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Exploring nonlinear supply chains: the dynamics of capacity constraints

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  • Borja Ponte
  • Xun Wang
  • David de la Fuente
  • Stephen M. Disney

Abstract

While most supply chain models assume linearity, real production and distribution systems often operate in constrained contexts. This article aims to analyse the consequences of capacity limits in the order-up-to replenishment policy with minimum mean squared error forecasting under independently and identically distributed random demand. Our study shows that the impact of this nonlinearity is often significant and should not be ignored. In this regard, we introduce the concept of a settling capacity, which informs when our knowledge from a linear analysis is a reasonable approximation in a nonlinear context. If the available capacity is less than the settling capacity, the nonlinear effects can have a significant impact. We compare the Bullwhip Effect and Fill Rate in constrained contexts to well-established results for linear supply chains. We reveal the capacity limit acts as a production smoothing mechanism, at the expense of increasing inventory variability. We proceed to analyse the economic consequences of the capacity constraint and show that it can actually reduce costs. We provide an approximate solution for determining the optimal capacity depending on the demand, the unit costs and the lead time.

Suggested Citation

  • Borja Ponte & Xun Wang & David de la Fuente & Stephen M. Disney, 2017. "Exploring nonlinear supply chains: the dynamics of capacity constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 4053-4067, July.
  • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:14:p:4053-4067
    DOI: 10.1080/00207543.2016.1245884
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    File URL: http://hdl.handle.net/10.1080/00207543.2016.1245884
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    Cited by:

    1. Dominguez, Roberto & Cannella, Salvatore & Ponte, Borja & Framinan, Jose M., 2020. "On the dynamics of closed-loop supply chains under remanufacturing lead time variability," Omega, Elsevier, vol. 97(C).
    2. Ponte, Borja & Naim, Mohamed M. & Syntetos, Aris A., 2019. "The value of regulating returns for enhancing the dynamic behaviour of hybrid manufacturing-remanufacturing systems," European Journal of Operational Research, Elsevier, vol. 278(2), pages 629-645.
    3. Cannella, Salvatore & Dominguez, Roberto & Ponte, Borja & Framinan, Jose M., 2018. "Capacity restrictions and supply chain performance: Modelling and analysing load-dependent lead times," International Journal of Production Economics, Elsevier, vol. 204(C), pages 264-277.
    4. Hedenstierna, Carl Philip T. & Disney, Stephen M., 2018. "Avoiding the capacity cost trap: Three means of smoothing under cyclical production planning," International Journal of Production Economics, Elsevier, vol. 201(C), pages 149-162.
    5. Ponte, Borja & Costas, José & Puche, Julio & Pino, Raúl & de la Fuente, David, 2018. "The value of lead time reduction and stabilization: A comparison between traditional and collaborative supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 165-185.

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