Mathematical Modeling of Dynamic Pricing in a Multi-Channel Supply Chain Considering Strategic Customers
Keywords:
Dynamic pricing, multi-channel supply chain, strategic customers, meta-heuristic algorithmsAbstract
This study aims to develop a mixed-integer linear optimization model for dynamic pricing in multi-channel supply chains while explicitly incorporating the behavior of strategic customers. A nonlinear dynamic pricing model was formulated to capture multiple sales channels, strategic and non-strategic customer classes, transportation modes, capacity constraints, daily price fluctuation limits, utility thresholds, and market-share requirements. The nonlinearities were addressed using separable quadratic transformation, piecewise linear approximation, and auxiliary variables, resulting in a solvable mixed-integer linear program. The model was validated using GAMS and the CPLEX solver. To handle large-scale instances, three metaheuristic algorithms—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO)—were designed, tuned, and benchmarked. The results indicate that the proposed model efficiently predicts optimal prices, realized demand, and sales volumes across time periods, significantly improving overall supply chain profitability. Sensitivity analysis revealed that transportation capacity, price sensitivity parameters, and base utility values are the most influential factors on profit. Among the solution methods, GWO produced the highest-quality solutions, with less than 0.02% deviation from the exact GAMS results, although it required slightly longer computation times compared to GA and PSO. The findings demonstrate that integrating strategic customer behavior with multi-channel dynamic pricing requires a comprehensive mathematical framework. The proposed model effectively captures the interplay among price, demand, utility, and supply constraints, providing a robust decision-support tool for firms operating in volatile markets. Furthermore, metaheuristic methods—especially GWO—offer reliable and scalable solutions for large real-world applications.
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Copyright (c) 2025 Mona Jamdar (Author); Mohammad Sheikhalishahi; Ata Allah Taleizadeh (Author)
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