Classical cost–volume–profit (CVP) analysis usually provides point-wise break-even or target-profit calculations under fixed-price assumptions. This paper developed a nonconvex feasible–profit framework for multi-producer CVP analysis in an oligopolistic market where the common price is endogenously determined by the joint production vector. The framework was applied to a three-country copper export market consisting of Mongolia, Chile, and Peru, which are interpreted as aggregate producers, using annual data for 2013–2025. Export volumes, China's copper import demand, and London Metal Exchange copper prices were obtained from Bloomberg, while cost parameters were calibrated benchmark values. For the three reduced-form price environments, the price coefficient was estimated by least squares, feasible–profit membership was tested, and a penalty method was used to compute local stationary points. The results showed that feasible–profit membership depends strongly on the assumed price mechanism. Under the linear aggregate-output and pairwise interaction specifications, the observed export vector is infeasible only in the early years and becomes feasible later, while under the inverse aggregate-output specification, the observed vector remains feasible throughout the sample but the computed stationary points are infeasible in 2024–2025. The findings suggest that multi–producer CVP analysis should account for endogenous price formation and export competition, and the proposed framework provides an interpretable tool for examining nonconvex feasible–profit regions.
Citation: Munkhbayar Byambadash, Bayanjargal Darkhijav, Tumendelger Lkhagvasuren, Enkhbat Rentsen. A nonconvex modeling approach to cost–volume–profit analysis with variable price in an oligopolistic market[J]. Journal of Industrial and Management Optimization, 2026, 22(7): 3123-3150. doi: 10.3934/jimo.2026114
Classical cost–volume–profit (CVP) analysis usually provides point-wise break-even or target-profit calculations under fixed-price assumptions. This paper developed a nonconvex feasible–profit framework for multi-producer CVP analysis in an oligopolistic market where the common price is endogenously determined by the joint production vector. The framework was applied to a three-country copper export market consisting of Mongolia, Chile, and Peru, which are interpreted as aggregate producers, using annual data for 2013–2025. Export volumes, China's copper import demand, and London Metal Exchange copper prices were obtained from Bloomberg, while cost parameters were calibrated benchmark values. For the three reduced-form price environments, the price coefficient was estimated by least squares, feasible–profit membership was tested, and a penalty method was used to compute local stationary points. The results showed that feasible–profit membership depends strongly on the assumed price mechanism. Under the linear aggregate-output and pairwise interaction specifications, the observed export vector is infeasible only in the early years and becomes feasible later, while under the inverse aggregate-output specification, the observed vector remains feasible throughout the sample but the computed stationary points are infeasible in 2024–2025. The findings suggest that multi–producer CVP analysis should account for endogenous price formation and export competition, and the proposed framework provides an interpretable tool for examining nonconvex feasible–profit regions.
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Munkhbayar Byambadash, Bayanjargal Darkhijav, Tumendelger Lkhagvasuren, Enkhbat Rentsen. A nonconvex modeling approach to cost–volume–profit analysis with variable price in an oligopolistic market[J]. Journal of Industrial and Management Optimization, 2026, 22(7): 3123-3150. doi: 10.3934/jimo.2026114
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