M. Safii*
| Husain | Ika Okta Kirana
© 2025 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
OPEN ACCESS
The need for an efficient and sustainable energy system has become a major challenge in the energy transition in Indonesia, although the country has great potential in renewable energy. The utilization of these resources is not yet optimal due to the lack of cost-effective production and distribution planning that meets regional needs. This research designs a Mixed-Integer Programming (MIP) based optimization model to optimally allocate energy production from various renewable power plants. The model considers generation capacity, regional demand, and technical distribution constraints. Implementation is carried out using LINGO for the main calculations and Python for result validation, ensuring accuracy and efficiency of the algorithm. The results show a global optimal solution with minimum costs and an even distribution of energy at the highest efficiency generation, while high marginal cost generation is automatically eliminated.
mixed-integer programming, renewable energy, optimization, production, distribution
The global energy transition towards sustainable and low-carbon energy sources has become a pressing strategic issue in the last decade [1]. Climate change, volatility in fossil fuel prices, and international pressures to reduce carbon emissions have prompted many countries, including Indonesia, to adopt and accelerate the integration of renewable energy into their national energy systems [2, 3]. Indonesia has significant and diverse renewable energy potential, such as solar power with potential exceeding 200 GW, widespread wind energy in the eastern regions, biomass from agricultural and forestry waste, as well as hydro and geothermal energy [4, 5]. Despite this potential, Indonesia still lacks an integrated, cost-efficient model for renewable energy production and distribution. The utilization of this potential is still far from optimal, primarily due to limitations in production planning, imbalances in distribution, and weak integrative infrastructure between regions [6].
Optimization of scheduling and distribution of renewable energy is crucial in ensuring the efficiency of energy systems, meeting load demands, and minimizing total system costs [7, 8]. Optimization-based mathematical models such as Mixed-Integer Programming (MIP) have been widely used to solve complex problems in energy system planning, especially for large-scale integration of renewable generation [9-11]. In the context of Indonesia, the application of MIP optimization models that consider the technical characteristics of generation and regional demand is still rarely found in the literature, thereby opening up research opportunities to make a tangible contribution to national energy policy.
Previous studies have demonstrated the effectiveness of the MIP approach in the energy sector. For example, developing an MIP model for power system expansion planning considers the integration of renewable energy [12]. The research [13] applied the application of the linear programming method in the construction of a mathematical model of optimization distributed energy, that it is believed that distributed energy can be an effective solution to the problems of conventional energy operations. Meanwhile, the research [14] presented a linear programming approach to the optimization of residential energy systems shows that the scheduling strategy proposed in this paper can save 22.8% of the operating cost under the same conditions. In the evaluation of renewable energy efficiency, a new scenario is constructed, and the result is still ideal. Although various studies have shown the success of applying MIP in energy systems, most of this research still focuses on global or regional contexts outside Indonesia. Research that integrates renewable energy scheduling and distribution aspects simultaneously on a national scale in Indonesia is still limited [5, 15]. Moreover, most previous studies have not considered cross-validation between optimization software and Python-based programming to ensure the accuracy of the model results. Thus, there is a gap in the literature regarding the development of applicable and verified optimization models for Indonesia's complex and dispersed geographical context.
This study develops an MIP-based optimization model for Indonesia’s renewable energy generation and distribution, considering plant capacity limits, regional demand, and cost efficiency. The model tested in LINGO and validated in Python, aims to minimize total costs while ensuring equitable supply. The main contributions are:
(1) a national-scale, multi-generator optimization model tailored to Indonesia’s geography;
(2) dual-platform validation to enhance result reliability;
(3) a practical framework to support the national renewable energy mix target of 23% by 2025 [16]. Furthermore, this quantitative approach is expected to serve as a reference for data-driven decision making by the government and energy stakeholders in formulating more efficient and sustainable electricity system planning policies.
This study uses a quantitative approach with a MIP based mathematical optimization method to develop a production scheduling model and distribution of renewable energy in Indonesia. The research process is conducted systematically through three main stages: Initial Stage, Modeling, and Final Stage, as shown in Figure 1.
Figure 1. Research flow
The research methodology is structured into three main stages, namely the Initial Stage, the Modeling Process, and the Final Stage, as shown in Figure 1. Each stage is carried out systematically to produce a valid and reliable optimization model for production scheduling and distribution of renewable energy in Indonesia.
2.1 Research design
This research is a quantitative study with an experimental numerical design approach through optimization simulation [17, 18]. The main focus is on the development of a mathematical model to minimize the total cost of renewable energy systems while considering capacity constraints and demand in various regions of Indonesia [19]. The model is formulated using a linear programming approach with the possibility of expanding to MIP for binary distribution control (active/inactive) [20, 21].
2.2 Subject and object of research
The subject of the research is the production and distribution system of renewable energy in Indonesia, which involves various types of power plants: Geothermal Power Plant (PLTP), Hydropower Plant (PLTA), Micro hydro Power Plant (PLTMH), Solar Power Plant (PLTS), Wind Power Plant (PLTB), and biomass-based or non-fossil thermal power plants (PLTU). The object of the research is a mathematical optimization model for scheduling the distribution of energy from the power plants to consumption areas based on cost efficiency [22, 23].
2.3 Data collection procedure
Data collection was carried out through two main stages. First, a literature study and problem identification were conducted to obtain secondary data from various authoritative sources, including official reports from the Ministry of Energy and Mineral Resources (ESDM) [4] and PT PLN (Persero) [24]. The main parameters collected include:
(1) maximum power plant capacity (in MWh) based on the type of plant (solar, wind, hydro, geothermal, biomass),
(2) regional energy demand (in MWh) referring to the latest national electricity load projections,
(3) production and distribution cost coefficients sourced from ESDM cost references, PLN operational data, and estimates from literature related to transmission lines and types of plants. Second, data compilation and pre-processing are carried out to ensure the compatibility of the optimization model input format. This process includes cleaning the data from missing or inconsistent values, standardizing units (MWh for energy and rupiah for costs), normalizing cost data to the same reference year, cross-verifying generation capacity from various sources, and compiling cost and distribution distance matrices between regions. The optimization model was first implemented and solved using LINGO software to obtain a basic optimal solution. The same formulation, parameters, and dataset were then replicated in Python using the equivalent MIP solver, PuLP. The validation process was carried out by comparing the objective function values (total costs) on both platforms, verifying the similarity of the decision variable values (energy allocation from each generator to each region), and conducting sensitivity tests to ensure the model's consistent responses to changes in input parameters. The validation of these two platforms ensures that the developed model has high robustness, repeatability, and computational accuracy.
2.4 Modeling and simulation procedures
The modeling steps in this research were carried out systematically as shown in Figure 1, namely:
The main problem in this study is how to optimally allocate the production and distribution of energy from various renewable generation sources to meet energy demands in various regions at minimum total cost. This issue is formulated into an MIP approach focused on a deterministic scenario based on historical data and system parameters [25, 26].
The developed mathematical model consists of an objective function and several constraints that are expressed linearly [27]. The model can be formulated as follows:
(1) Objective function:
Minimization of total production and distribution costs of energy [28]:
$\operatorname{Min} \mathrm{Z}=\sum_{i \in P} \sum_{j \in W}\left(C_i^P+C_{i, j}^d\right) x_{i, j}$ (1)
with $x_{i, j}=$ the amount of energy distributed from power plant $i$ to area $j$ (in MWh ). $C_i^P=$ production cost per unit of energy from the power plant $i . C_{i, j}^d=$ energy distribution cost from generator $i$ to area $j$.
(2) Constraints of power plant capacity:
$\sum_{j \in W} x_{i, j} \leq K_i, \forall_i \in P$ (2)
with $K_i$ being the maximum capacity of generator $i$.
(3) Constraints of regional demand limitations:
$\sum_{i \in P} x_{i, j} \geq D_j, \forall_j \in W$ (3)
with $D_j$ being the energy demand of region $j$.
(4) Constraints of binary distribution:
$x_{i, j} \leq M \cdot y_{i, j}, \forall_{i, j}$ (4)
$y_{i, j} \in\{0,1\}, \quad x_{i, j} \geq 0$ (5)
The binary variable $y_{i, j}$ represents the decision of energy distribution from generator $i$ to region $j$ where $y_{i, j}=1$ if the distribution is active and $y_{i, j}=0$ if it is not. The relationship between $y_{i, j} \mathrm{~d}$ and the continuous variable $x_{i, j}$ is governed by the constraint $x_{i, j} \leq M . y_{i, j}$, where $M$ is a large constant that limits the maximum distribution capacity. This MIP formulation combines discrete decisions (activation of distribution paths) and continuous decisions (volume of energy), allowing for the elimination of high-cost paths and efficient allocation of energy according to regional demand.
2.5 Simulation and model optimization
The model is implemented and optimized using LINGO software with linear programming methods. As a validation and comparison step, the same model is also rebuilt using Python with the Pulp library, in order to verify the accuracy of the objective values, the consistency of the constraints, and the stability of the solutions.
2.6 Model validation
Validation is carried out through a comparison between the results of LINGO and Python, including the objective function value (total cost), the energy distribution allocation pattern ($x_{i, j}$) and the slack and dual values of the capacity and demand constraints. This validation is important to ensure that the model is free from formulation errors and that the solver operates as expected in achieving the global optimal solution [29, 30].
2.7 Analysis and interpretation of results
The optimization results show the allocation of energy from the power plants to the regions in an optimal manner, demonstrating that power plants with lower marginal costs are prioritized. Information from the slack values and shadow prices provides insights related to the utilization of power plants as well as the marginal value of energy for each region. These findings can be utilized as a basis for strategic decision-making in national energy.
The results of the optimization process carried out using a Linear Programming model for energy generation system planning. An analysis was conducted on the objective function value, decision variables, and interpretation of dual parameters such as reduced cost, slack/surplus, and dual price. The results were obtained from a computational process using LINGO software, which efficiently produced a global optimal solution while satisfying all model constraints. The objective function value reflects the minimum total cost of the system, while the distribution of decision variable values indicates the optimal allocation of energy generation from each source. Next, the dual results are used to evaluate the sensitivity and efficiency of each power plant's contribution to the total costs. The discussion in this section focuses on the interpretation of these results to support strategic decision-making in sustainable and economical energy management. The results of this model testing can be seen in Figure 2:
Figure 2. Results of the LINGO model testing
The results of the optimization model testing show that the global optimal solution has been successfully found with an objective function value of 63,534.39 × 1013 which represents the total minimum cost of the combination of energy production and distribution according to the linear programming model formulation. An infeasibility value of 0.000000 indicates that all model constraints are satisfied without violation. The solution process was carried out efficiently, with a total solver iteration of 0 and a computation time of only 0.13 seconds. The model used is purely linear, with a total of 44 decision variables, no nonlinear variables, and no integer variables. The number of constraints in the model reaches 109, with a total of 171 non-zero coefficients, all of which are linear. This result confirms that the model has a simple mathematical structure but is capable of providing optimal solutions quickly, making it relevant for efficient planning of renewable energy production and distribution.
3.1 Distribution decision
The selection of generators in an optimal solution is greatly influenced by the structure of marginal costs. The model tends to choose generation units with low costs and high efficiency, while avoiding the use of units with high costs, even though those units are available in the system, as shown in Figure 3:
Figure 3. Distribution decision
Based on the results of the linear programming model optimization in the Figure 3, the value of the variables represents the optimal production or distribution amount from each power plant to specific regions to achieve minimum total cost. The X_PLTP2_LAMPUNG plant produces 12,497.96 units, while X_PLTP1_SUMUT and X_PLTA1_SUMUT have a value of zero, indicating that these plants are not used in the optimal solution. The high reduced costs at X_PLTP1_SUMUT (1.065072 × 10⁸) and X_PLTA1_SUMUT (2.450846 × 10⁸) indicate that the use of these units will significantly increase costs, so they are not selected in the optimal solution. Variables with a reduced cost value of zero indicate that the power plants directly contribute to achieving minimum costs or are at their optimal limit.
3.2 Analysis of system constraints and sensitivity
Identification of active and inactive constraints is important to determine further optimization strategies, such as relaxing capacity limits or strengthening generation components that have a significant contribution to overall system cost efficiency. This analysis can be seen in Figure 4.
Figure 4. Analysis of constraints
Based on Figure 4, the optimal value of the Objective Function is achieved at 63,534.39 × 10¹² with zero infeasibility, indicating that all constraints are satisfied without violations. This model consists of 44 variables and 109 constraints, all of which are linear without any non-linear variables or constraints. The Dual Price column represents the change in the Objective Function value if one more unit of resource is added to that constraint. A positive value indicates that increasing the resource at that constraint will raise the Objective Function value (profit), while a negative value indicates that adding resources will actually decrease the objective value. Row 2 has a dual price of 1.033204 × 1011, which means that each additional unit of resource added to that constraint will increase the profit by that amount. Conversely, Row 45 with a dual price of 1.465178 × 1011 indicates that additional resources will decrease the objective value by that amount. Thus, the results of this dual analysis provide strategic guidance for optimizing production, distribution, or resource utilization policies more effectively.
3.3 Implementation with Python
The results of the energy distribution optimization model test conducted using Python show that an optimal solution has been achieved, as indicated by the model status being optimal. The objective function value obtained is 56405002169769.4, which represents the minimum total cost of energy distribution to all analyzed areas. The energy distribution from various power plants to the demand areas is presented in Figure 5.
Figure 5. Energy distribution
Based on the image above, it can be explained that the energy distribution shows that several power plants provide a dominant contribution to meeting energy needs in certain areas. For example, PLTB 2 distributes a large amount of energy to South Sulawesi totaling 90,083.51 MWh, while PLTBio 5 and PLTBio 7 distribute energy of 50,546.92 MWh to South Sumatra and 23,227.57 MWh to Lampung, respectively. Renewable energy sources such as PLTS and PLTM/H also make significant contributions, such as PLTS 6 to Gorontalo (8,472.30 MWh) and PLTM/H 9 to Southeast Sulawesi (6,268.80 MWh), as can be seen in Figure 6.
Figure 6. Optimal energy distribution graph
The distribution carried out not only reflects cost efficiency but also demonstrates the optimization of utilizing local energy potential, by maximizing generation based on renewable natural resources. This result indicates that the optimization approach based on linear programming is capable of producing economically viable energy allocation scenarios and supports sustainable energy policies, with the total energy visible in Figure 7.
Figure 7. Total energy allocation
Figure 7 presents a visualization of the total energy allocation (measured in MWh) distributed to each provincial region in Indonesia based on the results of the developed MIP model optimization. It shows that South Sulawesi received the highest energy allocation, nearing 92,000 MWh, followed by South Sumatra and North Sumatra with allocations of approximately 58,000 MWh and 42,000 MWh, respectively. Other regions such as Lampung, Riau, and the Riau Islands also received significant energy distributions, indicating that areas with high demand or those near low-cost power generation facilities tend to receive larger energy allocations. Conversely, regions such as North Sulawesi, NTB, and Aceh receive relatively small energy allocations. This distribution reflects the results of the objective function of cost minimization and operational constraints of the model, where the system tends to prioritize supply to regions that are economically and operationally more efficient. This is in line with the principles of optimizing renewable energy systems that consider both the demand side and distribution efficiency.
3.4 Slack and dual price results
The analysis results on slack and dual price from capacity and demand constraints in the optimization model show the differing contributions of each generator and region to the objective function value. In the generator capacity constraints, it was found that most generators are not operating at their maximum operational limits, as indicated by positive slack values and a dual price of zero. This indicates that the actual generation capacity is still below the allowed limit, so these constraints do not directly affect the total system cost value as can be seen in Appendix.
It can be explained that several power plants have zero slack and negative dual prices, indicating that these power plants are operating at maximum capacity and are binding. For example, Geothermal Power Plant 2, Hydroelectric Power Plants 2 to 6, Hydroelectric Power Plant 12, Solar Power Plants 1 to 4, as well as Mini Hydro Power Plants 3 and 4 show significant negative dual price values, indicating that increasing the capacity of these plants could potentially reduce the total system costs substantially. In contrast, other plants like Bio Power Plant and Mini Hydro Power Plant mostly still have quite a large reserve capacity, as indicated by high positive slack. In the section of demand, all regions show a slack value of zero or close to zero with a positive dual price, which means that the entire energy demand in each region is optimally met and is active in the model (binding constraints). Regions with high dual prices such as South Sulawesi (Rp322,254,700/MWh), South Sumatra (Rp198,737,350/MWh), and Hydro Power Plant 12 in South Sulawesi (Rp315,690,250/MWh) indicate that increasing the supply to these regions can significantly reduce the total system costs. This finding emphasizes that the capacity expansion strategy for power generation needs to be directed towards plants and regions with high dual prices in order to achieve optimal cost efficiency.
The results of the implementation carried out using LINGO for the main calculations and Python for validating the results to ensure the accuracy and efficiency of the algorithm can be seen in Table 1.
Table 1. Comparative table
|
Comparative Aspects |
LINGO Results (1) |
Python Results (2) |
Analysis of Differences |
|
Total Energy Distribution Cost |
6.353439 × 1013 |
5.6405 × 1013 |
Python results show cost efficiency due to more optimal supply sources. |
|
Energy Distribution Pattern |
The distribution of supply is more random, with some regions supplied from distant power plants. |
More centralized distribution, regions are supplied from the nearest power plant. |
This difference indicates an improvement in the strategy for utilizing local power generation capacity. |
|
Utilization of Power Plant Capacity |
Not fully optimized for low-cost generators |
Maximizing low-cost power generation |
Direct effect on reducing total costs. |
|
Relevance to the Target Budget |
Exceeding the target |
Closer to the target or below the target |
The second scenario is more suitable for practical implementation. |
Based on the results of the MIP modeling obtained, this model is capable of determining the allocation of energy distribution from various types of power plants to each region in Indonesia. Python results show cost efficiency due to more optimal supply sources. The difference in results shows an improvement in the strategy for utilizing local power generation capacity. This optimization demonstrates the great potential of using MIP as a supporting tool for national energy policies, especially in designing efficient and equitable energy distribution. Through proper allocation management, the government can reduce disparities in energy access between regions, maximize the utilization of existing power generation resources, and minimize overall operational costs. The strategic implications of this result are that the MIP approach can serve as a foundation for long-term energy planning, assist in the transition towards renewable energy systems, and strengthen regional energy equity in Indonesia. Although the results obtained are already optimal within the framework of the model used, there are several limitations that need to be acknowledged. The current model is deterministic with the assumption of static energy demand, thus not accounting for the dynamics of demand fluctuations, supply uncertainties, or system disturbances. Furthermore, energy delivery is assumed to occur without real-time constraints, and does not accommodate energy storage technologies such as batteries or pumped storage that could enhance the system's flexibility. For future research, it is recommended that the model be expanded to consider uncertainty modeling (for example, through a stochastic optimization approach), dynamic demand and supply scenarios, as well as the integration of energy storage technology. The use of this approach will not only improve the robustness of optimization results but also bring the model closer to real operational conditions in the field. Furthermore, the addition of real-time dispatch aspects and multi-objective optimization considering carbon emissions will make a significant contribution towards achieving Indonesia's decarbonization targets.
Researchers express their gratitude to the Ministry of Higher Education, Science, and Technology of the Republic of Indonesia and the leadership of the Muhammad Nasir Foundation AMIK and STIKOM Tunas Bangsa as well as the Rector of Bumigiora Mataram University.
A. Distribution of slack and dual price
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