Simulated annealing approach for outpatient scheduling in a haemodialysis unit

: pp. 860–870
Received: August 11, 2022
Accepted: September 04, 2022

Mathematical Modeling and Computing, Vol. 9, No. 4, pp. 860–870 (2022)

Department of Mathematics and Statistics, Faculty of Science, University of Putra Malaysia
Department of Mathematics and Statistics, Faculty of Science, University of Putra Malaysia
Department of Mathematics and Statistics, Faculty of Science, University of Putra Malaysia
Department of Mathematics and Statistics, Faculty of Science, University of Putra Malaysia

National Renal Registry Malaysia has reported that the dialysis treatment demand among chronic kidney and end-stage kidney disease patients rises yearly.  However, available haemodialysis (HD) units have limited facilities to meet the current and increasing demand.  This leads to congestion, long waiting times, and an increase in the duration of treatment (DOT) among HD patients during their treatment sessions.  Two essential factors in providing optimal treatment plans are outpatient scheduling and nurse assignment.  Therefore, the objectives of this study are to minimise patients' total DOT, including the waiting time for pre-dialysis and post-dialysis sessions, which also includes determining the amount of patient flow in an HD unit.  Regarding the first objective, we include simulated annealing (SA) into our simple heuristics (SH) in the patient scheduling optimisation model.  Here, the initial solution obtained from the method can be improved.  The backtracking heuristic (BH) is then applied to the nurse assignment problem, where at least two nurses are needed for each dialysis patient.  The results show that the solutions obtained for outpatient scheduling by SA are efficient and have significantly reduced the computational time compared with the SH, even when considering more patients on the waiting list.  As for total DOT, we obtain the optimum value compared to the average DOT values for both 3-hour and 4-hour sessions.  Besides, a discrete-event simulation (DES) experiment of patient flow in an HD unit was performed by gradual variations in patient arrival rates, $\lambda$, to avoid congestion in the system.  DES has the potential to accommodate emergency patients that seek HD treatment without causing much disruption to the system.

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