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This study presents an inventory model based on the Stackelberg game, where the retailer acts as the leader, setting optimal ordering times, and the manufacturer follows, adjusting production accordingly. The model minimizes supply chain costs, considering time-varying demand, production schedules, and inventory holding within a finite planning horizon. Optimal replenishment schedules are calculated using an iterative approach in Wolfram Mathematica 13.0. Numerical results show that for a demand rate of a = 675, the model identifies five replenishment cycles, leading to a total cost of $16,124.879. Sensitivity analyses further highlight the impact of key parameters, such as wholesale pricing, demand variability, and inventory costs, on supply chain performance, illustrating how strategic ordering decisions can optimize costs. Additionally, a comparative analysis is conducted between the proposed Stackelberg-based decentralized inventory model and L. Benkherouf’s centralized model. While the Stackelberg model incurs higher total costs due to decentralized decision-making, it provides greater flexibility and adaptability to changing market conditions. A further comparison between Manufacturer-to-Retailer and Retailer-to-Manufacturer inventory strategies demonstrates that Retailer-to-Manufacturer is the more cost-effective approach. As the demand rate increases, the total cost rises for both strategies, but the Retailer-to-Manufacturer strategy results in lower total costs and a slower cost escalation, making it a more efficient choice. In contrast, the Manufacturer-to-Retailer strategy incurs higher costs due to increased production, storage, and transportation expenses. These findings suggest that allowing retailers to place orders based on real-time demand data can lead to better cost management and operational efficiency in decentralized supply chains. These specific outcomes from numerical examples and sensitivity analyses deepen the understanding of supply chain dynamics, offering valuable managerial insights. However, the chapter acknowledges limitations related to data assumptions and real-world implementation challenges, suggesting that further research is necessary to validate its applicability across diverse market scenarios.

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Optimizing Inventory Management with a Stackelberg Game Approach: A Retailer-Manufacturer Model

  • 会议论文

  • 发表日期：

    2026年

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  • Prerna Jain,
  • Nitin Kumar Mishra,
  • Ranu,
  • Renuka Namwad

摘要

This study presents an inventory model based on the Stackelberg game, where the retailer acts as the leader, setting optimal ordering times, and the manufacturer follows, adjusting production accordingly. The model minimizes supply chain costs, considering time-varying demand, production schedules, and inventory holding within a finite planning horizon. Optimal replenishment schedules are calculated using an iterative approach in Wolfram Mathematica 13.0. Numerical results show that for a demand rate of a = 675, the model identifies five replenishment cycles, leading to a total cost of $16,124.879. Sensitivity analyses further highlight the impact of key parameters, such as wholesale pricing, demand variability, and inventory costs, on supply chain performance, illustrating how strategic ordering decisions can optimize costs. Additionally, a comparative analysis is conducted between the proposed Stackelberg-based decentralized inventory model and L. Benkherouf’s centralized model. While the Stackelberg model incurs higher total costs due to decentralized decision-making, it provides greater flexibility and adaptability to changing market conditions. A further comparison between Manufacturer-to-Retailer and Retailer-to-Manufacturer inventory strategies demonstrates that Retailer-to-Manufacturer is the more cost-effective approach. As the demand rate increases, the total cost rises for both strategies, but the Retailer-to-Manufacturer strategy results in lower total costs and a slower cost escalation, making it a more efficient choice. In contrast, the Manufacturer-to-Retailer strategy incurs higher costs due to increased production, storage, and transportation expenses. These findings suggest that allowing retailers to place orders based on real-time demand data can lead to better cost management and operational efficiency in decentralized supply chains. These specific outcomes from numerical examples and sensitivity analyses deepen the understanding of supply chain dynamics, offering valuable managerial insights. However, the chapter acknowledges limitations related to data assumptions and real-world implementation challenges, suggesting that further research is necessary to validate its applicability across diverse market scenarios.