When does the Uncertainty Budget Change the Design? A Decision-Response Diagnostic for Robust Closed-Loop Supply Chain Network Design

Authors

  • Mahdi Razaghi * Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran. https://orcid.org/0009-0001-4711-4764
  • Mahtab Esmaeili Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran.
  • Seyed Esmaeil Najafi Department of Industrial Engineering, SR. C, Islamic Azad University, Tehran, Iran.

https://doi.org/10.48313/scodm.v3i3.67

Abstract

Budget-of-uncertainty robust optimization is widely used for demand uncertainty in closed-loop supply chain network design, and the price of robustness is commonly reported as its summary statistic. This paper shows that the statistic conflates responses a decision maker would treat differently, and proposes reporting them separately through a four-layer decomposition: strategic response as Hamming distance between facility-opening vectors, service in aggregate and by region, operational response as normalized L1 flow change per arc family, and penalty alongside the residual change in other cost. The layers can decouple dramatically. In a Bavaria-informed instance whose returns are the observed 2024 collections of all 86 disposal-responsible bodies, cost rises by up to 27.9 percent while the facility configuration and aggregate delivered volume are unchanged across all eighteen exact solves and upstream flows are invariant to the tonne, the operational response confined to terminal arcs. Two secondary results follow. The aggregate-service formulation is a different service policy rather than a repaired counterpart: matched on the protection they buy, the two coincide at the tested endpoints but diverge at every tested interior level, where the aggregate plan delivers less to up to 10 of 12 regions. And perturbation tests attribute the strategic inactivity to an endogenous installed-capacity ceiling 2.1 percent below an immovable physical one. We derive a design-conditional upper service-saturation boundary, confirmed by bisection at 0.9791, which governs the service layer alone and does not determine strategic response. A two-stage adjustable formulation on an aggregated instance reproduces the first-stage invariance at the reference ratio.

Keywords:

Closed-loop supply chain, Robust optimization, Budget of uncertainty, Price of robustness, Network design, Waste electrical and electronic equipment

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Published

2026-09-05

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Vol. 3 No. 3 (2026): Supply Chain and Operations Decision Making

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How to Cite

Razaghi, M. ., Esmaeili, M. ., & Najafi, S. E. . (2026). When does the Uncertainty Budget Change the Design? A Decision-Response Diagnostic for Robust Closed-Loop Supply Chain Network Design. Supply Chain and Operations Decision Making, 3(3), 223-248. https://doi.org/10.48313/scodm.v3i3.67

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