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Analysis of service level constraint in supply chain system with dynamic demand and time varying carbon emission via control theory
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DOI：10.1080/17509653.2026.2678309.png)
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Abstract
En 中文
In the current competitive market, service level, product price, and item quality are crucial components of supply chain management. This study integrates these concepts by formulating a two-level supply chain system. In this model, the retailer’s demand is dependent on price, quality, and time, while the end-customer demand is influenced by the price, time, and service level provided by the retailer. The manufacturer’s per-unit production cost is treated as a nonlinear, increasing function of the item’s quality index. Furthermore, the manufacturing firm’s carbon emission rate is linearly dependent on the production time. Centralized and decentralized scenarios are formulated and solved using Pontryagin’s maximum principle. The resulting optimal control problems exhibit significant nonlinearity. Due to these nonlinear assumptions, finding an analytical solution is challenging. To justify the model, a numerical example is considered. We employed the recently developed Crayfish Optimization Algorithm (COA) to find the best-found solution for the corresponding optimization problems (both centralized and decentralized systems). To validate the COA’s results, six additional metaheuristic algorithms (APO, AEFA, GBO, JSO, DA, and ZOA) were also utilized for comparison. Finally, a sensitivity analysis was conducted to examine how various system factors affect the optimal solution.
Keywords:
Supply chain management
service level constraint
nonlinear demand
time varying carbon emission
metaheuristics algorithms
C44
C61
L14
L23
Q55
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IF:
2.6
Papers:
237
Citations:
739
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