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Supply chain network equilibrium problem with capacity constraints

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  • Huey‐Kuo Chen
  • Huey‐Wen Chou

Abstract

The supply chain network equilibrium problem with capacity constraints (SCNE‐C) is an extension of the supply chain network equilibrium problem (SCNE), which also takes into account capacity constraints which refer to the maximum production capacity for a manufacturer or the maximum storage/display space for a retailer. Due to inherent link interactions in the demand functions and cost functions, the SCNE‐C problem is formulated as a mathematical model using the variational inequality (VI) approach. This VI model is characterised by the so‐called Wardrop second principle (in terms of the ‘generalised’ route cost). To solve the model, a path‐based four‐loop nested diagonalisation method, along with a supernetwork representation, is proposed and demonstrated with a few numerical examples. The obtained results fully comply with the Wardrop second principle at both retailer sector and demand markets and can provide useful route information of the product. In addition, the stricter the capacity constraints imposed, the lower the quantity demanded will be, and provided at a higher product price. The concepts developed in this paper can be extended into many other spatial price equilibrium problems. Resumen El problema de equilibrio en la red de la cadena de abastecimiento con restricciones de capacidad (SCNE‐C) es una ampliación del problema de equilibrio en la red de la cadena de abastecimiento, que además tiene en cuenta restricciones de capacidad relacionadas con la máxima capacidad de producción para un fabricante o el espacio máximo de almacenamiento/muestra al público para un comerciante al por menor. Debido a las interacciones inherentes entre vínculos en las funciones de demanda y de costos, formulamos el problema de SCNE‐C como un modelo matemático utilizando el enfoque de desigualdad variacional (VI). Este modelo VI se caracteriza por el así llamado segundo principio de Wardrop (en términos de costo de recorrido ‘generalizado’). Para resolver el modelo se propone un método de diagonalización anidado de cuatro bucles basado en la ruta, junto con una representación de red extendida (supernetwork), y se demuestra con algunos ejemplos numéricos. Los resultados obtenidos cumplen totalmente con el segundo principio de Wardrop tanto para el sector de minoristas como para las demandas del mercado y pueden proporcionar información de ruta útil del producto. Además, cuanto más estrictas sean las restricciones de capacidad impuestas, menor será la cantidad demandada del producto, y se ofrecerá con un precio mayor. Los conceptos desarrollados en este artículo pueden aplicarse a muchos otros problemas espaciales de equilibrio de precios.

Suggested Citation

  • Huey‐Kuo Chen & Huey‐Wen Chou, 2008. "Supply chain network equilibrium problem with capacity constraints," Papers in Regional Science, Wiley Blackwell, vol. 87(4), pages 605-621, November.
    • Handle: RePEc:bla:presci:v:87:y:2008:i:4:p:605-621
    DOI: 10.1111/j.1435-5957.2008.00174.x
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    References listed on IDEAS

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    1. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    2. Jayakrishnan, R. & Tsai, Wei T. & Prashker, Joseph N. & Rajadhyaksha, Subodh, 1994. "A Faster Path-Based Algorithm for Traffic Assignment," University of California Transportation Center, Working Papers qt2hf4541x, University of California Transportation Center.
    3. Nagurney, Anna & Dong, June & Zhang, Ding, 2002. "A supply chain network equilibrium model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 38(5), pages 281-303, September.
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    2. Hu, Xiaowei & Li, Peng, 2022. "Relief and stimulus in a cross-sector multi-product scarce resource supply chain network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).

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