Abstract Devising a model of the public orthodontic system in Ireland for young people using queuing theory tools so the system can be better understood and the most effective policy measures can be devised.1.
2 Background InIreland,theHSEprovidesfreeorthodontictreatmentforchildrenwiththemostsevereorthodontic problems as deemed with the Index of Treatment Need (IOTN) criteria. There are 16,092 children waiting for orthodontic treatment (as of March 2017 quarterly return). Many of these have been waiting for more than three years. It is extremely important that children are treated as early as possible, as early intervention is more cost effective and leads to better patient outcomes.1.
3 The Problem Thereiscurrentlynotenablewaytopredicttheresultsofpotentialpolicychanges(suchasincreasing the number of dentists or changing the scheduling policy) in this ?eld except to look at the effect of previous changes. Very little information can be gained from this, because with no way to control external variables, there is no way to really say what is impacting the system. This is the problem facing this area, with no suitable way of predicting the result of policy changes, inef?ciency arises and money can get wasted.
By applying queuing theory, it is possible to look at the possible effects of policy changes, allowing you to make an better informed choice when you are weighing them up.1.4 Current System Children with teeth deemed to be high enough on the IOTN scale are added to the waiting list. There is no consequential priority system and it works on a ?rst-come, ?rst-served (FCFS) basis. The Poisson distribution is applicable to the system as the system meets the established criteria.10 1.5 Methods 1.
k?N i.e. The event is something that can be counted in whole numbers. 2. Occurrences are independent, so that one occurrence neither diminishes nor increases the chance of another. 3. The average frequency of occurrence for the time period in question is known.
4. You can count how many events have occurred.1.5 Methods After receiving all the necessary data, I proceeded in testing different models until I had one that can accurately and consistently represent the current system. After doing this I established the current equilibrium through repeated testing and optimisation. I used this method because the system is complex and very volatile; small changes can have massive effects, simulation is the only way to test this system. This is because Utilization?100%. I used JSIMWiz and the Queuing Tool Pack Excel package to help me run my calculations and graph my results respectively.
Using the standard model building framework set out in Albin et al (1990) 1 I used queuing theory to achieve accurate macro results and then use simulation models to re?ne them.1.6 Key Results • If all variables were held except for arrival rate which increased by 10% (as population increases), wait time and queue length would tend to in?nity. • A 4% to 5% decrease in service time appears to be the most cost ef?cient decrease. • The most ef?cient appointment system is the least utilization method, using it could decrease queue length by more than 80%.1.7 Key Contributions OnceIhadsuccessfullyreplicatedthesystemIwasthenabletosimulatetheresultofpotentialpolicy changes.
This is done by adjusting variables such as?,? and the appointment method. This method couldallowpolicymakerstopredicttheresultsofpolicychangesbeforetheyareimplemented. From this the most effective policy measures can be selected thus saving money by increasing ef?ciency. I then worked on creating a base model which can be adapted to other areas in healthcare.1.8 Conclusions I have successfully modelled the Irish Public Orthodontic Treatment System over the course of a year to within 6% accuracy of the current system. The work presented in this project is novel, there is no evidence that I can ?nd which suggests that a regional orthodontic system has been modelled before.
This projects contributions are noteworthy because it solves a signi?cant issue in this area. Currently there is no effective way to predict the results of policy changes in this area but the model outlined in this project ?xes this issue. If this model was fully implemented it could dramatically cut queue lengths, save the state millions of Euro and improve children’s quality of care.
