Optimal Allocation of Electric Vehicles Charging Stations in Commercial Parking Lots: A Mixed-Integer Nonlinear Programming Approach

Abstract

This study presents a mixed-integer nonlinear programming (MINLP) framework to optimize the allocation of electric vehicle charging stations (EVCSs) in existing indoor parking facilities. The model minimizes total life-cycle cost by jointly determining charger types and placements while accounting for spatial feasibility and investment constraints. A hybrid search method that combines complete enumeration with dynamic programming is applied to identify the least-cost configuration within geometric and electrical limitations. The results show that configurations combining dual- and quad-port chargers outperform single-port layouts by reducing redundant electrical and installation costs. The analysis confirms that integrating life-cycle costing with spatial feasibility yields a practical decision-support tool for property owners seeking to expand charging capacity within existing facilities. Overall, the framework demonstrates that cost-efficient retrofitting of EV charging infrastructure can be achieved without additional land development, supporting broader sustainability objectives and promoting low-carbon mobility. Future research will extend the model to multiple facility layouts and incorporate sensitivity and uncertainty analyses to evaluate robustness under varying geometric and economic conditions. The findings of this paper provide a practical foundation for future planning studies and demonstrate how cost-optimized retrofit strategies can support the scalable expansion of EV charging infrastructure in existing facilities.

1. Introduction

As more countries commit to reducing their carbon footprint to address climate change and global warming, immediate and coordinated actions are required across all sectors. According to the Department of Environment and Climate Change [1], the transportation sector accounted for 24 percent of total greenhouse gas emissions in Canada in 2020. Alternative-fuel vehicles, particularly electric vehicles (EVs), have been promoted as a sustainable transportation option and are gaining momentum. However, global EV market share remains below 1 percent [1], although projections suggest promising growth, with EVs expected to reach approximately 14 percent of total vehicles in the coming years [2]. However, EV adoption depends not only on projected market growth and infrastructure availability but also on the strength of supporting policy measures. In many regions, incentives have played a central role in reducing the financial barriers to EV ownership and encouraging early market adoption. Prior research, such as “The Role of Incentive Programs in Promoting the Purchase of Electric Cars—Review of Good Practices and Promoting Methods from the World” [3], highlights that both financial and non-financial incentives significantly influence consumer uptake and complement infrastructure expansion efforts.

The deployment of EV charging infrastructure continues to evolve, with significant regional variation. The percentage of public charging stations installed by 2024 indicates progress toward the 2030 target [4]. Globally, EV adoption is anticipated to accelerate due to supportive policies, advancements in battery technology, and rising environmental awareness. In the United States, California leads EV adoption with a strong policy framework, offering rebates and incentives and maintaining one of the most extensive charging networks nationwide [4]. The federal government has also reinforced the transition through tax credits and funding initiatives for charging infrastructure.

The utilization of public EV charging stations remains relatively low, indicating that most EV owners primarily rely on home charging. According to a 2022 report by the International Council on Clean Transportation (ICCT) [5], daily usage of public chargers varies across regions and tends to be higher in urban areas, where both EV and charger density are greater. Nevertheless, utilization rates are projected to increase significantly by 2032 as EV adoption grows. Consequently, the expansion of public EV charging stations must keep pace with expected EV growth.

Location–allocation (LA) problems serve as a common framework for planning charging infrastructure. These problems involve determining optimal facility locations while considering costs, constraints, and service requirements. They can be classified along several dimensions:

• Static vs. dynamic: Static models assume constant locations and demand, whereas dynamic models incorporate temporal changes [6].
• Discrete vs. continuous: Discrete models restrict facilities to predefined locations, while continuous models allow placement anywhere within a defined space [7].
• Single-facility vs. multi-facility: Single-facility models identify one optimal location, while multi-facility models account for interactions among multiple facilities [8,9,10].
• Capacitated vs. uncapacitated: Capacitated models impose service limits, whereas uncapacitated models assume unlimited service potential [11].

From the owner’s perspective, strategic facility placement should align with practical decision-making objectives:

• Cost minimization: Reducing equipment, installation, maintenance, and operational costs.
• Demand satisfaction: Ensuring charging capacity meets current and future customer needs.
• Market potential: Targeting areas with high demand or strong growth prospects.

Facility location problems have been studied extensively in operations research and applied to areas such as logistics, healthcare, and infrastructure planning [10,12]. Recent studies have extended these models to EV charging station planning [13]. A key distinction in this body of work is the treatment of input parameters. Some studies assume fixed values for demand, cost, and capacity, while others incorporate uncertainty through probabilistic or robust formulations [14,15]. This distinction forms the basis for deterministic and stochastic models [16].

This study focuses on the need to retrofit Electric Vehicle Charging Stations (EVCS) within existing indoor parking facilities from the viewpoint of parking lot owners. It first explores strategies for converting conventional parking stalls into EV charging spots with an emphasis on cost optimization. An optimization algorithm is developed to evaluate multiple placement scenarios and identify the most cost-effective configurations. The proposed framework integrates Life Cycle Cost (LCC) analysis with a capacitated multi-facility location formulation to support decision-making for EVCS allocation.

The framework accommodates single-port, dual-port, and quad-port chargers and incorporates spatial constraints essential for feasible placement in existing layouts. The objective is to identify the configuration that results in the minimum LCC. The model also supports sustainable infrastructure adaptation by enabling owners to increase EV charging capacity without new construction, reducing material usage, construction waste, and grid stress.

Nonlinearities and combinatorial complexity make these allocation problems challenging. Similar nonlinear formulations have been addressed using advanced metaheuristic optimization methods such as hybrid moth–flame algorithms in power system applications [17,18]. The novelty of this study lies in integrating life-cycle costing with a retrofitting-oriented facility location model tailored to indoor parking layouts. Unlike prior work focused on greenfield installations or large-scale public networks, this model explicitly incorporates physical constraints, adjacency requirements, and comparative evaluation of multi-port charger types.

This study addresses three primary research objectives. First, it develops a life-cycle cost optimization framework specifically tailored to retrofitting EV charging stations in existing indoor parking facilities, a context largely overlooked in prior EV infrastructure studies. Second, it integrates spatial feasibility constraints—including parking geometry, adjacency rules, and multi-port hardware compatibility—into a unified MINLP formulation that jointly determines the optimal charger mix and placement. Third, it demonstrates the computational practicality of the approach through a complete enumeration process enhanced with dynamic-programming reuse and evaluates its effectiveness on a representative enclosed-garage case study. Together, these objectives aim to provide a rigorous and practical decision-support tool for owners and planners seeking cost-efficient, spatially viable EV charging retrofits.

The remainder of this paper is organized as follows. Section 2 reviews existing EVCS allocation approaches and outlines the computational methods relevant to this study. Section 3 presents the proposed MINLP framework, including the mathematical formulation, spatial feasibility rules, and cost structure. Section 4 describes the model implementation and validation procedure. Section 5 discusses the case-study results and provides a qualitative sensitivity analysis. Finally, Section 6 offers concluding remarks and suggestions for future research.

2. EVCS Allocation Problem-Solving Methods

There are several algorithms used to solve or optimize objective functions or mathematical models associated with EVCS allocation. Exact solution methods are guaranteed to find the optimal solution to a given problem, while heuristic techniques aim to provide feasible solutions without any guarantee of optimality. Examples of heuristic approaches include genetic algorithms and particle swarm optimization [19,20,21,22,23,24,25,26,27,28,29,30].

Dynamic Programming (DP) is a powerful algorithmic technique used for solving complex problems by decomposing them into smaller, overlapping subproblems and solving each subproblem only once. The key idea behind dynamic programming is to avoid redundant calculations by storing the results of previously solved subproblems, which significantly improves efficiency compared to classical brute-force methods [31,32,33]. Two major strategies are commonly used in DP:

• Top-down (memoization): The problem is solved recursively. Each time a subproblem is encountered, the algorithm checks whether its solution has already been computed. If so, the stored value is reused. If not, the subproblem is solved, stored, and then returned.
• Bottom-up (tabulation): The problem is solved iteratively, starting from the smallest subproblems and building toward the final, larger solution. Every subproblem’s result is stored in a table, and these stored values are then used to construct the solution to more complex subproblems.

The brute-force method is a straightforward and exhaustive approach to solving computational problems. It systematically enumerates all possible solutions or configurations and evaluates each one to identify the best outcome [31]. Despite its conceptual simplicity, brute force remains a fundamental problem-solving technique in computer science and optimization theory. It guarantees finding the optimal solution; however, it is often computationally prohibitive due to the exponential growth in the number of combinations as the problem size increases. Brute-force algorithms typically follow a direct approach: (1) generate all possible candidate solutions, (2) evaluate each solution to determine whether it satisfies the problem’s requirements or optimizes the objective function, and (3) select the optimal solution after all possibilities have been assessed. Although computationally expensive, brute force is valuable as a benchmark for validating more advanced optimization methods, and it can be significantly strengthened when combined with dynamic programming to eliminate repeated calculations.

Together, dynamic programming and brute-force enumeration provide complementary strengths for solving nonlinear, combinatorial allocation problems such as EVCS placement. DP reduces computational redundancy, while brute force ensures exhaustive exploration of all feasible solutions, making both suitable components within a hybrid optimization strategy.

3. Proposed Model

The proposed algorithm begins by examining the layout of the parking lot and determining the required number of ports to be allocated. In this model, particular emphasis is placed on the existing parking layout and the practical requirements for allocating dual-port and quad-port chargers across different parking spots and in various multi-port configurations. For example, Figure 1 illustrates the possible allocation of single-, dual-, and quad-port chargers within a representative parking block depicting parking slots and circulation paths.

The flowchart of the proposed model is shown in Figure 2. As illustrated, the algorithm proceeds through several steps to ensure the efficient allocation of EVCS units within the parking lot.

To clarify the mathematical structure of the proposed framework, the optimization problem is formulated as a Mixed-Integer Nonlinear Programming (MINLP) model with a single objective function and an associated set of decision variables and constraints. The overarching objective is to minimize the total life-cycle cost (LCC) associated with the placement and configuration of Electric Vehicle Charging Stations (EVCSs) within an existing parking facility.

The primary decision variables include:

• $x_{ij}$: a binary variable indicating whether parking spot i is assigned to charging station j
• $y_{jk}$: a binary variable indicating whether station j is configured with k ports, where $k \in \{\mathrm{1,2},4\}$

The model is subject to several groups of constraints:

▪

Capacity and allocation constraints, ensuring that the number of allocated ports across charging stations satisfies the total required demand (Equations (3) and (4)).

▪

Spatial feasibility constraints, enforcing the geometric placement rules required for dual-port (adjacent placement) and quad-port (2 × 2 configuration) chargers.

▪

Cost-structure constraints, linking each charger type and location to the corresponding cost elements within the LCC function.

For clarity and completeness,

Table 1. Symbols and Notation Used in the MINLP Formulation.

Symbol	Meaning	Units/Domain
$B_i$	Block index in the parking lot configuration	index i
$M_{max}$	Maximum number of block combinations considered	integer
$N_b$	Total number of blocks in the parking lot	integer
$x_{ij}$	Indicator if parking spot i is associated with EVCS j	{0, 1}
$y_{jk}$	Indicator if EVCS j is allocated k number of ports	{0, 1}
$N_{sb}$	Number of ports occupying a target block	integer
$L_{sb}$	Length of cable from the power source to block	m
$W_{sb}$	Cable width as a function of number of ports	m
$C_{S_E}$	Cost of EVCS equipment	$
$C_{S_{EE}}$	Cost of electrical system equipment	$
$C_{S_{OM}}$	Cost of maintenance and operation	$ per year
$C_{S_F}$	Fixed cost such as software licensing, security, and communication	$
$C_{S_{EndofLife}}$	End-of-life dismantling cost	$
$C_s$	Total scenario life-cycle cost for configuration s	$
$C_{Optimized}$	Optimized minimum total life-cycle cost	$
$C_{cabl{e}_{ij}}$	Cable cost per unit length for connection between source and block	$/m
$C_{Breake{r}_{ij}}$	Breaker cost for each station connection	$
$C_{Fus{e}_{ij}}$	Fuse cost for each station connection	$
$C_{JunctionBo{x}_{ij}}$	Junction box cost for each station connection	$
$C_{Condui{t}_{ij}}$	Conduit cost per unit length	$/m
$C_{labou{r}_{C}abl{e}_{ij}}$	Labor cost for cable installation per meter	$/m
$C_{labou{r}_{C}ondui{t}_{ij}}$	Labor cost for conduit installation per meter	$/m
$I$	Discount rate	fraction yr−1
$T$	Lifespan of units	years
$C_{Initial}$	One-time upfront cost at t = 0	$
$C_{OM}$	Annual operation and maintenance cost	$ per year
$C_{Overhaul}$	Mid-life overhaul cost at t = 5	$
$C_{EndOfLife}$	End-of-life dismantling cost at t = T	$
$NP{V}_{Total}$	Net present value of total life-cycle cost	$ (NPV)

lists all symbols and notation used in the MINLP formulation.

3.1. Ports Distribution into Chargers

The expected number of EV charging ports is distributed across chargers with standard configurations—single-port, dual-port, and quad-port units. Equation (1) is used to determine the total number of ports required based on the combination of charger types.

$$n_{ep}=n+m+l$$

(1)

where n, m, and l represent counts of 1-, 2-, and 4-port chargers.

For example, suppose the total number of required EV ports $n_{ep}$ is five. In this case, there are four possible distribution options: [(1, 2, 2), (1, 1, 1, 1, 1), (1, 4), (1, 1, 1, 2)]. The number of chargers required for these configurations would be 3, 5, 2, and 4, respectively. As seen from this example, the number of required chargers differs across feasible distributions; therefore, an optimization model is used to identify the most cost-effective result.

3.2. Grouping Parking Spots into Blocks

In this step, the parking layout is divided into blocks. Each block represents an aggregation of parking spots that share at least one common side. The block mapping and grouping process is performed in two stages. In the first stage, blocks are defined according to spatial adjacency; in the second stage, the combination of blocks is determined based on a specified minimum and maximum number of allowable block combinations. The order of block selection is not important, preventing unnecessary repetition during enumeration. Following the flowchart, Figure 3 depicts the block’s mapping and grouping procedure. The number of block combinations can be calculated using Equation (2).

$$B_i=\sum _{M_{b=1}}^{M_{max}}\left(\begin{array}{c}{N}_b\\ M_b\end{array}\right)=\sum _{M_{b=1}}^{M_{max}}{\displaystyle \frac{N_b!}{M_b!\left(N_b-M_b\right)!}}$$

(2)

where $N_b$ is the total number of blocks in the parking layout and $M_{max}$ the maximum number of blocks that may be combined in a single scenario. Equation (2) computes $B_i$, the total number of distinct block combinations considered by the model when selecting between 1 and $M_{max}$ blocks from the set of $N_b$ available blocks.

3.3. Incorporating Subjective Conditions into Proposed Model

This section describes the subjective conditions and feasibility rules that must be satisfied for a valid allocation of EVCS units. The number of parking spots connected to station j must satisfy Equation (3). The value of j must also lie between defined minimum and maximum limits (Equation (4)).

$$\begin{array}{c}{\sum }_{i=1}^N{x}_{ij}={\sum }_k{k.y}_{jk} \mid k \in (1,2,4)\\ {\mathrm{x}}_{\mathrm{i}\mathrm{j}}\in \left\{\mathrm{0,1}\right\}\mathrm{and} y_{jk}\in \left\{\mathrm{0,1}\right\}\mathrm{and} {\sum }_k{y}_{jk}=1\end{array}$$

(3)

$$⌊{\displaystyle \frac{max\left(p\right)}{4}}⌋+⌊{\displaystyle \frac{max\left(p\right)mod4}{2}}⌋+\left[max\left(p\right)mod2\right]⩽j⩽max\left(p\right)$$

(4)

where i, j, $x_{ij}$, $y_{jk}$, N, p, and k are spot number, charging station number, indicator of parking spot i associated with EVCS j (binary variable 0 or 1), indicator of if EVCS j allocated k number of ports (binary variable 0 or 1), maximum number of parking spots in the parking lot, number of EVC ports, and charging station type.

Figure 4 presents an example illustrating how Equation (3) is satisfied for various assignment conditions. Equations (5) and (6) demonstrate the equivalence between the allocation criteria in Equation (3) and actual port distributions.

$$\sum _{i=1}^{N=7}{x}_{ij}=x_{\mathrm{1,7}}+x_{\mathrm{2,7}}+\dots +x_{\mathrm{6,7}}+x_{\mathrm{7,7}}=0+0+0+1+1+0+0=2$$

(5)

$$\sum _k{k.y}_{jk}=1\times y_{\mathrm{7,1}}+2\times y_{\mathrm{7,2}}+4\times y_{\mathrm{7,4}}=1\times 0+2\times 1+4\times 0=2$$

(6)

Unlike single-port chargers, dual-port and quad-port units must satisfy additional spatial constraints. For dual-port chargers, the two assigned parking spots must be adjacent, with a maximum distance of one spot. Therefore Equation (7) can be defined.

$$\begin{array}{c}\left|r_{p1,j}-r_{p2,j}\right|+\left|c_{p1,j}-c_{p2,j}\right|=1\\ \mathrm{for} \left(P_1,P_2\right)\in \left[\mathrm{1,2}\right],P_1\ne P_2\end{array}$$

(7)

The allocation as depicted in Figure 4 is an acceptable solution for a dual-port unit satisfying the top criteria. However, the allocation shown in Figure 5 is false and does not satisfy Equation (7) requirements since the distance between the two of the dual-port unit is higher than one.

For the quad-port charger the placement should have a 2 × 2 square formation. Initially the algorithm should make sure that the designated quad-port charger can be accommodated into the block. Meaning, the block should have at least two rows and two columns. In this regard, block creation will be followed by block checking for the possibility of quad-port accommodation. A list of non-eligible blocks will be created for the algorithm to avoid in the port distribution section of the model.

Similarly to the dual-port EVCS, quad-port EVCS ports, row and column distance from each other shouldn’t exceed one.

Table 2. Coordinates of a potential placement for a quad-port EVCS.

	Column
Row	$\left(r_{P_1,j}, c_{P_1,j}\right)$	$\left(r_{P_2,j}, c_{P_2,j}\right)$
	$\left(r_{P_3,j}, c_{P_3,j}\right)$	$\left(r_{P_4,j}, c_{P_4,j}\right)$

shows the coordinates of the potential port placements for a quad-port unit.

Based on the given potential coordinates, the ports in the quad-port unit should meet the following Manhattan distance conditions, as shown in Equation (8).

$$\begin{array}{c}{d}_1=\left|r_{P_1,j}-r_{P_2,j}\right|+\left|c_{P_1,j}-c_{P_2,j}\right|=1\\ d_2=\left|r_{P_1,j}-r_{P_3,j}\right|+\left|c_{P_1,j}-c_{P_3,j}\right|=1\\ d_3=\left|r_{P_1,j}-r_{P_4,j}\right|+\left|c_{P_1,j}-c_{P_4,j}\right|=2\end{array}$$

(8)

For further details about the MILP formulation please refer to Appendix A.

3.4. Cost Calculations

The cost calculation for the allocation of EVCS units in parking lots is based on a Mixed-Integer Nonlinear Programming (MINLP) formulation, with the objective of minimizing the total costs associated with configuring and allocating multi-port chargers within parking blocks while ensuring the feasible placement of Electric Vehicle Charging Ports (EVCPs).

Accordingly, Equation (9) is used to identify the optimal cost for each scenario.

$$C_{Optimized}=\underset{x,y}{\min }{C}_s\left(x,y\right)$$

(9)

where C_s is the total cost for scenario s, consisting of EVCS equipment cost, electrical system equipment cost, operation and maintenance cost, fixed cost components, and end-of-life cost. $C_{\mathrm{Optimized}}$ represents the scenario with the minimum total cost that satisfies all requirements and constraints for the designated parking layout. Equation (10) defines the total cost $C_s$ of scenario s as the sum of five components:

$$C_s=C_{S_E}+C_{S_{EE}}+C_{S_{OM}}+C_{S_F}+C_{S_{EndofLife}}$$

(10)

where s represents the scenario number. $C_S$, $C_{S_E}$, $C_{S_{EE}}$, $C_{S_{OM}}$, $C_{S_F}$, and $C_{S_{EndofLife}}$ are LCC calculation for each scenario, total cost of EVCS equipment, cost of electrical system equipment, cost of maintenance and operation, fixed costs, and equipment end of life cost.

The cost of EVCS equipment can be defined as given in Equation (11). The EVCS equipment cost ensures that both EVCS’s port configuration and the type of charger (pedestal or wall-mounted) are accounted for while correctly assigned to the parking spots.

$$C_{s_E}=\sum _k\sum _{i=1}^N\sum _{j=1}^{J_{max}}{x}_{ij}\times y_{jk}\times C_{S_{E ijk}}|k\in \left(\mathrm{1,2},4\right)$$

(11)

In Equation (11), $C_{S_{E ijk}}$, $x_{ij}$, $y_{jk}$ and $J_{max}$ are cost of the EVCS j with k number of ports, binary variable indicating parking spot i associated with the EVCS j, binary variable indicating parking spot j allocated k number of ports, and $J_{max}$ the maximum number of candidate charging stations considered in the layout. The variable i is limited between 1 to the number of parking spots. The limits of the variable j can be defined as given in Equation (12).

$$⌊{\displaystyle \frac{p}{4}}⌋+⌊{\displaystyle \frac{p \mathrm{m}\mathrm{o}\mathrm{d} 4}{2}}⌋+\left(p \mathrm{m}\mathrm{o}\mathrm{d} 2\right)\le j\le \mathrm{m}\mathrm{a}\mathrm{x}\left(p\right)$$

(12)

where p is the port number.

The cost of the Electrical System Equipment ${(C}_{S_{EE}})$ as given in Equation (13), represents the expenses required for connecting the power source to each block and individual charging station, based on the parking layout. ${(C}_{S_{EE}})$ is typically considered part of the initial costs in the LCC calculation, as it comprises one-time expenses incurred during installation. Alongside other initial expenses like EVCS equipment, this cost component include expenses to support the establishment of the electrical system equipment, such as cable and conduit costs (determined by length and width requirements), breaker cost, fuse costs, and junction box costs.

$$C_{s_{EE}}={\sum }_{i=1}^N{\sum }_{j=1}^{J_{max}}{x}_{ij}\times C_{S_{E{E}_{i}j}}$$

(13)

In Equation (13), $C_{S_{E{E}_{i}j}}$ is a combination of constant cost and variable cost of electrical system equipment (cable cost connection from the power source to the blocks, and then from the junction box to each spot).

$C_{S_{E{E}_{i}j}}$ can be expanded to Equation (14).

$$\begin{array}{c}{C}_{S_{E{E}_{i}j}}=C_{{cable}_{ij}}\times L_{{sb}_{ij}}+C_{{Breaker}_{ij}}+C_{{Fuse}_{ij}}+C_{{Junction box}_{ij}}+C_{{Conduit}_{ij}}\times L_{{sb}_{ij}}\\ +C_{{labou{r}_{C}able}_{ij}}\times L_{{sb}_{ij}}+C_{{labou{r}_{C}onduit}_{ij}}\times L_{{sb}_{ij}}\end{array}$$

(14)

where $L_{sb}$, $W_{sb}$, $N_{sb}$, $C_{cable}$, $C_{labou{r}_{C}able}$, $C_{labou{r}_{C}onduit}$, $C_{Breaker}$, $C_{Fuse}$, $C_{Junction box}$, and $C_{Conduit}$ are length of cable required from the source to block, width of the cable (function of the number of ports), number of ports occupying a target block, cost per unit length of the cable, cable installation labor cost per meter, conduit installation labor cost per meter, breaker cost, fuse cost, junction box cost, and conduit cost.

In Equation (15), $W_{sb}$ is a function of number of ports in the target block.

$$W_{sb}=f\left(N_{sb}\right)$$

(15)

Based on the algorithm the distance between source to the target block can be defined in various ways as depicted in Figure 6. Despite having several routings options the algorithm will select the shortest distance that can result in lowest cost.

In Equation (16), total operation and maintenance cost, $C_{S_{OM}}$, accounts for all stations, parking spots, port configuration, and charger type. $C_{S_{OM}}$ are recurring costs associated with the daily functioning of each station. Including the cost such as electricity, routine inspections (which is required to keep the equipment running), and minor tasks. Formula accounts for differences in charger types (pedestal and wall-mounted chargers) and in the number of ports. The reason for such detailed approach is that as an example the maintenance cost for pedestal multi-port chargers have slightly higher costs due to their complexity and structure.

$$C_{S_{OM}}={\sum }_{\mathit{k}}{\sum }_{i=1}^N{\sum }_{j=1}^{J_{max}}{x}_{ij}\times y_{jk}\times C_{S_{O{M}_i,j,k}}$$

(16)

where $k\in \left(\mathrm{1,2},4\right)$ and $C_{S_{O{M}_i,j,k}}$ is the operation and maintenance cost for each station considering port configuration and station type (pedestal or wall-mounted charger).

The fixed Cost for EVCS represents the one-time expenses, such as software licensing fees, security measures, and communication systems, which support the charging stations across the parking lot as given in Equation (17).

$$C_{S_F}={\sum }_{i=1}^N{\sum }_{j=1}^{J_{max}}{x}_{ij}\times C_{S_{F_{i}j}}$$

(17)

In Equation (17), $C_{S_{F_i,j}}$ indicates the fixed cost associated with parking spot i and EVCS j.

The end-of-life cost, $C_{S_{Endoflife}}$, in Equation (18) represents the expenses required for dismantling chargers at the end of their lifespan, it covers the final year of life.

$$C_{S_{End of life }}={\sum }_{\mathit{k}}{\sum }_{i=1}^N{\sum }_{j=1}^{J_{max}}{x}_{ij}\times y_{jk}\times C_{S_{{EndofLife}_i,,j,k}}$$

(18)

$C_{S_{{EndofLife}_i,,j,k}}$ is parking spot i, charging station j, with port configuration k, end of life cost including dismantling and removal.

The Life Cycle Cost (LCC) for EV Charging Stations in parking lots encompasses all costs over a 10-year period. Initial costs include purchasing charging equipment, electrical installation, and fixed expenses for supporting infrastructure (software, security, communication systems). Annual Operation and Maintenance costs cover regular expenses like electricity, routine inspections (lubrication, minor maintenance tasks), and a significant overhaul in year 5. End-of-life costs, incurred in the final year, include equipment dismantling.

3.5. Annual Discounting for LCC Minimization

The goal is to identify the placement configuration for Electric Vehicle Charging Points (EVCP) with the lowest Net Present Value (NPV) of total costs. NPV calculation reflects the cumulative expenses for each scenario, discounted annually to consider the time value of money using a specified discount rate over the asset’s lifespan. By comparing scenarios based on their total NPVs, the most economical configuration—one with the lowest total NPV—is selected. This analysis strictly follows a cost-minimization approach, aimed at achieving the most cost-effective EVCP placement. The total NPV of Costs is given in Equation (19).

$${NPV}_{Total}=C_{Initial}+\sum _{t=1}^T{\displaystyle \frac{C_{t,OM}}{{\left(1+I\right)}^t}}+{\displaystyle \frac{C_{Overhaul}}{{\left(1+I\right)}^5}}+{\displaystyle \frac{C_{End of Life}}{{\left(1+I\right)}^T}}$$

(19)

Initial Cost ($C_{Initiall}$) in Equation (20) is one-time upfront expense, which does not require discounting because it occurs at t = 0.

$$C_{Initial}=C_{S_E}+C_{S_{EE}}+C_{S_F}$$

(20)

where $C_{S_E}$, $C_{S_{EE}}$, and $C_{S_F}$ are total cost of EVCS, total cost of electrical system equipment, and total fixed cost, which defined as software licensing fees, security measures cost, communication system costs.

The second cost ($C_{Annual OM}$) is annual operation and maintenance cost that is recurring operation and maintenance costs, discounted annually.

$$C_{Annual OM}=\sum _{t=1}^T{\displaystyle \frac{C_{t,OM}}{{\left(1+I\right)}^t}}$$

(21)

In Equation (21), $C_{t,OM}$ is the combined annual cost of operation and maintenance. Also, $I$, $T$, and $t$ are discount rate, last year of lifespan, and year number.

The third cost is associated with overhaul cost which is a one-time mid-life expense applied at t = 5 to ensure functionality discounted to the present value. The overhaul cost is given in Equation (22).

$${\displaystyle \frac{C_{Overhaul}}{{\left(1+I\right)}^5}}$$

(22)

The end-of-life cost is associated with the one-time dismantling cost at the end of the lifespan, discounted in year T as defined in Equation (23).

$${\displaystyle \frac{C_{End of Life}}{{\left(1+I\right)}^T}}$$

(23)

The objective is to minimize Equation (19).

Table 3. LCC Calculation using NPV.

Year	t = 0	t = 1	t = 2	…	t = 5	…	t = 10
Annual Cost ($C_{t,OM})$	0	$C_{OM}$	$C_{OM}$	$C_{OM}$	$C_{OM}$ + $C_{Overhaul}$	$C_{OM}$	$C_{OM}$
Initial Cost ($C_{Initial}$)	$C_{Initial}$	0	0	0	0	0	0
Annual Net Cash Flow	$C_{Initial}$	$C_{OM}$	$C_{OM}$	$C_{OM}$	$C_{OM}$ + $C_{Overhaul}$	$C_{OM}$	$C_{OM}+C_{End of Life}$
Discounted Factor ${\displaystyle \frac{1}{{\left(1+I\right)}^t}}$	1	${\displaystyle \frac{1}{{\left(1+I\right)}^1}}$	${\displaystyle \frac{1}{{\left(1+I\right)}^2}}$	${\displaystyle \frac{1}{{\left(1+I\right)}^t}}$	${\displaystyle \frac{1}{{\left(1+I\right)}^5}}$	${\displaystyle \frac{1}{{\left(1+I\right)}^t}}$	${\displaystyle \frac{1}{{\left(1+I\right)}^{10}}}$
Discounted Cash Flow	$C_{Initial}$	$C_{OM}$× ${\displaystyle \frac{1}{{\left(1+I\right)}^1}}$	$C_{OM}$× ${\displaystyle \frac{1}{{\left(1+I\right)}^2}}$	$C_{OM}$× ${\displaystyle \frac{1}{{\left(1+I\right)}^t}}$	${(C}_{OM}{+ C}_{Overhaul})$× ${\displaystyle \frac{1}{{\left(1+I\right)}^5}}$	$C_{OM}$× ${\displaystyle \frac{1}{{\left(1+I\right)}^t}}$	${(C}_{OM}+C_{End of Life)}$× ${\displaystyle \frac{1}{{\left(1+I\right)}^{10}}}$

provides the LCC calculations using NPV. This table presents a structured approach to calculating the total LCC for EV Charging Stations over a 10-year lifespan. Each row represents different cost components and how they are discounted to determine the total NPV, which helps identify the most cost-effective placement scenario.

4. Model Implementation and Validation

Optimizing EV Charging Station (EVCS) placement in existing parking areas requires evaluating a large number of charger configurations across multiple parking blocks. Each arrangement influences the total system cost and must satisfy spatial, electrical, and operational constraints. Because the number of potential configurations increases exponentially with the size of the parking facility, the problem calls for a systematic combinatorial approach that balances computational accuracy with efficiency. To address this, the proposed solution method combines dynamic programming—used to store intermediate results and eliminate redundant computations—with brute-force enumeration, which ensures that all feasible configurations are thoroughly evaluated. Although the model evaluates all feasible charger configurations through complete enumeration, many intermediate calculations—such as block-level wiring lengths, repeated conduit installation costs, and fixed cost components—occur across multiple scenarios. To avoid recalculating these identical subproblems, the algorithm employs dynamic programming memoization, which stores intermediate cost values and reuses them when the same block combination appears in different candidate layouts. This approach does not reduce the size of the search space, but it significantly reduces computational time by preventing redundant cost evaluations within the brute-force process. This hybrid strategy enables the model to identify the configuration that minimizes life-cycle cost (LCC) while maintaining the exhaustiveness and reliability of a full combinatorial search.

Combinatorial Optimization Algorithm

The solution algorithm operates through a structured two-stage process. In the first stage, a systematic enumeration (brute-force) method is used to generate all feasible combinations of charger placements and port configurations that satisfy the spatial and adjacency rules defined earlier. Each feasible configuration is treated as a candidate scenario in the optimization search space. In the second stage, dynamic-programming principles are applied within this enumeration process to store and reuse intermediate cost components—such as cable lengths, installation expenses, and recurring maintenance values. This reuse allows the algorithm to avoid recalculating identical subcomponents across different scenarios, significantly improving computational efficiency.

Figure 7 presents the overall flowchart of the optimization workflow for allocating Electric Vehicle Charging Ports (EVCPs). The key steps of the workflow are summarized as follows.

Step 1: The algorithm generates all feasible combinations of single-, dual-, and quad-port chargers that collectively satisfy the required number of charging ports. Every possible mix that meets the port demand constraint is included as an initial candidate.

Step 2: Each candidate charger mix is placed into the predefined parking blocks according to the adjacency, geometric feasibility, and block-capacity constraints. Only combinations that comply with the spatial feasibility rules for single-, dual-, and quad-port chargers proceed to the next stage.

Step 3: Configurations that violate geometric constraints, exceed block capacity limits, fail adjacency requirements, or result in infeasible distances from the power source are eliminated. Only spatially valid layouts are retained for cost evaluation.

Step 4: The LCC for each valid layout is evaluated by summing all cost components defined previously, including EVCS equipment, electrical balance-of-system (BOS), fixed overhead, O&M cost, and end-of-life cost. Dynamic programming ensures that repeated costs—such as cable lengths for identical block placements—are not recalculated.

Step 5: Among all feasible and validated scenarios, the algorithm identifies the layout with the minimum total life-cycle cost. This configuration is returned as the optimal EVCS allocation for the given facility.

This two-stage hybrid approach ensures that the solution space is fully explored, thereby maintaining the accuracy of brute-force enumeration, while dynamic programming improves computational performance by reducing redundancy.

Following the implementation steps described above, the model underwent a structured validation process to ensure correctness and reproducibility. To validate the model, a structured verification process was performed. First, all spatial feasibility rules—such as adjacency requirements for dual-port chargers and 2 × 2 configurations for quad-port units—were tested against manually constructed benchmark layouts to ensure that the algorithm correctly rejected infeasible placements. Second, the cost engine was validated by comparing the model’s internal cost calculations with independent hand-calculated samples for selected configurations, confirming consistency across EVCS equipment cost, electrical system cost, O&M, and fixed-cost components. Third, the combinatorial enumeration results were cross-checked to verify that all feasible charger mixes defined in Equation (1) were included and that no valid configurations were omitted. Finally, the optimal scenario identified by the algorithm was recreated manually to confirm that the model’s solution corresponded to the true minimum life-cycle cost. This multi-step validation procedure confirmed that both the feasibility logic and the cost-optimization components were functioning as intended.

5. Results and Discussion

From a sustainability perspective, retrofitting existing facilities for EV charging is particularly valuable because it avoids the material and energy burdens associated with new construction while accelerating the adoption of low-carbon mobility. The following discussion interprets the key results of the proposed framework, compares them with findings from prior research, and highlights its main contributions, limitations, and practical implications.

5.1. Case Study

A shopping complex parking lot with 236 parking spots is selected as the case study. The facility is currently equipped with four charging stations. Based on the expected growth data presented in [32], the demand for EV charging infrastructure at this location is projected to increase by a factor of 6.1 by the year 2035. Accordingly, the number of EV chargers required at the site should increase from the existing four units to approximately twenty-five units by 2035. Figure 8 illustrates the layout of the parking lot used in this study, with the utility distribution power facility located at the bottom-left corner of the site.

For this analysis, the EV charging devices are considered in three configurations: single-port, dual-port, and quad-port chargers. These variations are incorporated into the optimization model to evaluate all feasible combinations and identify the most cost-effective configuration for meeting the projected charging demand.

The minimum and maximum number of block combinations are set to 1 and 3, respectively. These Minimum and Maximum Block Combination settings define the range of block groupings the model is permitted to consider. For example, specifying a maximum of three blocks enables the algorithm to explore configurations that use up to three distinct blocks within a single scenario. This constraint limits impractical or overly dispersed layouts while maintaining sufficient flexibility in the search space.

The life-cycle discount rate and the estimated operational lifespan of the charging units are both defined as 10, reflecting a 10 percent discount rate and a 10-year service life for this case study.

Using the layout shown in Figure 8, the parking lot is segmented into blocks to create a mathematically manageable configuration, as illustrated in Figure 9.

The cost structure of the model accounts for retrofit-specific characteristics of indoor facilities through the Electrical System Equipment Cost (CSEE) and geometric feasibility mapping. Cable and conduit installation costs implicitly capture the additional labor and materials required for routing through existing walls, floors, and ceilings. The spatial occupancy matrix excludes areas affected by ventilation ducts, lighting fixtures, and structural elements such as columns or ramps to ensure that all selected charger locations are physically feasible. The existing power infrastructure is assumed to have sufficient capacity to support the selected charger mix; transformer and panel components are incorporated into the fixed-cost term of the CSEE.

As an example, Block F is defined as [4,5,7,14], corresponding to [Start Row, End Row, Start Column, End Column]. The cost parameters used in the algorithm incorporate all essential cost-related inputs of the model. Each cost component is provided as an input, as shown in Table 3, and the model applies these values throughout its calculations. By defining these costs individually, the model can more accurately project the total cost of each scenario over the infrastructure’s lifespan. The cost values presented here are based on available current data; however, they are subject to change over time and may vary across different jurisdictions.

The assumed prices for wall-mounted and pedestal EV charging units are provided in

Table 4. General Cost Parameters.

Category	Type	Configuration	Cost ($)
Fixed Costs	Communication System Cost	-	5000
	Software License Fees	-	3000
	Security Measures Cost	-	2500
Maintenance Costs (Yearly)	Pedestal Units	1-Port	100
		2-Port	150
		4-Port	250
	Wall-Mounted Units	1-Port	80
		2-Port	130
		4-Port	200
Dismantling Costs	Pedestal Units	1-Port	150
		2-Port	200
		4-Port	300
	Wall-Mounted Units	1-Port	120
		2-Port	170
		4-Port	260
Labor Costs	Cable Installation per Meter	-	5
	Conduit Installation per Meter	-	3
Charging Unit Installation Costs	Pedestal Units	1-Port	150
		2-Port	200
		4-Port	300
	Wall-Mounted Units	1-Port	120
		2-Port	170
		4-Port	260

. The cable and associated electrical equipment costs used in the model are listed in

Table 5. Port Price Parameters.

Category	Unit Type	Cost ($)
Regular EVC Prices	1-Port Pedestal Unit	2000
	2-Port Pedestal Unit	3800
	4-Port Pedestal Unit	7200
Wall-Mounted EVC Prices	1-Port Wall-Mounted Unit	1800
	2-Port Wall-Mounted Unit	3400
	4-Port Wall-Mounted Unit	6400

.

The most optimized result for the case study is shown in the corresponding figure. As illustrated, Blocks F and L yield the best overall configuration. The optimized solution includes a combination of single-port, dual-port, and quad-port EVCS units. As shown in Figure 10 and summarized in

Table 6. Cable and Equipment Cost.

Category	Unit Type	Cost ($)
Electrical Equipment Costs	Breaker Cost	500
	Fuse Cost	50
	Junction Box Cost	200
	Conduit Cost per Meter	15
Cable Costs Based on Number of Ports	Port Count 1	6
	⋮	…
	Port Count 26	150

, the allocation is divided between Block F and Block L. As expected, the pedestal quad-port units and wall-mounted dual-port units produce the most cost-effective outcome. This result follows from the fact that combining these two charger types minimizes redundant installation requirements and reduces total life-cycle cost.

While the optimal and all-single-port configurations result in concentrated charger placement within a limited number of blocks, this outcome reflects the model’s objective of minimizing life-cycle cost under the assumption of sufficient upstream electrical capacity. In practical applications, however, highly clustered layouts may introduce additional considerations such as localized electrical loading, transformer or feeder constraints, ventilation requirements, and potential congestion around charging areas. These factors may lead facility operators to distribute chargers more evenly across a parking structure despite the slight cost premium. Incorporating such operational and capacity-related constraints into the optimization framework presents a valuable direction for future work and would enable the model to balance cost efficiency with operational resilience and user accessibility.

Although this study validated the framework using a single shopping-complex parking lot, the modeling approach is inherently scalable to facilities of different sizes, geometries, and use profiles. Because the formulation defines spatial blocks parametrically, it can accommodate varying parking densities, aisle orientations, and charger-access constraints by adjusting the matrix mapping and feasibility rules. The same optimization logic can be applied to multi-level structures, open-air parking lots, or mixed-use facilities by redefining boundary conditions and spatial adjacency parameters. Therefore, the case study serves as a proof of concept that demonstrates the methodological validity of the framework rather than a limitation of scope. Future work will incorporate additional facility configurations to further evaluate the model’s performance across diverse layouts and usage conditions.

The optimization results demonstrated that combining dual- and quad-port chargers outperformed single-port configurations in terms of total life-cycle cost. The single-port-only configuration, which was included within the optimization search space, consistently produced higher life-cycle costs because each charger required separate cabling and individual installation work. Based on the case study data, the optimized mixed configuration resulted in a total life-cycle cost of approximately $143,800, compared with about $175,000 for an equivalent all-single-port layout, representing a reduction of roughly 22 percent. This confirms that multi-port combinations offer substantial cost advantages by sharing electrical infrastructure and minimizing redundant installation components. This outcome is expected, as multi-port units consolidate installation requirements and electrical components, thereby reducing both per-port capital and operational expenses. The model also revealed that spatial constraints significantly influence cost efficiency; maximizing port density within available spaces contributes to the greatest overall savings.

In our experiments, multi-port layouts significantly reduced per-port electrical balance-of-system costs and annual operations and maintenance (O&M) expenses relative to single-port configurations, as shown in

Table 7. Optimal Solution.

Block Combination	F, L
Port Combination	[1, 2, 2, 2, 2, 2, 2, 4, 4, 4]
Port Distribution in Block F	Three Quad-ports
Port Distribution in Block L	One Single-port, Six Dual-ports

. These reductions result from shared conduit and cabling runs, as well as consolidated protection and communication systems. Compared with the single-port baseline (NPV ≈ $168,000), the optimized dual- and quad-port mix (NPV ≈ $143,800) achieved approximately a 15 percent lower total life-cycle cost while maintaining the same charging capacity. Average wiring length and conduit installation requirements per port decreased by a similar proportion, reflecting the reduced number of independent circuits and shorter overall installation runs. Even simplified practical layouts that utilized only one type of multi-port charger produced cost savings of approximately 16 percent compared with the all-single-port configuration (

Table 8. Optimal Solution for only single port option.

Block Combination	C, G, W
Port Combination	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
Port Distribution in Block C	One Single-ports
Port Distribution in Block G	Twenty-three Single-ports
Port Distribution in Block W	One Single-ports

), reinforcing that shared-infrastructure efficiencies are the primary drivers of cost reduction.

The model further revealed that spatial constraints have a substantial influence on cost efficiency; maximizing port density within the available spaces yielded the greatest overall savings.

The comparative results also reveal the underlying cost drivers behind the optimal configuration. The model showed that dual- and quad-port chargers achieved lower life-cycle costs primarily because they share electrical balance-of-system components such as conduits, breakers, and protective devices, thereby reducing per-port installation costs. In addition, multi-port configurations lowered recurring maintenance costs per charging point by consolidating service, monitoring, and communication systems. In contrast, single-port options generated higher per-port costs because each unit required its own dedicated electrical runs and protective hardware. These interactions among equipment sharing, space utilization, and maintenance demands explain the consistent advantage of multi-port setups in both capital and operational terms.

This study advances recent research on electric-vehicle charging-station planning by integrating complementary perspectives and addressing critical gaps in prior work. Zhang et al. [34] optimized techno-economic scheduling for community charging hubs in multi-unit dwellings, focusing on levelized costs and shared-hub operations, but their analysis did not incorporate spatial feasibility or retrofit constraints arising from fixed building geometries. In contrast, our framework addresses the micro-siting problem directly by enforcing adjacency and footprint rules to ensure that multi-port hardware is physically deployable within existing indoor layouts.

Similarly, Zheng and Zheng [35] employed an enhanced particle-swarm optimization (PSO) algorithm to optimize regional charging layouts for improved renewable-energy integration, prioritizing grid-level coordination. Our approach, however, resolves site-specific life-cycle cost trade-offs—including equipment, electrical balance-of-system, and fixed costs—at the facility scale, where local retrofit conditions significantly influence total cost. Likewise, Campaña and Inga [36] developed a graph-based mixed-integer optimization model for public charging infrastructure in smart cities, accounting for vehicle flow and traffic density, but their work did not capture the geometric and structural constraints of existing facilities. Our model extends these efforts by integrating physical layout feasibility with cost minimization for indoor retrofits, effectively bridging urban-scale planning with facility-level implementation, where spatial constraints frequently dominate cost outcomes.

The primary contribution of this study lies in its integration of spatial feasibility with life-cycle cost optimization for retrofitting existing indoor parking facilities. This approach fills an important gap in prior research, which has largely focused on new or open-air installations, and provides a practical, owner-focused framework for designing EV charging layouts that are both cost-efficient and compatible with the physical constraints of existing structures.

By combining spatial feasibility with life-cycle costing, this framework offers property owners a more realistic decision-making tool compared with earlier location-only or coverage-based models. It demonstrates that cost efficiency can be achieved without expanding facility footprints or requiring extensive infrastructure upgrades, thereby improving the practicality of EV charging optimization in existing commercial spaces. While the formulation builds on the classical facility-location structure, its application here differs fundamentally from standard siting models. The novelty lies in adapting the problem to existing indoor environments where charger placement must adhere to discrete parking geometries, adjacency requirements, and shared electrical infrastructure constraints. These spatial considerations, combined with a life-cycle cost formulation that captures both capital and recurring elements, transform the problem into a layout-constrained cost-minimization task rather than a traditional open-space location problem. Consequently, the framework extends facility-location theory into retrofit contexts that have received limited analytical attention in previous work.

From an owner’s perspective, these results highlight the importance of incorporating life-cycle cost analysis into investment planning. Rather than focusing solely on initial equipment costs, the model accounts for ongoing operations, maintenance, and end-of-life expenses, offering a comprehensive long-term financial assessment. Ultimately, the findings show that cost-optimal solutions are achievable within existing facilities, enabling owners to meet increasing EV charging demand without securing additional land or undertaking major infrastructure upgrades. Beyond facility owners, the results also provide valuable insights for utilities and municipalities seeking to design targeted incentives that support retrofits capable of adding charging capacity without requiring new land use or significant service enhancements.

Practically, these findings provide parking facility owners with clear guidance for planning retrofit investments that support broader sustainability and decarbonization objectives. By leveraging existing structures, such retrofits can substantially expand EV charging capacity with minimal additional land or material use. This approach aligns with municipal emission-reduction goals and promotes more efficient urban space utilization. Moreover, it demonstrates how private investment decisions can support public sustainability policies by balancing economic viability with environmental benefits.

The current model is deterministic, relying on fixed demand and cost inputs, simplified tariff and grid-capacity assumptions, and a single enclosed-garage geometry. Nevertheless, it is readily extensible through sensitivity or scenario analyses to assess robustness under uncertain conditions, including stochastic variations in EV uptake, equipment and installation costs, and energy prices. Future enhancements could incorporate additional garage layouts, more detailed tariff modules (such as time-of-use (TOU) rates or demand charges), and explicit grid-capacity constraints to improve the model’s applicability for broader planning studies.

As shown in the optimization results, the configuration with the minimum total cost over a 10-year lifespan selects Blocks F and L for charger installation. The optimal setup includes a mix of port types consisting of single-port units (4 percent of the total), dual-port units (48 percent), and quad-port units (48 percent). The high initial cost in year 0 corresponds to the EVCS equipment cost, electrical system equipment cost, and fixed costs associated with installation.

Table 9. LCC Calculation for Minimum Total Cost Result.

Year	Zero	One	…	Five	…	Ten
Annual Cost ($)	0	11,840.00	…	11,840.00	…	11,840.00
One-time Cost ($)	60,358.75	0		11,840.00		8700.00
Annual Net Cash Flow ($)	60,358.75	11,860.00		23,680.0		20,540.0
Discounted Rate ($)	1	0.90		0.62		0.38
Discounted Cash Flow ($)	60,358.75	10,763.63		14,703.4		7919.05
Total Cost (NPV) ($)	$143,816.35

provides a detailed breakdown of the life-cycle cost (LCC) calculation based on the total net present value (NPV) using a discount rate of 10 percent. The discounted cash flow of the optimal result is depicted in Figure 11.

Additionally, the percentage of the yearly discounted cash flow relative to the optimal result’s initial cost is shown in Figure 12. As expected, the annual discounted cash flow represents only a portion of the initial investment cost.

The comparison between the number of wall-mounted and pedestal EV charging stations (EVCs) in the optimized result is shown in Figure 13. As expected, the distribution reflects a balance between the two types, driven by the direct influence of equipment cost, electrical system costs, and the labor associated with installing electrical components.

A 10 percent annual discount rate was applied to represent the owner’s opportunity cost of capital, consistent with typical values used in EV infrastructure investment analyses (8–12 percent). Equipment, installation, and maintenance costs were sourced from publicly available manufacturer data, industry cost guides such as RSMeans (construction cost database) (2023), and published EV infrastructure reports. These standardized values ensure that the case study reflects representative market conditions rather than project-specific quotations.

Overall, the results demonstrate the practicality and flexibility of this framework for optimizing indoor EV charging retrofits.

5.2. Qualitative Sensitivity Analysis

To further strengthen the discussion and demonstrate the robustness of the model, a qualitative sensitivity analysis is included here. The optimal configuration and total life-cycle cost depend on several key input assumptions. We examined the directional impact of varying these parameters and outlined the observed effects below.

1.

Discount rate: Increasing the discount rate places more weight on upfront capital relative to future O&M. This can make lower-capex options more attractive, even if per-port O&M is higher. Decreasing the discount rate has the opposite effect and strengthens the case for multi-port sharing because future O&M savings are valued more.

2.

Service life: Shorter lifespans reduce the importance of O&M and end-of-life terms and may favor cheaper hardware with less sharing. Longer lifespans increase the value of O&M savings and typically reinforce multi-port solutions.

3.

Unit cost of cable, conduit, and labor per meter: Higher per-meter costs favor designs that minimize total run length. This tends to push the solution toward higher-port-count units and denser siting near the power source, since multi-port devices share feeders and protective devices.

4.

Relative hardware prices across port counts: If quad-port hardware prices rise relative to dual-port units, the mix can shift toward dual-port dominance, and vice versa.

5.

Uniform fixed costs (software, communications, security). Uniform fixed costs shift total NPV but have a limited influence on the optimal mix because they do not change relative tradeoffs among layouts.

6.

Distance-to-power and geometry: Tighter geometric limits or longer average distances to the power source increase the benefit of port sharing and compact placement, which again tends to favor dual- and quad-port units.

These patterns indicate that the mixed dual- and quad-port configuration remains preferred across typical ranges of financial and installation assumptions. Future enhancements could formalize these observations through one-way sensitivity sweeps or scenario-based analyses to quantify the effects of parameter uncertainty on both total cost and configuration outcomes.

6. Conclusions

This study developed a mixed-integer nonlinear programming (MINLP) framework to minimize the life-cycle cost of retrofitting electric vehicle charging stations in existing indoor parking facilities and evaluated its performance over a ten-year period using annual discounting. The main contribution of this paper was threefold. First, the model introduced a cost-minimizing framework from the owner’s perspective. It was specifically tailored to indoor retrofit conditions, a context rarely addressed in previous EV charging studies, and incorporated explicit spatial feasibility rules for dual-port and quad-port charger placements. Second, it presented a unified decision model that jointly selected the charger mix and placement across parking blocks while accounting for all life-cycle cost components, including electrical system equipment and fixed costs relevant to investment planning. Third, it established a transparent computational structure that combined brute-force enumeration for feasible configuration generation with dynamic programming for subproblem reuse, enabling reproducible and auditable cost evaluations. The results demonstrated that multi-port configurations effectively balance spatial constraints and cost efficiency, indicating that optimized retrofitting strategies can accommodate projected growth in charging demand while minimizing total expenditures. The findings also carry several practical and sustainability implications. For property owners, the framework provides a quantitative basis for selecting cost-effective and spatially feasible charger configurations before committing to capital investment, thereby supporting data-driven retrofit decisions. From a planning standpoint, the study shows how life-cycle cost optimization can be integrated with geometric feasibility analysis to guide efficient use of existing parking assets. In a broader sustainability context, the approach offers a pathway to expand EV charging infrastructure without additional land use, aligning private investment decisions with public low-carbon mobility goals and long-term decarbonization strategies. Overall, the framework provides a practical decision-support tool for property owners seeking to expand charging capacity within existing facilities, improving cost effectiveness and contributing to sustainability goals without requiring additional land development. The current model is limited by its deterministic assumptions and simplified representation of the grid and cost factors. Future work could extend the framework by incorporating uncertainty analysis and validating its applicability across different parking layouts and cost environments. Additionally, optimizing multi-port configurations improves energy efficiency and reduces redundant cabling and material use, aligning with circular economy principles. The framework therefore supports multiple dimensions of sustainability, including economic, environmental, and spatial, by lowering life-cycle costs, preserving existing infrastructure, and enabling more equitable access to clean mobility. The case-study results demonstrated that the optimal configuration relied heavily on dual- and quad-port chargers, which together reduced total life-cycle cost by approximately 22 percent compared with an equivalent all-single-port layout. This reduction was driven primarily by shared electrical balance-of-system components and lower installation and O&M requirements per port. The spatial allocation results further showed that Blocks F and L consistently offered the most cost-effective placement due to their proximity to the power source and ability to accommodate multi-port units without violating geometric constraints. These findings confirm that optimizing port density and equipment sharing provides measurable economic benefits for indoor retrofits.