to take into account variations from planned durations and the arrival of emergency patients. The rescheduling of patients may be necessary. We consider the priority of patients and ensure that top priority patients be considered first in the scheduling and less important patients can be rescheduled if necessary.

Under the local search technique, we swap every pair of patients if they satisfy the conditions imposed. After the patients are swapped, we check the total cost of the swap and compare it with the current cost. If the new total cost is less than the current cost, the swap will be finalised. We then consider the next patient until all remaining patients in the list are accounted for and we come out with the new list of schedule.

Continuing from that, we utilise simulating annealing technique where we calculate the difference of the total cost (total new cost - total current cost), Δ between a pair of patients that we plan to swap. With this approach, as opposed to the local search procedure, even when the di↵erence of the total cost is positive, swapping might still take place but only with a certain probability.

Besides single operating theatre, we also consider the scheduling of multiple operation theatres in a single day. Rather than using the algorithm technique, we propose an integer programming model, the Zero-One Programming model and develop an algorithm that utilises the model in scheduling multiple parallel OTs. If a surgery runs longer that expected or an emergency patient arrived into the system, patients can be moved between the available OTs to ensure that surgeries can still be performed; or if the model decides it is better to reschedule therefore the patients will be rescheduled to the next day.

In order to test the efficiency of our models and look at the compatibility of the models with our algorithm, data are generated with different parameters to see if our proposed models have the ability to lower cost as well as prevent delays and rescheduling. Moreover, we check the computational time of our algorithm to ascertain whether it can provide solutions within a short amount of time. Overall, our models show improvement in reducing cost and minimising delay and rescheduling.

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Identifiers

ORCID for Marion Penn: orcid.org/0000-0002-7269-7981

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