A DECISION MODEL FOR CONTROLLING OUT-OF-POCKET EXPENSES THROUGH TELEMEDICINE ENGAGEMENT IN PRIMARY CARE

ABSTRACT

In resource-constrained developing countries like India, delivering low cost primary care services is a challenge. Patients requiring primary healthcare spend a sizeable amount on travel, medicines, diagnostic services etc. that leads to a rise in out-of-pocket (OOP) expenses. Encouraging telemedicine practices for primary healthcare can be helpful in reducing OOP payments by patients. Additionally, telemedicine also holds the potential to handle sudden healthcare demand in pandemics like COVID-19. This article presents an optimization model for regulating OOP payments by integrating telemedicine services in existing primary healthcare network. The objective is to maximize patient coverage by regulating OOP expenses simultaneously. A trade-off between new facilities and telemedicine services is to be obtained for this purpose. Solution methods based on greedy search and genetic algorithm have also been provided. The algorithms are novel as they are based on cost-effectivenss of the facility/telemedicine center that is driven by OOP expenses and establishment cost. Numerical experiments have been conducted for validating the proposed model and to derive useful insights for policy making.

Keywords:
location-allocation; out-of-pocket expense; primary healthcare; telemedicine; universal health coverage

1 INTRODUCTION

Universal health coverage requires financial protection towards getting desired health services. Traditional sources of healthcare financing include public health insurance, private health insurance, taxes and Out-of-pocket payments (Yusefi et al., 2022). Out-of-pocket (OOP) payments are a predominant source of financing healthcare. OOP expenditure includes direct expenses on consultation, medicines, diagnostic services along with expenses incurred on accommodation, travel, food, etc. (Bardhan & Kumar, 2018; Herberholz & Phuntsho, 2021). The OOP expenses increase financial health burden on families (Kord et al., 2022) and have a direct impact on the poverty level (Khan et al., 2017; Mulaga et al., 2022; Sangar et al., 2018). OOP health payment is a major problem for households as it affects their basic living standards (Mulaga et al., 2022; Sangar et al., 2022).

As elaborated in Leightner (2021), OOP health expenditure for a household consists of self-medication, sharing of cost and additional expense incurred by the household, regardless of being in contact with the healthcare provider or not. In developing countries like India, there is a lack of public health financing and insurance based financing and therefore health care expenses are primarily supported by OOP payments (Sangar et al., 2022). A major reason for a high proportion of OOP expenses is the inefficiency of existing primary care system (Yadav et al., 2021).

Primary healthcare includes preventive and curative services that should be accessible to every section of the society. An efficient primary care system is inevitable to increase patient footfall and reduce OOP payments (Barkley et al., 2020). Success of primary care depends on its accessibility (Sacks et al., 2020; Schaub et al., 2022) and lack of access to primary care services may lead to a large scale disease spread. This article presents an optimization model for improving the effectiveness of primary healthcare system by regulating OOP patient expenses.

Emergencies like COVID-19 increase the demand for primary care and delivery of primary care services becomes a challenge in such situations (Huston et al., 2020; Kadir, 2020; Alghanmi et al., 2022). It becomes inevitable to expand existing network of primary care services to deal with such a sudden rise in demand for primary care (Bailwal et al., 2020). Virtual practices like telemedicine may be used in such situations for the delivery of primary care services (Cooper-Jones et al., 2022; Krist et al., 2020; Vosburg & Robinson, 2022). These practices have the potential to provide proper and continuous healthcare services (Anthony Jnr, 2021) and should be an integral part of existing primary care system.

The study by Mishra & Sharma (2022) found telemedicine to be useful for reducing indirect costs incurred by patients of diabetes care system. Anthony Jnr (2021) advocated to integrate telemedicine into conventional medical care for ensuring efficient delivery of health services during and after the COVID-19 outbreak. Sindhu (2022) supports the adoption and implementation of virtual care services on a large scale in coming future. Dash & Sahoo (2021) asserts that developing countries like India should adopt digital health consultation practices for strengthening the deficient health system. The proposed study also advocates to integrate telemedicine services in existing primary healthcare network and provides an optimization framework for the same.

Finding location of facilities is an important strategic decision for a service system. It finds applications in various service systems, viz. retail, healthcare, banking, fire station, police station etc. In a health system, facility location decision is extremely important as it influences the health status of the society. An incorrect facility location decision in a healthcare system may result in adverse health outcomes. Numerous studies concerned with location-allocation in health are available and majority of healthcare location-allocation literature caters to emergency-free environments (Gulzari & Tarakci, 2021). Emergencies enforce a sharp rise in demand for care and swift location-allocation decision-making is needed in such situations (Wang et al., 2021). Further, a sustainable emergency response system requires judicious decision-making concerned with location and allocation of health facilities (Liu et al., 2021). The outbreak of COVID-19 in recent times necessitates to make telemedicine an integral part of the health system for handling emergencies (Portnoy et al., 2020; Xie et al., 2022). Gulzari & Tarakci (2021) and Gao et al. (2017) proposed location-allocation models for dealing with emergencies. This article also presents a location-allocation model for coalescing telemedicine in existing primary care network.

The maximal covering location problem (MCLP) proposed by Church & ReVelle (1974) is a useful location-allocation problem that looks for covering maximum population and finds applications in various areas, viz. health, retail, hotel, etc. (Celik Turkoglu & Erol Genevois, 2020). The importance of maximum population coverage increases in emergency situations. Numerous studies have demonstrated the utility of MCLP in health emergencies. Alizadeh et al. (2021) and Zhang et al. (2017) proposed MCLP based optimization frameworks for handling emergencies. Hassan et al. (2021) utilized MCLP for finding locations of field hospitals to control COVID-19 pandemic. Taiwo (2020) used MCLP in Nigeria to find locations of additional testing laboratories for COVID-19. This article also proposes an extension of MCLP for incorporating telemedicine services in the primary care network for regulating OOP expenditure.

Attractiveness of a primary care facility relies on its location to a great extent. Nearness to a primary care facility encourages patients to utilize its services and it also reduces their OOP expenses (Bardhan & Kumar, 2018). Therefore, patient preferences should be considered while identifying locations of primary care facilities. Kumar & Bardhan (2020) advocated to make use of patients preferences for increasing the utilization of primary care facilities to reduce excess load on hospitals. Adongo et al. (2021) conducted a study in Ghana to identify the determinants of patient choice towards use of hospitals. This article also considers patient-choice in the proposed decision making framework.

Geographical separation of facilities ensures their equitable distribution and it also influences their usage and effectiveness. The concept of anti-covering can be applied in location-allocation problems for ensuring equitable dispersion of facilities (Kumar & Bardhan, 2020). An application of anti-covering location model has been presented by Park et al. (2021) for ensuring social distancing inside indoor sports stadium to prohibit COVID-19 transmission. The work by Burtner & Murray (2022) deployed anti-covering methodology for reducing the risk of COVID-19 spread within office environment. Another useful application of anti-covering has been provided by Kumar & Bardhan (2020) for locating primary health centers to reduce excess load on hospitals. The study conducted by Chea et al. (2022) applied the concept of anti-covering for identifying locations of trauma centres. In this article, the methodology of anti-covering has been deployed to ascertain equitable distribution of new primary care facilities.

Objective of the study

This article provides a useful expansion of MCLP for integrating telemedicine services in primary healthcare network. The proposed optimization model finds a trade-off between new facilities and telemedicine for primary care. The objective is to maximize overall coverage by regulating OOP expenditure simultaneously. The model is a patient-choice model and considers anti-covering restrictions for new facilities to ensure equal dispersion of these facilities. The model also contains budget and capacity restrictions. To deal with larger instances efficiently, the article also presents greedy based heuristic and genetic algorithm based hybrid heuristic. These heuristics are driven by cost effectiveness (based on OOP expense and establishment cost) of the facility/telemedicine center.

The next section presents a brief review of related work. Section 3 presents assumptions of this study and the proposed optimization model. Solution methods based on greedy search and genetic algorithm are provided in Section 4. Section 5 presents numerical experiments for validating the proposed model. Section 6 presents conclusion.

2 LITERATURE REVIEW

Primary healthcare is the foundation of a health system that mainly emphasizes accessibility (Cu et al., 2021), equity (Clark et al., 2021) and comprehensive care (Singh et al., 2024). Primary healthcare is a cost-effective mechanism for achieving universal health coverage (Singh et al., 2021) as it helps in minimizing unnecessary hospitalizations and specialist visits. However, there are some concerns in the context of primary healthcare that need to be addressed, e.g. out of pocket expenses incurred by patients. Out-of-pocket expenses may be regarded as payments made by patients for availing healthcare services that are not covered by insurance (Fan et al., 2024) and include payments towards consultations, diagnostics, medications, and follow-up care (Du et al., 2022). In low and middle income countries like India, excessive out-of-pocket expenditures may be regarded as a leading cause of financial hardships (Kumar, 2022b). Therefore, a high proportion of out-of-pocket expenditure in health financing weakens the primary healthcare system.

It is essential to maintain a balance between accessibility and affordability for improving the efficiency of a primary healthcare system. Integration of telemedicine services within the primary care system may help in this regard to a great extent as these services have the potential to reduce the geographical barriers. It is important to find a trade-off among primary care facilities and telemedicine servers to ensure maximum patient coverage at minimum cost. In this article, we have proposed a useful extension of the MCLP for finding a trade-off between primary healthcare facilities and telemedicine servers to regulate out-of-pocket expenditure. Next, we provide a brief discussion on the importance of telemedicine and maximal covering location problem in healthcare.

2.1 Role of telemedicine in health care

Virtual care practices ensure smooth delivery of primary care by regulating congestion and thereby improving the utilization (Ohannessian, 2015; Wang et al., 2019). Further, virtual care practices can cater to a larger population in addition to being cost-effective as compared to traditional practices of healthcare delivery (Borycki & Kushniruk, 2022; Gulzari & Tarakci, 2021). Therefore, these practices help in improving the access to care in addition to upgrading the quality of services (Mehrotra et al., 2016; Xie et al., 2022). Kadir (2020) and Jnr (2020) highlighted the significance of digital practices like telemedicine for dealing with emergencies like COVID-19.

Sindhu (2022) advocated the large scale implementation of virtual care services. The study identifies that trust of patients is significant for ensuring widespread acceptance of virtual care services. Patient trust depends on doctor-patient relationship and quality and extent of healthcare services. However, patients also have various concerns related to virtual care services, viz. accessibility issues due to internet, software and internet related cost concerns, security and privacy concerns etc. Dash & Sahoo (2021) advised the adoption of digital health for strengthening health system. Additionally, the study highlights gender as a significant moderating variable towards implementation of virtual healthcare services. Daly et al. (2022) carried out a study to understand the influence of telehealth on mental healthcare and found these services to be accessible and time efficient in comparison to physical visits. However, telehealth cannot be a replacement for face-to-face interactions and users of telehealth services have privacy and security concerns.

Telemedicine uses digital technology to provide health care services. Telemedicine reduces the dependence on physical visits and is a cost-effective option to both patients and healthcare providers. To carry out emergency relief operations during natural disasters, telemedicine may be very helpful in building well-planned medical response team. Gulzari & Tarakci (2021) advocated to make use of telemedicine in disaster situations and provided a mathematical model for its implementation. Xiong et al. (2012) and Delana et al. (2023) discuss the usefulness of telemedicine in the context of emergency responses, but they have not provided any mathematical model. Kumar (2022a) provided a location-allocation model for integrating telemedicine into primary healthcare, for reducing the burden of primary care on existing public health facilities.

2.2 Maximal covering location problem in primary healthcare

The maximal covering location problem was first introduced by Church & ReVelle (1974) that was focused on locating warehouses to cover maximum population within a specific distance. Some of the recent works on MCLP include Chouksey et al. (2022) that utilized MCLP for establishing maternal healthcare facilities. The article by Pan et al. (2023) provided a two-step maximal covering location model for evaluating spatial accessibility of tertiary hospitals. The work by Mendoza-Gómez & Ríos-Mercado (2022) used MCLP for identifying new primary care facilities along with upgrading existing facilities. Vatsa & Jayaswal (2021) proposed a multi-period formulation of MCLP for reassigning doctors to non-operational primary healthcare facilities. Manupati et al. (2021) discussed a location-allocation problem for establishing convalescent plasma bank facilities. Kumar (2023) provided an extension of MCLP for finding a trade-off between new primary care facilities and telemedicine based facilities.

Table 1 presents a comparison of this study with recent literature on related work.

Table 1
Related work.

Article	Objective Type	Objective Function	Model Type	Algorithm	Location Decision	Allocation Decision	Patient Expenses	Case Study
This Study	Max.	Patient Coverage	MILP	Greedy Search and Genetic Algorithm	Primary Care facilities and Telemedicine servers	Demand for primary care	✓	-
Mendoza-Gómez & Ríos-Mercado (2024)	Min.	Travel Distance	ILP	Iterative Greedy Search	Healthcare Units	Demand Points	×	Mexico
Vázquez-Serrano et al. (2024)	Max.	Treatment Quality	MILP	Two Phase Heuristic	-	Patients to Exam Room	×	Mexico
Kumar (2023)	Max.	Demand	MILP	-	Primary Care and Telemedicine Based Facilities	Demand for primary care	×	Delhi, India
Pan et al. (2023)	Max.	Polpulation Coverage	ILP	-	Hospitals	Residential Locations	×	Chengdu, China
Chouksey et al. (2022)	Min.	Overall Costs	MILP	Simultaneous & Sequential Approach	Maternal Care Facilities	Mother-to-be	✓	Chandauli, Uttar Pradesh
Kumar (2022a)	Min.	Patient Load	MILP	Greedy Based Heuristic	Primary Care and Teleconsultation Based Facilities	Demand for Primary Care	×	Delhi, India
Kumar (2022b)	Min.	Patient Expenses	MILP	Greedy Based Heuristic	Capacity Reconfiguration and public-private partnership decisions	Demand for primary care	✓	-
Mendoza-Gómez & Ríos-Mercado (2022)	Max.	Coverage of Complementary Services	ILP	Augmented ε-constraint	Primary Care Facilities (location & upgradation)	Outpatient Service	×	Mexico
Pourrezaie-Khaligh et al. (2022)	Min. and Max.	Min. Cost & Inequity, Max. accessibility	MINLP	Enhanced Tabu Search Based Algorithm	Primary Care Facilities	Multi-Period Demand	×	Ardabil, Iran
Manupati et al. (2021)	Min.	Travel Time and Cost	MILP	NonnDominated Sorting Genetic Algorithm-III	Plasma banks	Plasma Collection Facilities	×	India
Vatsa & Jayaswal (2021)	Max.	Demand	MIP	Benders Decomposition	Primary Health Centres	Doctors	×	Lohardaga, Jharkhand

• Abbreviations: ILP - Integer Linear Programming; MIP - Mixed Integer Programming; MILP - Mixed Integer Linear Programming; MINLP- Mixed Integer Non Linear Programming.

3 METHODOLOGY

Public health systems in developing countries require substantial improvements to be of internally acceptable standards. A sound primary care system is needed to improve the effectiveness of existing public health system. Numerous obstacles arise that are hard to transcend; one of the major impediments is out-of-pocket expenditure. A location-allocation decision framework engaging telemedicine has the potential to address this concern. Inclusion of patient-choice in the framework improves the practicality of the framework. A choice-based optimization model engaging telemedicine services is presented below for regulating OOP expenditure. The model is based on following assumptions:

Patients depend on primary care facilities and telemedicine for primary care needs.

1. OOP expenditures are costs incurred on travel, medicines, diagnostic tests and waiting for service.

2. The model is a discrete-choice model.

3. To ensure equitable distribution of primary care facilities, a minimum separation distance is used.

4. Budget is limited for decision-making.

5. Capacities of facilities and telemedicine services are limited.

3.1 Optimization model for regulating OOP payments

Consider a region that requires a primary healthcare network engaging telemedicine services. Locations of new primary care facilities along with identification of telemedicine opportunities are needed for the program. The program requires locating new primary care facilities and identifying telemedicine opportunities. The intention is to maximize primary care coverage by regulating OOP expenditure. Let us say, P _i represents primary care demand in region i∈I while j ₁∈J ₁ is a probable location for locating a new primary care facility and j ₂∈J ₂ represents a telemedicine based facility. Define J=J ₁∪J ₂.

Consider a binary parameter a _ij , i∈I, j∈J ₁ that captures patient preferences for a new physical facility in region i at j∈J ₁. If the facility j∈J ₁ is preferred by patients in region i, then a _ij takes the value 1 else it is 0. Similarly, b _ij , i∈I, j∈J ₂ is a binary parameter that captures the patient-choice for patients in region i for telemedicine services at j∈J ₂. By expanding the maximal covering location model (Church & ReVelle, 1974), the model presented below maximizes patient coverage by new facilities and telemedicine collectively by regulating OOP expenditure.

Optimization model

$Maximize\sum _{i\in I}\sum _{j\in J_1}{P}_i{X}_{ij}+\sum _{i\in I}\sum _{j\in J_2}{P}_i{Y}_{ij}$ (1)

subject to

$\begin{array}{cc}\sum _{j\in J_1}{a}_{ij}{X}_{ij}+\sum _{j\in J_2}{b}_{ij}{Y}_{ij}=1& \forall i\in I\end{array}$ (2)

$\sum _{j\in J_1}{\theta }_{1j}{U}_j+\sum _{j\in J_2}{\theta }_{2j}{V}_j\le B$ (3)

$\begin{array}{cc}\sum _{i\in I}{P}_i{X}_{ij}\le {\alpha }_j^1& \forall j\in J_1\end{array}$ (4)

$\begin{array}{cc}\sum _{i\in I}{P}_i{Y}_{ij}\le {\alpha }_j^2& \forall j\in J_2\end{array}$ (5)

$\begin{array}{cc}\beta \left(1-U_j\right)\ge \sum _{k\in T_j}{U}_k& \forall j\in J_1\end{array}$ (6)

$\begin{array}{cc}{X}_{ij}\le U_j& \forall i\in I,j\in J_1\end{array}$ (7)

$\begin{array}{cc}{Y}_{ij}\le V_j& \forall i\in I,j\in J_2\end{array}$ (8)

$\sum _{i\in I}\sum _{j\in J_1}{P}_i\left(t_{ij}+E_j\right)\left(X_{ij}\right)+\sum _{i\in I}\sum _{j\in J_2}{P}_i\left(t_{ij}+E_j\right)\left(Y_{ij}\right)\le E_{max}$ (9)

$\begin{array}{cc}{X}_{ij}\in \left[0,1\right]& \forall i\in I,j\in J_1\\ Y_{ij}\in \left[0,1\right]& \forall i\in I,j\in J_2\\ U_j\in \left\{0,1\right\}& \forall j\in J_1\\ V_j\in \left\{0,1\right\}& \forall j\in J_2\end{array}$

Additional notations deployed are explained below:

θ_1j and θ_2j represent costs of locating new facility at j∈J ₁ and starting telemedicine services at j∈J ₂ respectively; U _j and V _j respectively are binary variables indicating location of new facility at j∈J ₁ and starting telemedicine services at j∈J ₂; X _ij and Y _ij represent coverage of population in region i by facility at j∈J ₁ and telemedicine service at j∈J ₂ respectively; ${\alpha }_j^1$ and ${\alpha }_j^2$ are capacities of new facility at j∈J ₁ and telemedicine service at j∈J ₂ respectively; B is available budget; T _j ={k∈J ₁: for k≠j, d _kj ≤D}; d _kj is distance between k and j; D is separation distance for new facilities; β is a very large number. Total OOP expenditure resulting from patients in region i using primary care services at j∈J, is the sum of travel cost (t _ij ) and expenses incurred on medicines, diagnostic services and waiting for service (E _j ); E _max is the limit on OOP payments in the system.

The function (1) maximizes the collective coverage of new facilities and telemedicine services. Constraint (2) is covering constraint and ensures coverage of population in region i either through new facility or telemedicine. (3) is the budget constraint while (4) and (5) are capacity restrictions. Constraint (6) guarantees equal distribution of new primary care facilities. Contingency conditions are given by constraints (7) and (8). Constraint (9) controls the OOP expenditure.

4 SOLUTION METHODS

The proposed optimization model is an integer programming based formulation. Such formulations are computationally complex and solution methods are needed to deal with larger instances efficiently. In this article, we have proposed two solution methods based on greedy search and genetic algorithm. The working of both the algorithms is given below:

4.1 Greedy based heuristic

Greedy Search Algorithm is a fundamental heuristic approach that provides practical and efficient solution for location-allocation problems. An adaptation of the greedy search heuristic for a facility location problem can be found in Guha & Khuller (1999). This section presents a greedy based heuristic for the proposed problem as a 2-stage procedure. In stage 1, the algorithm seeks to evaluate the cost-effectiveness value for every decision pertaining to allocation of a facility to a population and performs allocation of the facility to the population based on higher cost-effectiveness value. The cost-effectiveness value is a function of demand, cost associated with location decision and patient out-of-pocket payments. Then, the heuristic executes the location decision based on this assignment. The notations defined before have been used in the following procedure.

4.1.1 Step 0: Inputs and Initialization

Set U _j =0, X _ij =0∀i∈I, j∈J ₁.

Set V _j =0,Y _ij =0∀i∈I, j∈J ₂.

Initialize: density Pi∀i∈I, preferences a _ij ∀i∈I, j∈J ₁, b _ij ∀i∈I, j∈J ₂, establishment costs (θ_1j ∀j∈J ₁ & θ_2j ∀j∈J ₂), capacities ${\alpha }_j^1\forall j\in J_1,{\alpha }_j^2\forall j\in J_2$, travel cost t _ij ∀i∈I, j∈J, miscellaneous expenses E _j ∀j∈J, available budget B and OOP expense limit E _max and set $J_1^{\text{'}}=\left\{\right\}$.

Define total coverage $T=\sum _{i\in I}{P}_i·\left(\sum _{j\in J_1}{X}_{ij}+\sum _{j\in J_2}{Y}_{ij}\right)$.

4.1.2 Step 1: Cost-Effectiveness Matrix

The proposed greedy based heuristic is based on a cost-effectiveness matrix, CE=[CE _ij ]. This matrix provides cost-effectiveness values associated with establishing a facility j∈J in a region i∈I. The cost-effectiveness value is a function of a user-defined parameter γ∈[0, 1], patient density Pi, normalized density to OOP expense ratio ${\overline{M}}_{ij}$, and normalized density to establishment cost ratio ${\overline{N}}_{ij}$ (Algorithm (1)).

Algorithm 1
Greedy Based Heuristic (Pseudo code).

The cost-effectiveness (CE) matrix can be constructed as follows:

$C{E}_{ij}=\gamma *{\overline{M}}_{ij}+\left(1-\gamma \right)*{\overline{N}}_{ij}$

The matrices consisting of density to OOP expense ratios (M _ij ) and density to establishment cost ratios (N _ij ) are constructed as given below:

$M_{ij}=\left\{\begin{array}{l}\frac{P_i}{a_{ij}·t_{ij}+E_j}\forall i\in I\&j\in J_1\\ \frac{P_i}{b_{ij}·t_{ij}+E_j}\forall i\in I\&j\in J_2\end{array}\right.$

and

$N_{ij}=\left\{\begin{array}{l}\frac{P_i}{{\theta }_{1j}}\forall i\in I\&j\in J_1\\ \frac{P_i}{{\theta }_{2j}}\forall i\in I\&j\in J_2\end{array}\right.$

We normalize both these ratios (M _ij and N _ij ) to generate ${\overline{M}}_{ij}$ and ${\overline{N}}_{ij}$ respectively to ensure that all matrices have consistent scales for comparison. These normalized matrices can be calculated as given below:

${\overline{M}}_{ij}=\frac{M_{ij}-mi{n}_{k\in J_1}\left\{M_{ik}\right\}}{mi{n}_{k\in J_1}\left\{M_{ik}\right\}-mi{n}_{k\in J_1}\left\{M_{ik}\right\}}\forall i\in I\&j\in J_1$

and

${\overline{N}}_{ij}=\frac{N_{ij}-mi{n}_{k\in J_2}\left\{N_{ik}\right\}}{mi{n}_{k\in J_2}\left\{N_{ik}\right\}-mi{n}_{k\in J_2}\left\{N_{ik}\right\}}\forall i\in I\&j\in J_2$

The user-defined parameter ‘γ’ allows for finding a trade-off between minimizing out-of-pocket expenditure and minimizing facility cost. A higher ‘γ’ indicates that cost-effectiveness being driven by minimum out-of-pocket expense while a lower ‘γ’ prioritizes minimum facility cost for computing cost-effectiveness values. If γ=0.5, then both the criteria are considered equally important. Sensitivity analysis can be conducted by varying the values of ‘γ’. Next, allocation and location decisions will be executed based on the cost-effectiveness matrix generated in this step.

4.1.3 Step 2: Allocation and Location

Define $C{E}_{ij}^{max}=Max\left\{C{E}_{ij}:i\in I,j\in J\right\}$. The algorithm seeks for maximum cost-effectiveness value in the matrix. If a cost-effectiveness value is highest for a facility at ‘j∈J’ when population in region ‘i∈I’ utilizes its services, then the algorithm assigns population in ‘i∈I’ to facility at ‘j∈J’ and thereby locates a facility at ‘j∈J’(see flowchart in figure 1). The allocation and location tasks are executed as given below:

Figure 1
Flowchart for Greedy Based Heuristic.

If $C{E}_{ij}^{max}=C{E}_{ij}$, where i∈I, j∈J ₁, then assign population i∈I to a new facility at j∈J ₁ by updating X _ij , where i∈I, j∈J ₁, as given below:

$X_{ij}=\left\{\begin{array}{c}\frac{{\alpha }_j^1}{P_i}if0<P_i\le {\alpha }_j^{1}and{d}_{kj}<D\forall k\in J_1^{\text{'}},i\in I\&j\in J_1\\ 1if{P}_i>{\alpha }_j^{1}and{d}_{kj}>D\forall k\in J_1^{\text{'}},i\in I\&j\in J_1\\ 0if{P}_i=0,i\in I\&j\in J_1\end{array}\right.$

and update U _j =1, B=B-θ_1j ·U _j , ${\alpha }_j^1={\alpha }_j^1·\left(1-X_{ij}\right)$, E _max =E _max -P _i ·X _ij ·(t _ij +E _j ), P _i =Pi·(1-X _ij ), CE _ij =-1 and insert j in the set $J_1^{\text{'}}$.

Otherwise, if $C{E}_{ij}^{max}=\left\{C{E}_{ij},i\in I,j\in J_2\right\}$, then assign population i∈I to a telemedicine center at j∈J ₂ by updating Y _ij , i∈I, j∈J ₂, as given below:

$Y_{ij}=\left\{\begin{array}{c}\frac{{\alpha }_j^2}{P_i}if0<P_i\le {\alpha }_j^2,i\in I\&j\in J_2\\ 1if{P}_i>{\alpha }_j^2,\forall i\in I\&j\in J_2\\ 0if{P}_i=0,\forall i\in I\&j\in J_2\end{array}\right.$

and update V _j =1, B=B-θ_2j ·V _j , ${\alpha }_j^2={\alpha }_j^2·\left(1-Y_{ij}\right)$, E _max =E _max -P _i ·Y _ij ·(t _ij +E _j ), P _i =P _i ·(1-Y _ij ), CE _ij =-1.

4.1.4 Step 3: Termination criterion

The algorithm terminates when one or more of the following conditions are reached:

• The remaining budget $\overline{B}<{\theta }_j,\forall j\in J$, where θ_j =θ₁, for j∈J ₁ and θ_j =θ_2j , for j∈J ₂

• Patient density (remaining) ${\overline{P}}_i=0,\forall i\in I$.

• Facility capacity (remaining) ${\alpha }_j^1=0,\forall j\in J_1$ and ${\alpha }_j^2=0,\forall j\in J_2$

• $\sum _{i\in I}\sum _{j\in J_1}{P}_i\left(t_{ij}+E_j\right)\left(X_{ij}\right)+\sum _{i\in I}\sum _{j\in J_2}{P}_i\left(t_{ij}+E_j\right)\left(Y_{ij}\right)>E_{max}$.

• Cost-effectiveness values, CE _ij =-1,∀i∈I, j∈J.

• A predefined calculation time limit is exceeded.

4.2 Genetic based hybrid heuristic

A Genetic Algorithm (GA) is a computational optimization technique inspired by natural selection and genetics. It operates by maintaining a population of potential solutions (chromosomes) and evolves them over generations. Through processes like selection, crossover (recombination), and mutation, GAs gradually improve the solutions by exploring the solution space. The fittest individuals are more likely to be selected for reproduction, mimicking the survival of the fittest theory (Bhattacharjee & Mukhopadhyay, 2023). GAs are widely used for solving complex optimization problems in various domains, from engineering to finance, offering a versatile and robust search method. Different applications of the GAs along with a detailed explanation can be found in: Katoch et al. (2021). An adaptation of the genetic algorithm is provided in the article: Rahmani & MirHassani (2014).

The proposed hybrid algorithm also works in 2 stages (Algorithm 2). In stage 1, the algorithm executes the location decision based on genetic algorithm. In stage 2, the algorithm performs allocation of a facility to the population based on higher cost-effectiveness value.

Algorithm 2
Genetic based hybrid Algorithm (Pseudo-code).

For the development of the genetic algorithm, U _j and V _j can be considered as vectors of cardinality J ₁ and J ₂ respectively. The vectors U and V represent the solution of the algorithm. There are two other decision variables involved, viz. X _ij and Y _ij . Since, X _ij ,Y _ij ∈[0, 1], greedy search technique based on cost-effectiveness value has therefore been applied for generating these variables to avoid slow convergence in the algorithm.

The working of the proposed genetic based hybrid algorithm is explained below:

Stage 1: Location using Genetic algorithm

• Step 0: Initialization: The Genetic Algorithm (GA) begins with an initial population of different chromosomes (feasible solutions). Each possible solution represents a set of facilities to be established. Define U _j =0∀j∈J ₁, V _j =0∀j∈J ₂, and $J_1^{\text{'}}=\left\{\right\}$.

• Step 1: Chromosome Development In this genetic algorithm, a chromosome is represented as a binary array, where each bit (or gene) corresponds to a facility. If the gene is set to 1, it indicates that the facility is established; otherwise, if it is 0, the facility is not established. The initial basic feasible solution, or chromosome, is a binary vector that includes both new facilities and telemedicine centers. For instance, a chromosome looks like [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], where the first six elements represent the establishment decision of new facilities and the next six represent the establishment decision of telemedicine centers. Therefore, the chromosome in this algorithm is a set of U∪V where vector U=[U _j ] where all j∈J ₁ and vector V=[V _j ] where all j∈J ₂.

• To create a chromosome select any j randomly from the set J=J ₁∪J ₂. If j∈J ₁, select any random value for U _j , where U _j ∈{0, 1}, now if U _j is 1 and d _kj ≤D for any $k\in J_1^{\text{'}}$ then change U _j =1-U _j , and if j∈J ₂, select any random value for V _j , where V _j ∈{0, 1} and remove this j from the set J. Repeat this process until J becomes an empty set.

• Step 2: Fitness Evaluation The fitness function assesses the performance of the solution. In the given context, fitness is based on establishment cost of facilities. Therefore the fitness function $=\sum _{j\in J_1}{U}_j·{\theta }_{1j}+\sum _{j\in J_2}{V}_j·{\theta }_{2j}$.

• Step 3: Population Development Let the population size be pop size. Repeat step 1 till number of chromosomes=pop size.

• Step 4: Parent Selection A selection process is used to choose individuals for the next generation. The random selection method is being used and a subset of k solutions is selected from the population initially. A set of 2 solutions (parents) is then selected from this subset based on fitness values.

• Step 5: Crossover Crossover is the process of combining genetic material from two parents from a selected population to create two offspring (child). In the given context, it signifies the combination of facility choices of two solutions to create two new solutions. Single-point crossover has been applied to the parents to generate two children.

• Step 6: Mutation Mutation is the process of introducing small random changes to an individual’s genetic code. In the given context, mutation may represent the selection or deselection of a facility. Mutation ensures diversity in the population and can help escape local optima. For a chromosome like [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], select a random point and flip its value, if it is 0 replace it with 1 and vice versa if it satisfies d _kj >D∀j, k∈J ₁. Perform the mutation process for both the children generated in step 5 and recognize these children as the mutated children.

• Step 7: New Population Insert the mutated children into the new population. Repeat steps 4, 5 and 6 until required number of iterations are performed.

• Step 8: Update population Select the best chromosome from the new population created in step 7. Calculate the fitness of this chromosome and replace the worst chromosome in the old population created in step 3 with this chromosome. Repeat step 7 until maximum number of generations are performed.

• Step 9: Best Chromosome Selection The algorithm terminates after required number of generations are passed. The best chromosome obtained from the updated population obtained in step 8 has been selected based on the fitness function provided in step 2. This solution provides established facilities under a given budget.

Stage 2: Allocation based on cost-effectiveness: A cost-effectiveness matrix (as defined in section 4.1) will be constructed in this stage. The population will be allocated to the facilities/telemedicine centers identified in stage 1 on the basis of greedy search methodology. This process is explained below.

For all U _j =1, j∈J ₁ and V _j =1, j∈J ₂, calculate, $C{E}_{ij}^{max}=Max\left\{C{E}_{ij},i\in I,j\in J=J_1\cup J_2\right\}$.

If $C{E}_{ij}^{max}=\left\{C{E}_{ij},i\in I,j\in J_1\right\}$, then assign population i∈I to a new facility at j∈J ₁ by updating X _ij , i∈I, j∈J ₁, as given below:

$X_{ij}=\left\{\begin{array}{c}\frac{{\alpha }_j^1}{P_i}if0<P_i\le {\alpha }_j^1,i\in I\&j\in J_1\\ 1if{P}_i>{\alpha }_j^1,i\in I\&j\in J_1\\ 0if{P}_i=0,i\in I\&j\in J_1\end{array}\right.$

and update B=B-θ_1j ·U _j , ${\alpha }_j^1={\alpha }_j^1·\left(1-X_{ij}\right)$, E _max =E _max -P _i ·X _ij ·(t _ij +E _j ), P _i =P _i ·(1-X _ij ), CE _ij =-1.

Otherwise, if $C{E}_{ij}^{max}=\left\{C{E}_{ij},i\in I,j\in J_2\right\}$, then assign population i∈I to a telemedicine center at j∈J ₂ by updating Y _ij , i∈I, j∈J ₂, as given below:

$Y_{ij}=\left\{\begin{array}{c}\frac{{\alpha }_j^2}{P_i}if0<P_i\le {\alpha }_j^2,i\in I\&j\in J_2\\ 1if{P}_i>{\alpha }_j^2,\forall i\in I\&j\in J_2\\ 0if{P}_i=0,\forall i\in I\&j\in J_2\end{array}\right.$

and update B=B-θ_2j ·V _j , ${\alpha }_j^2={\alpha }_j^2·\left(1-Y_{ij}\right)$, E _max =E _max -P _i ·Y _ij ·(t _ij +E _j ), P _i =P _i ·(1-Y _ij ), CE _ij =-1.

Termination criterion The algorithm terminates when one or more of the following conditions are reached:

• The remaining budget $\overline{B}<{\theta }_j,\forall j\in J$, where θ_j =θ_1j , for j∈J ₁ and θ_j =θ_2j , for j∈J ₂

• Patient density (remaining) ${\overline{P}}_i=0,\forall i\in I$.

• Facility capacity (remaining) ${\alpha }_j^1=0,\forall j\in J_1$ and ${\alpha }_j^2=0,\forall j\in J_2$.

• $\sum _{i\in I}\sum _{j\in J_1}{P}_i\left(t_{ij}+E_j\right)\left(X_{ij}\right)+\sum _{i\in I}\sum _{j\in J_2}{P}_i\left(t_{ij}+E_j\right)\left(Y_{ij}\right)>E_{max}$.

• Cost-effectiveness values, CE _ij =-1,∀i∈I, j∈J.

• A predefined calculation time limit is exceeded.

The flowchart and pseudo-code of the proposed genetic algorithm can be seen in Figure 2 and Algorithm 2 respectively.

Figure 2
Flowchart for Genetic based hybrid Algorithm.

5 NUMERICAL ILLUSTRATION

This section presents a numerical experiment for validating the proposed model. Consider 12 regions, viz. R1, R2, ..., R12 with demand for primary care as presented in Table 2.

Table 2
Population and site characteristics.

Population characteristics			Site characteristics new facility
Region	Demand	Preferred locations for new facility	Site	Neighborhood	Establishment cost
R1	81	F1, F3, F5	F1	F2	52
R2	112	F1, F3, F4
R3	95	F1, F3, F4, F5, F6	F2	F1, F6	48
R4	72	F1, F2, F4
R5	108	F1, F4, F5	F3	F4, F5	64
R6	124	F1, F4, F6
R7	89	F1, F3, F5	F4	F3	45
R8	118	F2, F5
R9	78	F2, F5, F6	F5	F3	55
R10	65	F2, F3, F6
R11	92	F2, F3, F5	F6	F2	65
R12	105	F2, F3, F6

Six sites have been identified for new facilities, viz. F1, F2, F3, F4, F5, F6 and six telemedicine based facilities (F7, F8, F9, F10, F11, F12) have been identified. Population density and preference for new facility for each region is displayed in Table 2. Table 2 also presents the facilities lying in the anti-covering range for each facility.

Table 3 presents the travel cost values between respective regions and facilities. Expenses incurred on medicines, diagnostic services, waiting etc. concerned with visit to primary care facility are taken as 200 while the same cost for each telemedicine service is assumed as 250. Each telemedicine based facility is preferred by all the regions for primary care services. Set-up cost for each teleconmedicine service is assumed to be 25. Capacity of a new facility is taken as 150 and that of telemedicine as 100. By varying the parameters of the model, the sensitivity analysis has been conducted. Results of the sensitivity analysis are presented in Tables 4, 5, 6 and 7.

Table 3
Travel Cost Matrix.

Region	Demand	Facility (Travel cost from region to facility)
		F1	F2	F3	F4	F5	F6	F7	F8	F9	F10	F11	F12
R1	81	30	40	45	15	25	20	0	0	0	0	0	0
R2	112	50	25	20	45	30	35	0	0	0	0	0	0
R3	95	20	15	45	50	15	25	0	0	0	0	0	0
R4	72	40	25	20	40	35	15	0	0	0	0	0	0
R5	108	20	10	35	50	35	30	0	0	0	0	0	0
R6	124	25	45	50	20	10	40	0	0	0	0	0	0
R7	89	35	40	10	30	15	50	0	0	0	0	0	0
R8	118	20	15	35	10	40	45	0	0	0	0	0	0
R9	78	25	40	20	45	35	20	0	0	0	0	0	0
R10	65	30	15	20	40	25	50	0	0	0	0	0	0
R11	92	25	40	45	35	45	15	0	0	0	0	0	0
R12	105	20	35	50	15	40	10	0	0	0	0	0	0

Table 4
Sensitivity analysis budget variations.

Budget	Coverage	Telemedicine	Tele coverage	New facilities	New facilities coverage
50	17.56%	2	17.56%	-	0%
100	35.12%	4	35.12%	-	0%
150	52.68%	6	52.68%	-	0%
200	65.85%	6	52.68%	1	13.17%
250	79.02%	6	52.68%	2	26.34%
300	92.19%	6	52.68%	3	39.51%
350	96.58%	5	43.90%	4	52.68%
400	100%	6	52.68%	4	47.32%

Table 5
Sensitivity analysis OOP variations.

OOP Expense	Coverage	New facilities	Coverage of new faciliites	Telemedicine	Coverage of Telemedicine
10,000	4.18%	4	4.18%	6	0%
20,000	8.36%	4	8.36%	6	0%
30,000	12.54%	3	12.54%%	6	0%
40,000	16.72%	3	16.72%	6	0%
50,000	20.73%	3	20.73%	6	0%
60,000	24.72%	3	24.72%	6	0%
70,000	28.71%	3	28.71%	6	0%
80,000	32.70%	3	32.70%	6	0%
90,000	36.69%	3	36.69%	6	0%
100,000	40.63%	4	40.63%	6	0%
150,000	59.42%	4	52.68%	6	6.74%
200,000	76.98%	4	52.68%	6	24.30%
250,000	94.54%	4	52.68%	6	41.86%
270,000	100%	4	47.32%	6	52.68%

Table 6
Sensitivity analysis capacity variations.

Capacity new facility	Capacity teleconsultation	Overall coverage	New facilities coverage	Telemedicine coverage
19	12	12.99%	6.67%	6.32%
38	25	26.51%	13.35%	13.16%
75	50	52.68%	26.34%	26.34%
112	75	78.84%	39.33%	39.51%
150	100	100%	47.32%	52.68%

Table 7
Sensitivity analysis combined experiment.

Budget	OOP expense	Capacity new facility	Capacity teleconsultation	Overall coverage	New facilities coverage	Telemedicine coverage
50	10,000	19	12	4.08%	4.08%	0%
50	10,000	150	100	4.08%	4.08%	0%
50	270,000	19	12	2.11%	0%	2.11%
50	270,000	150	100	17.56%	0%	17.56%
400	10,000	19	12	4.14%	4.14%	0%
400	10,000	150	100	4.18%	4.18%	0%
400	270,000	19	12	12.99%	6.67%	6.32%
400	270,000	150	100	100%	47.32%	52.68%

The proposed model was applied on the data given in Section 5. It was initially solved at different levels of budget and experimental results are presented in Table 4. OOP expenditure was fixed as 270,000 for this experiment. As expected, overall coverage increases with increment in levels of budget (Figure 3). Variations were seen in the combinations of new facilities and telemedicine servers and a definite trend was not observed (Figure 4). Number of telemedicine contracts surpass number of new facilities at all budget levels. This is due to the application of anti-covering restrictions on new facilities. In the existing set-up, complete coverage could be achieved at budget level of 400.

Figure 3
Experiment Budget vs Coverage.

Figure 4
Experiment Budget vs Count of facilities.

Next, the model was tested at different levels of OOP expenditure. Budget was fixed as 400 for this experiment. Experimental results can be found in Table 5. It was observed that telemedicine services are not required when OOP expense is low and need of telemedicine services arises when the system experiences a higher OOP expenditure (Figure 5).

Figure 5
Experiment OOP expense vs Coverage.

The model was later observed by varying the levels of capacities of new facilities and telemedicine services. A proportionate change in the capacity levels of new facilities and telemedicine was made for the experiment. Budget and OOP expense were fixed at 400 and 270,000 for conducting this experiment. Results of this capacity experiment can be seen in Table 6. Overall coverage increases by increasing capacities of facilities and teleconsultaton simultaneously. At lower capacity levels, coverage of new facilities and telemedicine remain approximately the same. Coverage through telemedicine exceed coverage of new facilities at higher capacity levels.

A combined experiment was also conducted to visualize the simultaneous effects of changing budget, OOP expense and capacity. Results are displayed in Table 7. It was observed that telemedicine services are not required when OOP expense is low. When OOP expense in the system increases, telemedicine services and primary care facilities are equally prevalent at higher budget level. At lower levels of budget, telemedicine services can control rising OOP expenditure.

Implementation of the algorithms

The solution algorithms explained in Section 4 were applied to the given problem. The experiments were performed at different levels of budget. Table 8 provides the results of the experiments for greedy based heuristic while Table 9 presents the experiments for genetic algorithm. Computation times for these algorithms are lesser as compared to the optimization model. On an average, the computation time for solving the optimization model using LINGO 19 software for similar budget experiments (Table 4) was more than 3 seconds. At lower budget levels, the results from greedy based heuristic are similar to the optimization model while the genetic algorithm provided somewhat inferior results. The genetic algorithm could find the solution quickly as compared to greedy based heuristic at lower budget levels. At higher budget levels, both algorithms produced results that were inferior to the optimization model. As seen in Table 4, the optimization model could achieve complete coverage at budget level of 400. The greedy based heuristic could achieve a coverage of 92.19% while genetic algorithm could cover 93.33% population at same level of budget. The algorithms however could find these solutions quickly.

Table 8
Greedy Based Heuristic Solutions-Budget variations.

Gamma	Budget	Coverage	Telemedicine	Tele coverage	New facilities	New facilities coverage	Time (in seconds)
0	50	17.56%	2	17.56%	0	0%	2.48744
0.5	50	17.56%	2	17.56%	0	0%	1.73292
0.9	50	13.17%	0	0%	1	13.17%	0.30381
0	200	65.85%	6	52.68%	1	13.17%	3.03610
0.5	200	57.07%	5	43.90%	1	13.17%	2.20962
0.9	200	52.68%	3	26.34%	2	26.34%	1.60400
0	400	79.02%	6	52.68%	2	26.34%	2.33055
0.5	400	92.19%	6	52.68%	3	39.51%	0.84647
0.9	400	92.19%	6	52.68%	3	39.51%	0.90643

Table 9
Genetic Algorithm Solutions-Budget variations.

Budget	Coverage	Telemedicine	Tele coverage	New facilities	New facilities coverage	Time (in seconds)
50	13.17%	0	0%	1	13.17%	0.28982
100	30.73%	2	17.56%	1	13.17%	1.43011
150	48.29%	4	35.12%	1	13.17%	2.02973
200	65.85%	6	52.68%	1	13.17%	2.10568
250	79.02%	6	52.68%	3	26.34%	1.84385
300	90.96%	6	52.68%	3	38.28%	0.64559
350	92.19%	5	43.90%	4	48.29%	0.69757
400	93.33%	6	52.68%	4	40.65%	0.90643

6 CONCLUSION

The objective of universal healthcare could be achieved by improving the standards of primary healthcare. Moreover, pandemics like COVID-19 increase the demand for primary healthcare by an immense amount. It is essential to find locations of new primary care facilities in a short duration to meet rising demand in such cases that seems unrealistic. Telemedicine services can help to a great extent in such situations. Therefore, policy makers should pursue telemedicine services along with finding location of new facilities. Additionally, encouraging telemedicine practices for primary healthcare can also be helpful in reducing OOP payments by patients.

This article presents an optimization model for amalgamating telemedicine services in primary healthcare system. The objective is to maximize patient coverage by regulating OOP expenses simultaneously. Numerical experiments have been conducted for validating the model and to derive policy directives. Telemedicine outweigh the number of facilities at higher budget levels. Moreover, telemedicine services are not required when OOP expense is low and requirement of telemedicine services arises in the presence of high OOP expenditure.

This article also presents two heuristics (Greedy based and Genetic based) for dealing with larger instances of the problem in an efficient manner. The advantage of these algorithms is their adaptability. In this article, these algorithms are based on cost-effectiveness values and offer a pragmatic approach to address the proposed location-allocation decision problem. The algorithms are efficient and effective and can be applied to location-allocation decision problems for maximizing patient coverage.

The social concern of increasing OOP expenditure requires a sustainable solution. Making telemedicine an integral part of primary healthcare system has been advocated to address this concern. Moreover, telemedicine can supplement existing facilities to satisfy the primary healthcare requirements of an abrupt demand during pandemics like COVID-19 (Myronuk, 2022). It is therefore advisable to make telemedicine an integral part of primary healthcare system for regulating patient OOP expenditure and improving utilization of health facilities.

Acknowledgment

The authors are grateful to the Editor-in-Chief and reviewer(s) for suggesting useful changes to improve this article.

References

• ADONGO AA, DAPAAH JM, AZUMAH FD & NACHINAAB JO. 2021. The influence of sociodemographic behavioural variables on health-seeking behaviour and the utilisation of public and private hospitals in Ghana. International Journal of Sociology and Social Policy, 42(5/6): 455-472.
• ALGHANMI N, ALOTAIBI R, ALSHAMMARI S, ALHOTHALI A, BAMASAG O & FAISAL K. 2022. A survey of location-allocation of points of dispensing during public health emergencies. Frontiers in public health, 10: 811858.
• ALIZADEH R, NISHI T, BAGHERINEJAD J & BASHIRI M. 2021. Multi-Period Maximal Covering Location Problem with Capacitated Facilities and Modules for Natural Disaster Relief Services. Applied Sciences, 11(1): 397.
• ANTHONY JNR B. 2021. Integrating telemedicine to support digital health care for the management of COVID-19 pandemic. International Journal of Healthcare Management, 14(1): 280-289.
• BAILWAL N, KAUSHIK R & SAH T. 2020. Importance of Primary Healthcare in Delhi in the Times of COVID-19. Indian Journal of Human Development, 14(3): 527-535.
• BARDHAN AK & KUMAR K. 2018. Restructuring Primary Health Care Network to Maximize Utilization and Reduce Patient Out-of-pocket Expenses. Asian Journal of Innovation and Policy (2019), 8: 122-140.
• BARKLEY S, MARTEN R, REYNOLDS T, KELLEY E, DALIL S, SWAMINATHAN S & GHAFFAR A. 2020. Primary health care: realizing the vision. Bulletin of the World Health Organization, 98(11): 727.
• BHATTACHARJEE AK & MUKHOPADHYAY A. 2023. An improved genetic algorithm with local refinement for solving hierarchical single-allocation hub median facility location problem. Soft Computing, 27(3): 1493-1509.
• BORYCKI EM & KUSHNIRUK AW. 2022. Reinventing virtual care: Bridging the healthcare system and citizen silos to create an integrated future. Healthcare Management Forum, 35(3): 135-139.
• BURTNER S & MURRAY AT. 2022. COVID-19 and Minimizing Micro-Spatial Interactions. ACM Transactions on Spatial Algorithms and Systems (TSAS), 8(3): 1-17.
• CELIK TURKOGLU D & EROL GENEVOIS M. 2020. A comparative survey of service facility location problems. Annals of Operations Research, 292(1): 399-468.
• CHEA H, KIM H, SHAW SL & CHUN Y. 2022. Assessing trauma center accessibility for healthcare equity using an anti-covering approach. International journal of environmental research and public health, 19(3): 1459.
• CHOUKSEY A, AGRAWAL AK & TANKSALE AN. 2022. A hierarchical capacitated facility location-allocation model for planning maternal healthcare facilities in India. Computers & Industrial Engineering, 167: 107991.
• CHURCH R & REVELLE C. 1974. The maximal covering location problem. Papers in Regional Science, 32(1): 101-118.
• CLARK CR, WILKINS CH, RODRIGUEZ JA, PREININGER AM, HARRIS J, DESAUTELS S, KARUNAKARAM H, RHEE K, BATES DW & DANKWA-MULLAN I. 2021. Health care equity in the use of advanced analytics and artificial intelligence technologies in primary care. Journal of General Internal Medicine, 36: 3188-3193.
• COOPER-JONES B, MASON J, KAMEL C, MITTMANN N & DUNFIELD L. 2022. Virtual care and health technology assessment considerations. Healthcare Management Forum, 35(3): 127-129.
• CU A, MEISTER S, LEFEBVRE B & RIDDE V. 2021. Assessing healthcare access using the Levesque’s conceptual framework-a scoping review. International journal for equity in health, 20(1): 116.
• DALY K, ISDELL E, MOYNIHAN L, O’CALLAGHAN K, O’LEARY S, PEPPER A & PENNISI Y. 2022. An exploration of service users’ experience of telehealth occupational therapy interventions in adult mental health services, Ireland, during COVID-19. Irish Journal of Occupational Therapy, Ahead-of-print.
• DASH A & SAHOO AK. 2021. Moderating effect of gender on adoption of digital health consultation: a patient perspective study. International Journal of Pharmaceutical and Healthcare Marketing.
• DELANA K, DEO S, RAMDAS K, SUBBURAMAN GBB & RAVILLA T. 2023. Multichannel delivery in healthcare: the impact of telemedicine centers in southern India. Management Science, 69(5): 2568-2586.
• DU W, LIU P & XU W. 2022. Effects of decreasing the out-of-pocket expenses for outpatient care on health-seeking behaviors, health outcomes and medical expenses of people with diabetes: evidence from China. International journal for equity in health, 21(1): 162.
• FAN W, JIANG Y, PEI J, YAN P & QIU L. 2024. The impact of medical insurance payment systems on patient choice, provider behavior, and out-of-pocket rate: Fee-for-service versus diagnosis-related groups. Decision Sciences, 55(3): 245-261.
• GAO X, ZHOU Y, AMIR MIH, ROSYIDAH FA & LEE GM. 2017. A hybrid genetic algorithm for multi-emergency medical service center location-allocation problem in disaster response. International Journal of Industrial Engineering, 24(6).
• GUHA S & KHULLER S. 1999. Greedy Strikes Back: Improved Facility Location Algorithms. Journal of Algorithms, 31(1): 228-248.
• GULZARI A & TARAKCI H. 2021. A healthcare location-allocation model with an application of telemedicine for an earthquake response phase. International Journal of Disaster Risk Reduction, 55: 102100.
• HASSAN SA, ALNOWIBET K, AGRAWAL P & MOHAMED AW. 2021. Optimum Location of Field Hospitals for COVID-19: A Nonlinear Binary Metaheuristic Algorithm. CMC-COMPUTERS MATERIALS & CONTINUA, 68(1): 1183-1202.
• HERBERHOLZ C & PHUNTSHO S. 2021. Medical, transportation and spiritual out-of-pocket health expenditure on outpatient and inpatient visits in Bhutan. Social Science & Medicine, 273: 113780.
• HUSTON P, CAMPBELL J, RUSSELL G, GOODYEAR-SMITH F, PHILLIPS RL, VAN WEEL C & HOGG W. 2020. COVID-19 and primary care in six countries. BJGP open, 4(4).
• JNR BA. 2020. Use of telemedicine and virtual care for remote treatment in response to COVID-19 pandemic. Journal of Medical Systems, 44(7): 1-9.
• KADIR MA. 2020. Role of Telemedicine in Healthcare during COVID-19 pandemic in Developing Countries. Telehealth and Medicine Today.
• KATOCH S, CHAUHAN SS & KUMAR V. 2021. A review on genetic algorithm: past, present, and future. Multimedia tools and applications, 80: 8091-8126.
• KHAN JA, AHMED S & EVANS TG. 2017. Catastrophic healthcare expenditure and poverty related to out-of-pocket payments for healthcare in Bangladesh-an estimation of financial risk protection of universal health coverage. Health policy and planning, 32(8): 1102-1110.
• KORD R, RAD EH & KIAKALAYEH AD. 2022. Inequity in out-of-pocket expenditure and utilization of laboratory tests in Iran: lessons learned in human rights. International Journal of Human Rights in Healthcare, Ahead-of-print.
• KRIST AH, DEVOE JE, CHENG A, EHRLICH T & JONES SM. 2020. Redesigning primary care to address the COVID-19 pandemic in the midst of the pandemic. The Annals of Family Medicine, 18(4): 349-354.
• KUMAR K. 2022a. A location-allocation model for implementing telemedicine services in primary healthcare network. Nonlinear Studies, 29(4).
• KUMAR K. 2022b. A public-private partnership based model for regulating out-of-pocket expenditures to strengthen primary care system. The International Journal of Health Planning and Management, 37(5): 2964-2991.
• KUMAR K. 2023. Primary Health Care Facility Location and Telemedicine. In: Applications of Operational Research in Business and Industries: Proceedings of 54th Annual Conference of ORSI. pp. 351-365. Springer.
• KUMAR K & BARDHAN AK. 2020. A choice-based model to reduce primary care load on tertiary hospitals. International Journal of Management Science and Engineering Management, 15(3): 155-164.
• LEIGHTNER JE. 2021. Covid-19, out-of-pocket medical expenses and consumption. Journal of Financial Economic Policy, 13(4): 462-478.
• LIU Y, YUAN Y, SHEN J & GAO W. 2021. Emergency response facility location in transportation networks: a literature review. Journal of traffic and transportation engineering (English edition).
• MANUPATI VK, SCHOENHERR T, WAGNER SM, SONI B, PANIGRAHI S & RAMKUMAR M. 2021. Convalescent plasma bank facility location-allocation problem for COVID-19. Transportation Research Part E: Logistics and Transportation Review, 156: 102517.
• MEHROTRA A, JENA AB, BUSCH AB, SOUZA J, USCHER-PINES L & LANDON BE. 2016. Utilization of telemedicine among rural Medicare beneficiaries. Jama, 315(18): 2015-2016.
• MENDOZA-GÓMEZ R & RÍOS-MERCADO RZ. 2022. Location of primary health care centers for demand coverage of complementary services. Computers & Industrial Engineering, 169: 108237.
• MENDOZA-GÓMEZ R & RÍOS-MERCADO RZ. 2024. Regionalization of primary health care units: An iterated greedy algorithm for large-scale instances. Expert Systems with Applications, 250: 123924.
• MISHRA V & SHARMA MG. 2022. Telemedicine as frugal intervention to health care: A case of diabetes management. International Journal of Healthcare Management, 15(2): 165-170.
• MULAGA AN, KAMNDAYA MS & MASANGWI SJ. 2022. Spatial disparities in impoverishing effects of out-of-pocket health payments in Malawi. Global Health Action, 15(1): 2047465.
• MYRONUK L. 2022. Effect of telemedicine via videoconference on provider fatigue and empathy: Implications for the Quadruple Aim. Healthcare Management Forum, 35(3): 174-178.
• OHANNESSIAN R. 2015. Telemedicine: potential applications in epidemic situations. European Research in Telemedicine/La Recherche Européenne en Télémédecine, 4(3): 95-98.
• PAN J, DENG Y, YANG Y & ZHANG Y. 2023. Location-allocation modelling for rational health planning: applying a two-step optimization approach to evaluate the spatial accessibility improvement of newly added tertiary hospitals in a metropolitan city of China. Social Science & Medicine, 338: 116296.
• PARK J, CHOI M & KANG JY. 2021. Spatial optimization of indoor sports stadium seats under social distancing practice during the COVID-19 pandemic. Journal of the Korean Geographical Society, 56(1): 53-66.
• PORTNOY J, WALLER M & ELLIOTT T. 2020. Telemedicine in the era of COVID-19. The Journal of Allergy and Clinical Immunology: In Practice, 8(5): 1489-1491.
• POURREZAIE-KHALIGH P, BOZORGI-AMIRI A, YOUSEFI-BABADI A & MOON I. 2022. Fix-and-optimize approach for a healthcare facility location/network design problem considering equity and accessibility: A case study. Applied Mathematical Modelling, 102: 243-267.
• RAHMANI A & MIRHASSANI S. 2014. A hybrid firefly-genetic algorithm for the capacitated facility location problem. Information Sciences, 283: 70-78.
• SACKS E, SCHLEIFF M, WERE M, CHOWDHURY AM & PERRY HB. 2020. Communities, universal health coverage and primary health care. Bulletin of the World Health Organization, 98(11): 773.
• SANGAR S, DUTT V & THAKUR R. 2018. Economic burden, impoverishment and coping mechanisms associated with out-of-pocket health expenditure: analysis of rural-urban differentials in India. Journal of Public Health, pp. 1-10.
• SANGAR S, DUTT V & THAKUR R. 2022. Burden of out-of-pocket health expenditure and its impoverishment impact in India: evidence from National Sample Survey. Journal of Asian Public Policy, 15(1): 60-77.
• SCHAUB J, SHPILKERMAN YI, ROLAND H, KEYKO K & PARISÉ K. 2022. Transitions of care for hospital discharges in a primary care network. Healthcare Management Forum, 35(3): 147-152.
• SINDHU S. 2022. Digital health care services in post COVID-19 scenario: modeling the enabling factors. International Journal of Pharmaceutical and Healthcare Marketing, Ahead-of-print.
• SINGH D, PRINJA S, BAHUGUNA P, CHAUHAN AS, GUINNESS L, SHARMA S & LAKSHMI P. 2021. Cost of scaling-up comprehensive primary health care in India: Implications for universal health coverage. Health policy and planning, 36(4): 407-417.
• SINGH P, FU N, DALE S, ORZOL S, LAIRD J, MARKOVITZ A, SHIN E, O’MALLEY AS, MCCALL N & DAY TJ. 2024. The Comprehensive Primary Care Plus Model and Health Care Spending, Service Use, and Quality. JAMA, 331(2): 132-146.
• TAIWO OJ. 2020. Maximal Covering Location Problem (MCLP) for the identification of potential optimal COVID-19 testing facility sites in Nigeria. African Geographical Review, pp. 1-17.
• VATSA AK & JAYASWAL S. 2021. Capacitated multi-period maximal covering location problem with server uncertainty. European Journal of Operational Research, 289(3): 1107-1126.
• VÁZQUEZ-SERRANO JI, CÁRDENAS-BARRÓN LE, VICENCIO-ORTIZ JC, MATIS T, GAITÁ N-MERCADO CM & PEIMBERT-GARCÍA RE. 2024. Hybrid optimization and discrete-event simulation model to reduce waiting times in a primary health center. Expert Systems with Applications, 238: 121920.
• VOSBURG RW & ROBINSON KA. 2022. Telemedicine in primary care during the COVID-19 pandemic: provider and patient satisfaction examined. Telemedicine and e-Health, 28(2): 167-175.
• WANG W, WU S, WANG S, ZHEN L & QU X. 2021. Emergency facility location problems in logistics: Status and perspectives. Transportation Research Part E: Logistics and Transportation Review, 154: 102465.
• WANG X, ZHANG Z, ZHAO J & SHI Y. 2019. Impact of telemedicine on healthcare service system considering patients’ choice. Discrete Dynamics in Nature and Society, 2019.
• XIE JS, NANJI K, KHAN M, KHALID MF, GARG SJ, THABANE L, SIVAPRASAD S & CHAUDHARY V. 2022. Publication trends in telemedicine research originating from Canada. Healthcare Management Forum, 35(3): 153-160.
• XIONG W, BAIR A, SANDROCK C, WANG S, SIDDIQUI J & HUPERT N. 2012. Implementing telemedicine in medical emergency response: concept of operation for a regional telemedicine hub. Journal of Medical Systems, 36: 1651-1660.
• YADAV J, MENON GR & JOHN D. 2021. Disease-Specific Out-of-Pocket Payments, Catastrophic Health Expenditure and Impoverishment Effects in India: An Analysis of National Health Survey Data. Applied Health Economics and Health Policy, pp. 1-14.
• YUSEFI AR, MEHRALIAN G, KHODAMORADI A, ABBASI R, VATANKHAH F, HEAIDARI F & BASTANI P. 2022. Out-of-pocket payments for treatment of COVID-19 in Iran. Cost Effectiveness and Resource Allocation, 20(1): 1-10.
• ZHANG B, PENG J & LI S. 2017. Covering location problem of emergency service facilities in an uncertain environment. Applied Mathematical Modelling, 51: 429-447.

• Data Availability:
  The data utilized for this study has been provided in the article itself.
• Funding:
  This research has been supported by the Faculty Research Programme (FRP) Grant 2024-25 sanctioned by the Institute of Eminence, University of Delhi, Delhi, India.

Edited by

• Review Process:
  Editor - Annibal Parracho Sant’Anna.

Data availability

The data utilized for this study has been provided in the article itself.

Publication Dates

• Publication in this collection
  19 May 2025
• Date of issue
  2025

History

• Received
  12 July 2024
• Accepted
  03 Feb 2025