# Day and Night: Locating the General Practitioner's Panel after Hours
## 1 Introduction  
Primary healthcare is the first step in treatment for most non-emergency health issues, and patients need to be able to easily access primary health services. Access to health services can be measured in many ways (e.g., geographically, financially, or timeliness), but when planning health resource locations, distance between patients and services is a typical measure of access [1]. Normally, patients have greater difficulty accessing health services as distance increases; thus, it is valuable to patients to reduce distance to services. Distance-based access can be optimised by modelling different objectives, such as minimising the average distance between patients and services, minimising the maximum distance travelled by any patient, or maximising the percentage of patients within an acceptable distance from the nearest service.  
It is possible to predict locations where general practitioners (GPs) or primary care practices (PCPs) will most effectively improve patient access based on these measures. In regions where there is a shortage of GPs, this represents an opportunity to determine where recruited physicians will be most effective at meeting needs for services. It is also a common problem in many countries that certain types of areas such as rural or urban hot spots are underserved per capita by primary care services [2]. In these cases, it is also valuable to determine the optimal placement of existing or additional GPs to promote balanced access.  
While meeting demands for patient service is crucial, it is also important to consider physician preferences for practice location, hours of service, and style of practice and the trade-offs with patient preferences for access [3]. For example, physicians typically prefer to have a large number of patients as part of their clinic (often referred to as the clinic's panel size) to ensure consistent work, but not so large as to be overwhelming; however, patients may prefer to be in smaller panels so their GPs have more frequent available appointments. GPs may also prefer working with multiple physicians rather than independently. This hasthe potential to improve access to patients through shared delivery of services or coverage of after-hours demand.  
In many areas, primary care services are provided differently during daytime and nighttime hours. Typically, when night services are offered by PCPs, physicians will pool panels to allow them breaks from working while covering for each other [4; 5]. While this means a greater panel size, fewer physicians, and greater distances for patients, this is typically acceptable since the expectation of services during night is lower and fewer patients use them. While there are optimisation models for primary care service locations, none are known to account for dual services such as the day and night primary care system. Usually, only-day services are considered, or day and night hours are considered separately. By accounting for both service periods within the same model, trade-offs between patient and provider preferences can be considered and improvements to patient and physician satisfaction can be obtained.