In an increasingly complex supply chain network, market demand integrates structural and nonlinear dynamics to reshape the current landscape. Due to these advancements, the concept of barter exchange has emerged as an innovative approach for exchanging products/services without capital investment in the smart production system. It recommends a variety of advantages to facilitate commercialism. The proposed study demonstrates information-based smart supply chain business models and transforms physical activities into digital challenges by highlighting the analytical complexity of verifying retail profitability. Despite the challenges, the study initiates a novel approach to establishing the barter mechanism with promotional efficiency under a stochastic demand function. To facilitate digital implementation, the methodology derives several differential equations with random nonlinearity and proposes complex intelligent optimization algorithms to determine the optimal parameters in the nonlinear mathematical system. The numerical experiment yields a mathematically grounded closed-form solution for an enhanced profit of 42.47% and reduces carbon emissions by 33.33% on a dual digital platform using a stochastic optimization technique. The sensitivity analysis identifies the key elements that emphasize the precision of a flexible alternative decision. It offers significant managerial insights to guide suitable pricing policies and diverse retail interests, and manage complex retail dynamics. Indeed, the barter mechanism supports nonlinear transformation to retail businesses by easing financing and reveals practical applicability in mitigating the complexities of the circular economy.
Citation: Sandipa Bhattacharya, Mitali Sarkar, Biswajit Sarkar, Leopoldo Eduardo Cárdenas-Barrón, Angappa Gunasekaran. An application of stochastic optimization through barter exchange[J]. AIMS Mathematics, 2026, 11(7): 21251-21292. doi: 10.3934/math.2026863
In an increasingly complex supply chain network, market demand integrates structural and nonlinear dynamics to reshape the current landscape. Due to these advancements, the concept of barter exchange has emerged as an innovative approach for exchanging products/services without capital investment in the smart production system. It recommends a variety of advantages to facilitate commercialism. The proposed study demonstrates information-based smart supply chain business models and transforms physical activities into digital challenges by highlighting the analytical complexity of verifying retail profitability. Despite the challenges, the study initiates a novel approach to establishing the barter mechanism with promotional efficiency under a stochastic demand function. To facilitate digital implementation, the methodology derives several differential equations with random nonlinearity and proposes complex intelligent optimization algorithms to determine the optimal parameters in the nonlinear mathematical system. The numerical experiment yields a mathematically grounded closed-form solution for an enhanced profit of 42.47% and reduces carbon emissions by 33.33% on a dual digital platform using a stochastic optimization technique. The sensitivity analysis identifies the key elements that emphasize the precision of a flexible alternative decision. It offers significant managerial insights to guide suitable pricing policies and diverse retail interests, and manage complex retail dynamics. Indeed, the barter mechanism supports nonlinear transformation to retail businesses by easing financing and reveals practical applicability in mitigating the complexities of the circular economy.
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Figures(5) / Tables(2)
Sandipa Bhattacharya, Mitali Sarkar, Biswajit Sarkar, Leopoldo Eduardo Cárdenas-Barrón, Angappa Gunasekaran. An application of stochastic optimization through barter exchange[J]. AIMS Mathematics, 2026, 11(7): 21251-21292. doi: 10.3934/math.2026863
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