Nowadays, the limited availability of fossil fuel resources and the environmental risks associated with their use have led to increased attention and investment in renewable energy. Expanding the utilization of renewable energy as an alternative energy source, along with restructuring electricity supply chain networks, can contribute to optimizing the electricity supply chain. Given the growing importance of renewable energy, which addresses not only economic concerns but also environmental sustainability, electricity generation from renewable sources has become increasingly significant. The design of electricity supply chain networks incorporating Renewable Energy Sources (RES), such as solar, wind, and biomass, is an issue that requires country-specific and specialized investigation. Determining the optimal electricity price is also of considerable importance, as electricity companies and consumers may have conflicting interests regarding pricing strategies aimed at minimizing electricity prices while simultaneously maximizing profitability. Given the importance of competitive electricity pricing, this study specifically focuses on designing a competitive biomass-to-electricity supply chain network while considering a buyback contract.

Karimi et al. [1] proposed a bi-level optimization problem to model the interconnection between a Virtual Power Plant (VPP) and Private Owners (POs) in distribution systems. The upper level of the model focuses on the sustainable operation of the distribution system, where the VPP solves a multi-objective optimization problem to simultaneously maximize profit and minimize excessive water withdrawal. Acting as an intermediary, the VPP facilitates interactions between wholesale and retail electricity markets by purchasing energy from the wholesale market and selling it to POs in the retail market. At the lower level, POs participate in the retail market with the objective of minimizing their costs and can either generate electricity using their own resources or purchase it from the VPP. The coordination between the VPP and POs is formulated as a bi-level optimization problem.Testado et al. [2] addressed the challenge of supplying electricity to isolated areas by developing an innovative optimal sizing tool for hybrid power plants integrating biomass gasifiers. The proposed tool was specifically designed for isolated regions with access to locally produced biomass. Their study was motivated by the fact that millions of people living in remote areas lack an uninterrupted power supply because they are not connected to the main electricity grid. Under such circumstances, local electricity generation is generally the only feasible means of obtaining access to electricity and often relies on diesel engine–generator sets or Photovoltaic (PV) arrays. In many cases, however, such configurations do not fully utilize all locally available resources, including biomass. Indeed, most isolated regions have access to biomass generated through local agricultural activities, which can be used for local electricity generation through gasification. Erol and Filik [3] found that microgrid energy management algorithms have attracted increasing attention because of their potential to ensure efficient operation and coordinate active end users. In developing such algorithms, leader–follower game-theoretic approaches can provide effective strategies for incorporating the behavioral and operational characteristics of active end users into the decision-making framework. Nevertheless, because these approaches require the accurate implementation of the strategy determined by the leader, addressing uncertainties associated with renewable energy generation, the charging and discharging of energy storage systems, and load consumption is of considerable importance. Alizadeh et al. [4] identified Transactive Energy Control (TEC) as a market-based control mechanism and a critical concept for scheduling Multi-Carrier Energy Systems (MCESs) in local networks and forming an Energy Hub (EH). Nevertheless, implementing TEC for the scheduling and control of MCESs remains highly challenging because of the absence of a collaborative TEC model that simultaneously accounts for network constraints and uncertainties associated with RESs. Dianat et al. [5] investigated energy development scenarios in countries characterized by intense competition in the renewable energy sector and proposed appropriate policies by evaluating alternative development plans. By integrating system dynamics, agent-based modeling, and game theory, they developed a framework for analyzing energy development trends and the responses of competitors and investors. Li et al. [6] proposed a stochastic programming approach based on Conditional Value at Risk (CVaR) to address a retailer’s expected losses under renewable energy uncertainty. They formulated a nonlinear bi-level model and transformed it into a Mixed-Integer Linear Programming (MILP) problem in the first stage by applying the Karush–Kuhn–Tucker (KKT) optimality conditions. Bi and Li [7] employed a real-options model to evaluate valley–peak pricing and subsidy policies under uncertainty and incorporated a policy-adjustment mechanism into their framework. Their results demonstrated that the optimal subsidy decreases while the optimal peak-to-valley price ratio increases. However, cost fluctuations create uncertainty among investors and consequently slow PV development. Tsao et al. [8] developed a distribution network design model incorporating voltage control and electricity pricing mechanisms, including dynamic pricing. The model aimed to maximize network profit under uncertain demand and parameters such as generation capacity, investment and production costs, and penalty budgets. Jamali and Rasti-Barzoki [9] applied game theory to examine the roles of governmental support and licensing contracts in promoting innovation under market failure. They analyzed two policy instruments, Feed-in Tariffs (FITs) and Government Subsidies (GSs), as well as cooperation among competitors through Royalty Licensing (RL) and Joint Venture (JV) contracts. Tan et al. [10] analyzed the development and operation of VPPs from multiple perspectives and proposed prospective marketing models and market mechanisms for China. Using the business model canvas, they also designed the VPP business development pathway across the initial, development, and maturity stages.

The primary contribution of this research is the development of an integrated competitive biomass-to-electricity supply chain network model in which centralized power plants and Distributed Generation (DG) units are examined simultaneously as competing actors within a common decision-making framework. Unlike many previous studies that have focused exclusively on power plant operation, microgrid energy management, or electricity pricing, the present research models the entire supply chain from biomass procurement and electricity generation to market competition and the electricity buyback mechanism. Furthermore, users, represented by DG units, are not regarded solely as electricity consumers. When they generate surplus electricity, they can sell it back to the grid under a buyback contract. Accordingly, supply and demand decisions are analyzed within an interactive and bidirectional framework. This structure explicitly captures the dual role of users as both consumers and producers, or prosumers, in the electricity market. Previous studies have generally examined individual aspects of the problem, such as microgrids, VPPs, biomass gasification, or electricity pricing. In contrast, the proposed model integrates these components into a unified competitive supply chain network. Compared with conventional energy network design frameworks, the present model simultaneously incorporates the biomass supply chain, competition between centralized power plants and DG units, and the dual consumer–producer role of users. It also models the purchase and sale of surplus electricity through a buyback contract.

Consequently, the main contributions of this study can be summarized as follows:

I. Developing an integrated competitive biomass-to-electricity supply chain network that covers biomass procurement, electricity generation, market competition, electricity consumption, and surplus electricity transactions.

II. Simultaneously modeling centralized power plants and DG units as competitive participants within a unified decision-making framework.

III. Capturing the dual role of DG units as both consumers and producers, thereby representing bidirectional electricity transactions between users and the main grid.

IV. Incorporating a buyback contract through which surplus electricity generated by DG units can be sold to the grid.

V. Integrating supply chain design and competitive electricity pricing decisions, rather than addressing network configuration, operational management, and pricing as isolated problems.

VI. Bridging multiple streams of the existing literature, including biomass gasification, microgrid energy management, VPP operation, competitive electricity pricing, and prosumer participation, within a single modeling framework.

This section develops a competitive biomass-to-electricity supply chain network design model to determine the optimal economic distribution of electricity flows from the power plant and DG units to end users while maximizing total system profit. Under the proposed framework, the users and the power plant enter into a buyback contract that allows DG units to sell their surplus electricity to the power plant. Each user is equipped with a smart meter to monitor electricity consumption and determine the amount of renewable electricity sold back to the power company. This mechanism enables bidirectional electricity transactions and allows users to participate in the market as both consumers and producers (prosumers). The users’ electricity demand is defined as a nonlinear function of the electricity price, as follows:

DemCτ = MCτ − βCτ (PCτ)αCτ, (1)

where PCτ denotes the electricity price charged to users per unit of electricity at time period τ. In practice, the electricity price should be greater than or equal to the electricity generation cost to ensure the economic viability of electricity suppliers. The DG units and the power plant make their decisions independently. To represent the strategic interactions among market participants, a game-theoretic decision-making scheme is adopted. In this framework, the power plant acts as the leader, while DG units act as the followers. Accordingly, the power plant first determines its strategic decisions, such as electricity selling price and electricity buyback price, and then the DG units respond by determining their electricity generation, consumption, purchase, and surplus electricity selling decisions. The interaction between the power plant and DG units is therefore modeled as a leader–follower game, also known as a Stackelberg game. The assumptions of the proposed model are described as follows:

I. A decentralized supply chain model is used to formulate and solve the problem.

II. In the proposed problem, the power plant also serves as the electricity distribution company.

III. The system includes one power plant.

IV. The location of each DG unit is known in advance, and each DG unit is assumed to serve its own associated user.

V. Multiple potential biomass suppliers are considered.

VI. Multiple potential warehouses are available for biomass storage and distribution.

VII. Multiple potential biomass cultivation centers are considered.

VIII. The electricity demand of each user is modeled as a nonlinear function of the electricity price.

TCΛΓντ Unit transportation cost of biomass from supplier Λ to warehouse Γ using vehicle ν in period τ TCΓΔντ Unit transportation cost of biomass from warehouse Γ to power plant Δ using vehicle ν in period τ TCΔДντ Unit transportation cost of ash from power plant Δ to ash sales center Д using vehicle ν in period τ CPTΔCτ Unit electricity transmission cost from power plant Δ to user C in period τ CPTθΔτ Unit electricity transmission cost from DG unit θ to power plant Δ in period τ CPTΔθτ Unit electricity transmission cost from power plant Δ to DG unit θ in period τ PCΔτ Unit electricity generation cost of power plant Δ in period τ PCASHΔτ Unit ash processing cost at power plant Δ in period τ PCϴτ Unit electricity generation cost from RES (wind and solar) at DG unit θ in period

CPωτ Unit biomass cultivation, harvesting, and maintenance cost at cultivation center ω in period τ CPΛτ Unit biomass processing cost at supplier Λ in period τ Demθτ Electricity demand of DG unit θ in period τ DemCτ Electricity demand of user C in period τ Variable Description Contω Binary variable equal to 1 if a connection is established with biomass cultivation center ω; 0 otherwise ContΛ Binary variable equal to 1 if a connection is established with biomass supplier Λ; 0 otherwise LΓ Binary variable equal to 1 if a warehouse is established at location Γ; 0 otherwise

ASν Binary variable equal to 1 if vehicle ν is procured; 0 otherwise PWGΔτ Amount of electricity generated by power plant Δ in period τ EGθτ Amount of electricity generated by DG unit θ in period τ PCτ Electricity selling price charged to user C in period τ ABMωΛντ Amount of biomass transported from cultivation center ω to supplier Λ using vehicle ν in period τ Amount of biomass transported from supplier Λ to warehouse Γ using vehicle ν ABMΛΓντ in period τ

ABMΓΔντ Amount of biomass transported from warehouse Γ to power plant Δ using vehicle ν in period τ AΔДντ Amount of ash transported from power plant Δ\DeltaΔ to ash sales center Д using vehicle ν in period τ PTΔCτ Amount of electricity transmitted from power plant Δ to user C in period τ PTθΔT Amount of electricity transmitted from DG unit θ to power plant Δ in period τ PTΔθτ Amount of electricity transmitted from power plant Δ to DG unit θ in period τ

To solve the proposed bi-level model using the Stackelberg approach, the decision variables controlled by the upper-level player (i.e., the main power plant as the leader) are first considered fixed. Subsequently, the lower-level model corresponding to the DG units, as followers, is solved. In particular, the first-order optimality condition of the lower-level problem is obtained by taking the partial derivative of the DG objective function with respect to the follower-controlled decision variable EGθτ, namely the electricity generated by DG unit θ during time period τ, and setting it equal to zero:

∂πϴ CLRθ2

= Pbuyback − 2 EGθτ + Pθτ = 0, (11)

∂EGθτ Vθ Pbuyback + Pθτ 2

EGθτ = . Vθ . (12)

2CLRθ The derived response function represents the optimal renewable electricity generation decision of each DG unit in response to the decisions of the power plant. It is then substituted into the upper-level objective function and constraints. Consequently, the original bi-level Stackelberg model is transformed into an equivalent single-level optimization model, which can be solved using appropriate nonlinear or mixed-integer nonlinear programming methods. The optimal value obtained for EGθτ is then substituted into the upper-level model. Consequently, the main power plant incorporates the optimal reaction of each DG unit into its own decision-making process. Accordingly, the original bi-level Stackelberg model is transformed into a single-level optimization model, which can be solved to determine the optimal decisions of the power plant, including electricity generation, electricity pricing, biomass procurement and transportation flows, warehouse establishment, electricity transactions with users and DG units, and the buyback of surplus electricity generated by DG units.

Max πC = ∑c. ∑τ PCτ DemCτ + ∑v. ∑Д. ∑τ PД AΔДντ + ∑θ. ∑τ Pθτ (Demθτ −

Pbuyback+Pθτ 2 Pbuyback+Pθτ 2

. Vθ ) − ∑θ. ∑ Pbuyback ( . Vθ − Demθτ) − ∑ν CνASν −

2CLRθ τ 2CLRθ

∑ω CCOFωContω − ∑Λ CCOSΛContΛ − ∑Γ CESTΓLΓ − ∑ω. ∑Λ. ∑ν. ∑τ CPωτABMωΛντ − ∑Λ. ∑Γ. ∑ν. ∑τ CPΛτABMΛΓντ − ∑ω. ∑Λ. ∑ν. ∑τ TCωΛντABMωΛντ −

(13)

∑Λ. ∑Γ. ∑ν. ∑τ TCΛΓντABMΛΓντ − ∑Γ. ∑ν. ∑τ TCΓΔντABMΓΔντ − ∑Λ. ∑Γ. ∑ν. ∑τ HCBMΓABMΓΔντ − ∑C. ∑τ CPTΔCτ(1 + l)DemCτ −

Pbuyback+Pθτ 2

∑θ. ∑ CPTθΔτ ( . Vθ − Demθτ) + − ∑θ. ∑ CPTΔθτ(1 + l) (Demθτ −

τ 2CLRθ τ Pbuyback+Pθτ 2

. Vθ ) − ∑Д. ∑ν. ∑τ TCAΔДντAΔДντ − ∑τ PCΔτPWGΔτ,

2CLRθ

s.t.

Pbuyback + Pθτ 2 PWGΔτ + ∑ ( . Vθ − Demθτ) 2CLRθ

θ (14)

Pbuyback + Pθτ 2 = ∑(1 + l)DemCτ + ∑(1 + l) (Demθτ − . Vθ ), ∀τ, 2CLRθ

∑ω. ∑ν ABMωΛντ = ∑ν. ∑Γ ABMΛΓντ, ∀Λ, τ, (15)

∑. ∑ ABMΛΓντ = ∑ ABMΓΔντ, ∀Γ, τ, (16)

Λ ν ν ∑. ∑ ȠABMΓΔντ = ∑. ∑ AΔДντ, ∀τ, (17)

Γ ν Д v

∑. ∑ ψABMΓΔντ = PWGΔτ, ∀τ, (18)

PWGΔτ, ABMΓΔντ, ABMΛΓντ, ABMωΛντ, AΔДντ, Pθτ, PCτ ≥ 0,

(19)

ASν, Contω, ContΛ, LΓ = {0,1}.

In this study, the proposed model was formulated based on a Stackelberg game to simulate the strategic interactions between the power plant, as the leader, and DG units, as the followers. The bi-level problem was transformed into a single-level model using the followers’ optimal reaction functions and was solved for a network comprising four biomass cultivation centers, three suppliers, three warehouses, one power plant, four DG units, one ash sales center, three vehicles, four users, and three time periods. The optimal objective-function value was obtained as 3,847,620 monetary units, representing the total profit of the supply chain over the planning horizon. An analysis of the equilibrium prices during the first, second, and third periods indicates that the electricity prices of the power plant are 1,450, 1,580, and 1,710, respectively, whereas the corresponding electricity prices of the DG units are 1,320, 1,410, and 1,530, respectively. The findings reveal an increasing trend in electricity prices for both the power plant and DG units over the planning horizon. However, the electricity price offered by DG units remains significantly lower than that of the power plant in all periods. This price difference reflects the competitive advantage of DG units and their role in reducing the final electricity cost for consumers. In fact, applying the Stackelberg model not only improves the overall profitability of the supply chain but also provides an effective economic structure for managing biomass-based electricity generation, energy transactions, and the sale of by-products, particularly ash. To examine the robustness of the model under changes in support policies, the parameter Pbuyback, representing the price paid by the power plant to purchase surplus electricity from DG units, was subjected to sensitivity analysis. As shown in Table 2, increasing Pbuyback leads to strategic changes in the objective values of both the leader and the followers.

effects of the buyback price on leader and follower profits.

The results indicate that, across all scenarios, the objective-function value under the centralized configuration, πc, is greater than the aggregate profits of the leader and followers under the decentralized configuration. This efficiency gap, which results from decentralized decision-making in the Stackelberg model, is a well-recognized phenomenon in supply chain management. The persistence of this gap at different levels of Pbuyback supports the validity and consistency of the proposed solution algorithm. Moreover, as Pbuyback increases, DG units reduce their electricity selling prices in order to maintain their competitiveness. This strategic response affects the profit distribution between the leader and the followers, while the power plant’s profit decreases at a relatively moderate rate. To further ensure the reliability and logical behavior of the model under varying operating conditions, the equilibrium prices were evaluated over three time periods with different demand levels. To further evaluate the pricing behavior and stability of the proposed model under different demand conditions, the equilibrium electricity prices of the power plant and DG units were compared across the three time periods. The results, including the price spread and the corresponding stability status, are presented in Table 3.

The persistence of a stable price difference across all time periods demonstrates the model’s logical and consistent response to demand fluctuations. As peak-related costs increase, the proposed pricing model maintains the price difference within a stable competitive margin. This finding quantitatively confirms the structural validity and computational reliability of the proposed model.

This study developed a competitive biomass-to-electricity supply chain network design model considering buyback contracts between the power plant and DG unit owners. One of the most important issues in electricity supply chains is the use of biomass as an input for electricity generation. Depending on climatic and geographical conditions, biomass can be considered a reliable renewable energy source compared with other renewable sources, such as wind and solar energy. In the proposed model, DG units generate their required electricity using solar and wind energy. When a DG unit produces surplus electricity, it sells the excess power to the power plant, which also represents the electricity distribution company, at a predetermined buyback price. Conversely, when the generated electricity is insufficient to meet its demand, the DG unit purchases the required electricity from the power plant at an agreed price. The proposed supply chain network includes four biomass cultivation centers, three biomass suppliers, three warehouses, one power plant, four DG units, one ash sales center, and four users. The resulting model was solved using GAMS. The results demonstrate that integrating biomass-based electricity generation, DG, competitive pricing, and buyback contracts can provide an effective framework for coordinating electricity supply and demand while improving the economic performance of the supply chain. Several extensions can be considered for future research. First, different forms of cooperation and non-cooperation between the electricity company and DG units may be incorporated into the model. Second, time-dependent demand functions can be developed to provide a more realistic representation of electricity consumption patterns. Further extensions may also include uncertainty in biomass availability, renewable energy generation, electricity demand, and market prices, as well as the integration of energy storage systems and environmental objectives into the proposed framework.

The authors sincerely appreciate all those who contributed to the completion of this research.

This research was conducted without financial support from any public, private, or non-profit organization.

The data used in this study are available from the corresponding author upon reasonable request.