This paper investigated optimal green advertising investment and referral reward strategies for sustainable energy product companies. We developed a dynamic optimization model that extends the Bass diffusion framework to simultaneously optimize referral rewards and green advertising investments throughout the product lifecycle. Our model integrates both marketing interventions and word-of-mouth effects, captured via a reduced-form Bass imitation mechanism, to analyze the diffusion of sustainable energy products. Applying optimal control theory, we derived analytical solutions and conducted sensitivity analyses across key parameters, including unit margin, referral efficiency, green advertising efficiency, spontaneous adoption rate, and word-of-mouth strength. Under our model parameterization, results revealed that the optimal referral reward strategy follows a U-shaped curve—initially high, decreasing during the middle phase, and gradually increasing in later stages—while optimal advertising investment decreases monotonically over time. Sensitivity analyses further demonstrate that (1) higher-margin sustainable technologies require greater referral rewards; (2) strong social network effects warrant simultaneous increases in both reward levels and advertising investments; and (3) technologies with strong intrinsic appeal require less marketing support. These findings provide theoretical guidance for sustainable energy companies seeking to optimize marketing strategies and offer insights for policymakers aiming to accelerate clean energy transitions through effective incentive mechanism design.
Citation: Qi Chen. The green incentive wave: Dynamic optimization of referral rewards and green advertising in sustainable energy diffusion[J]. Journal of Industrial and Management Optimization, 2026, 22(5): 2410-2427. doi: 10.3934/jimo.2026088
This paper investigated optimal green advertising investment and referral reward strategies for sustainable energy product companies. We developed a dynamic optimization model that extends the Bass diffusion framework to simultaneously optimize referral rewards and green advertising investments throughout the product lifecycle. Our model integrates both marketing interventions and word-of-mouth effects, captured via a reduced-form Bass imitation mechanism, to analyze the diffusion of sustainable energy products. Applying optimal control theory, we derived analytical solutions and conducted sensitivity analyses across key parameters, including unit margin, referral efficiency, green advertising efficiency, spontaneous adoption rate, and word-of-mouth strength. Under our model parameterization, results revealed that the optimal referral reward strategy follows a U-shaped curve—initially high, decreasing during the middle phase, and gradually increasing in later stages—while optimal advertising investment decreases monotonically over time. Sensitivity analyses further demonstrate that (1) higher-margin sustainable technologies require greater referral rewards; (2) strong social network effects warrant simultaneous increases in both reward levels and advertising investments; and (3) technologies with strong intrinsic appeal require less marketing support. These findings provide theoretical guidance for sustainable energy companies seeking to optimize marketing strategies and offer insights for policymakers aiming to accelerate clean energy transitions through effective incentive mechanism design.
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Qi Chen. The green incentive wave: Dynamic optimization of referral rewards and green advertising in sustainable energy diffusion[J]. Journal of Industrial and Management Optimization, 2026, 22(5): 2410-2427. doi: 10.3934/jimo.2026088
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