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<p>In this paper, optimal decisions are searched for both the wholesaler and the retailer in a three-layer business chain of coastal biomass. The biomass deteriorates over time, and hence, its freshness decreases dynamically. The expiration period of the biomass is a fuzzy parameter, and the freshness of units is expiration-period dependent, so it is also fuzzy. The rate of selling of the biomass is influenced by the freshness of units and unit selling price, so it is also fuzzy. Depending upon the unit purchase cost, the retailer optimizes the retail price function and order volume, and knowing this order volume, the wholesaler fixes his/her order volume. The models are formulated as leader-follower Stackelberg game (SG) problems and coordinated decision-making for the decision-makers, i.e., the model is studied under three distinct scenarios: the wholesaler-retailer Stackelberg game (WRSG), the retailer-wholesaler Stackelberg game (RWSG), and the coordination scenario (CS). While the wholesaler determines the wholesale price and order volume, the retailer fixes the order quantity, ordering time, and retail price to optimize the respective profits. The model is mathematically represented with the help of fuzzy differential equations and fuzzy Riemann integration. At first, a fuzzy goal of the fuzzy average profit of the retailer is determined. Then the credibility measure of the retailer’s average profit concerning this goal is optimized for the marketing decisions. A simulation process is followed to determine this fuzzy measure. The efficiency of the Artificial Bee Colony (ABC) algorithm is enhanced by incorporating its search in multiple dimensions and is named MDABC. It is tested and trusted using CEC2017 and CEC2022 datasets and is applied in a nested way to determine the decisions for the decision-makers. Numerical illustrations and parametric studies are presented to analyse the models, and it is established that the coordinated decision is better compared to both Stackelberg game decisions. However, the WRSG is more realistic compared to RWSG.</p>

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A supply chain of coastal biomass with fuzzy freshness induced dynamic demand: a Stackelberg game approach

  • 期刊论文

  • 发表日期：

    2026年7月25日

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  • Rumpa Sau,
  • Kallol Bera,
  • Chayan Ranjit,
  • Manas Kumar Maiti

摘要

In this paper, optimal decisions are searched for both the wholesaler and the retailer in a three-layer business chain of coastal biomass. The biomass deteriorates over time, and hence, its freshness decreases dynamically. The expiration period of the biomass is a fuzzy parameter, and the freshness of units is expiration-period dependent, so it is also fuzzy. The rate of selling of the biomass is influenced by the freshness of units and unit selling price, so it is also fuzzy. Depending upon the unit purchase cost, the retailer optimizes the retail price function and order volume, and knowing this order volume, the wholesaler fixes his/her order volume. The models are formulated as leader-follower Stackelberg game (SG) problems and coordinated decision-making for the decision-makers, i.e., the model is studied under three distinct scenarios: the wholesaler-retailer Stackelberg game (WRSG), the retailer-wholesaler Stackelberg game (RWSG), and the coordination scenario (CS). While the wholesaler determines the wholesale price and order volume, the retailer fixes the order quantity, ordering time, and retail price to optimize the respective profits. The model is mathematically represented with the help of fuzzy differential equations and fuzzy Riemann integration. At first, a fuzzy goal of the fuzzy average profit of the retailer is determined. Then the credibility measure of the retailer’s average profit concerning this goal is optimized for the marketing decisions. A simulation process is followed to determine this fuzzy measure. The efficiency of the Artificial Bee Colony (ABC) algorithm is enhanced by incorporating its search in multiple dimensions and is named MDABC. It is tested and trusted using CEC2017 and CEC2022 datasets and is applied in a nested way to determine the decisions for the decision-makers. Numerical illustrations and parametric studies are presented to analyse the models, and it is established that the coordinated decision is better compared to both Stackelberg game decisions. However, the WRSG is more realistic compared to RWSG.