When Shortages Lead to Export Restrictions: A Computational Study
Pith reviewed 2026-06-28 18:04 UTC · model grok-4.3
The pith
A supply chain model that treats export bans as a direct consequence of projected drug shortages improves design decisions under disruption.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The authors show that by embedding the relationship between conventional disruptions and induced export bans into the supply chain design optimization, using a two-stage stochastic program solved with alternating cut methods, one can quantify the impact of systemic induced risk on optimal facility and capacity decisions in a pharmaceutical network, as illustrated by the oncology drug case study.
What carries the argument
Two-stage stochastic mixed-integer program with a second-stage subproblem containing one binary variable for the export ban, addressed by alternating integer L-shaped, disjunctive, and bilinear cut methods.
Load-bearing premise
Export bans arise reliably and predictably as a secondary effect precisely when shortages are projected, and this can be represented by a second-stage problem with only one binary variable.
What would settle it
Compare historical instances of drug shortages against whether export bans were enacted at the predicted times and check if the model's second-stage decisions match observed outcomes.
Figures
read the original abstract
Globalization has enabled companies to leverage cost efficiencies; however, it has increased exposure to disruption risks that threaten supply stability. Among these, export bans have emerged as a systemic challenge, often arising as a secondary effect of conventional supply capacity disruptions. The pharmaceutical industry is particularly vulnerable to bans because of the criticality of keeping life-saving medications available, yet such disruptions also jeopardize patient health globally as well as challenge company operations. This paper proposes a supply chain design model that incorporates the relationship between conventional disruption risks (quality-related capacity failures and natural disasters) and export bans that may be induced when the drug is projected to be in short supply. The model is a two-stage stochastic mixed integer program, where the systemic setting yields a second-stage problem with one binary variable and continuous variables. The structure motivates the study of three tailored solution methods: the Alternating Integer L-shaped Cut, Alternating Disjunctive Cut, and Alternating Bilinear Cut methods. In the nearly-continuous second stage context, the Alternating Integer L-shaped cuts perform best. Using an oncology drug case study, we study effects of systemic, induced risk and quantify the value of incorporating disruptions into supply chain design.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript develops a two-stage stochastic mixed-integer program for pharmaceutical supply chain design that explicitly links conventional disruption risks (quality failures, natural disasters) to induced export bans triggered when shortages are projected. The systemic relationship is claimed to produce a second-stage subproblem containing exactly one binary variable together with continuous variables; this structure motivates three alternating cut algorithms (Alternating Integer L-shaped, Disjunctive, and Bilinear). Computational experiments on an oncology-drug case study compare the methods, conclude that Alternating Integer L-shaped cuts perform best, and quantify the value of incorporating the induced-risk relationship into design decisions.
Significance. If the one-binary second-stage encoding accurately captures the induced-ban mechanism, the work supplies both a practically relevant modeling framework for global pharmaceutical resilience and a set of tailored decomposition methods whose relative performance is demonstrated on a realistic instance. The explicit quantification of the value of modeling systemic induced risk is a concrete contribution that could inform both academic follow-up and industry practice.
major comments (2)
- [§3 (Model Formulation)] §3 (Model Formulation) and abstract: The central modeling claim that the induced-export-ban relationship 'yields a second-stage problem with one binary variable and continuous variables' is load-bearing for both the algorithmic development and the case-study value quantification. The manuscript must supply the explicit second-stage formulation (including the shortage-projection constraint and ban-trigger logic) together with a justification that no additional binaries are required for multi-period decisions, quality checks, or threshold nonlinearities; without this derivation the reported superiority of Alternating Integer L-shaped cuts and the quantified value of incorporating disruptions rest on an unverified structural assumption.
- [§5 (Computational Results)] §5 (Computational Results) and Table X (case-study outcomes): The performance ranking among the three alternating cut methods and the reported value of including induced risk are obtained under the one-binary second-stage structure. If the actual ban-trigger logic requires additional discrete decisions, both the CPU-time comparisons and the cost-benefit numbers become unreliable; the paper should therefore include a sensitivity table that relaxes the single-binary restriction and reports the resulting changes in solution quality and run time.
minor comments (2)
- [§2] Notation for the shortage-projection indicator and the export-ban variable should be introduced with an explicit equation reference in §2 before being used in the second-stage formulation.
- [Abstract] The abstract states that 'Alternating Integer L-shaped cuts perform best' but does not report the specific metrics (optimality gap, CPU time, number of cuts) that support this conclusion; these numbers should appear in the abstract or a summary table.
Simulated Author's Rebuttal
We thank the referee for the constructive and detailed report. The comments highlight important aspects of the modeling and computational validation that we address point by point below. We believe the requested clarifications can be incorporated without altering the core contributions.
read point-by-point responses
-
Referee: [§3 (Model Formulation)] §3 (Model Formulation) and abstract: The central modeling claim that the induced-export-ban relationship 'yields a second-stage problem with one binary variable and continuous variables' is load-bearing for both the algorithmic development and the case-study value quantification. The manuscript must supply the explicit second-stage formulation (including the shortage-projection constraint and ban-trigger logic) together with a justification that no additional binaries are required for multi-period decisions, quality checks, or threshold nonlinearities; without this derivation the reported superiority of Alternating Integer L-shaped cuts and the quantified value of incorporating disruptions rest on an unverified structural assumption.
Authors: We agree that an explicit derivation strengthens the paper. Section 3 already derives the second-stage subproblem from the systemic induced-ban relationship: the first-stage design variables are fixed, and the second stage minimizes recourse costs subject to a shortage-projection constraint (continuous variable tracking projected unmet demand under each scenario) that triggers a single binary variable y via a big-M inequality when shortage exceeds a regulatory threshold. This y activates the export ban, which in turn affects continuous flow and penalty variables. Multi-period aspects and quality failures are encoded as first-stage or scenario parameters rather than additional second-stage binaries; threshold nonlinearities are linearized through the binary indicator. To make this fully transparent, we will insert the complete second-stage constraint set (shortage projection, ban trigger, and recourse) plus a dedicated justification paragraph in the revised §3. revision: yes
-
Referee: [§5 (Computational Results)] §5 (Computational Results) and Table X (case-study outcomes): The performance ranking among the three alternating cut methods and the reported value of including induced risk are obtained under the one-binary second-stage structure. If the actual ban-trigger logic requires additional discrete decisions, both the CPU-time comparisons and the cost-benefit numbers become unreliable; the paper should therefore include a sensitivity table that relaxes the single-binary restriction and reports the resulting changes in solution quality and run time.
Authors: The one-binary structure follows directly from the induced-ban mechanism as formulated; additional discrete decisions would represent a different modeling choice outside the scope of the systemic relationship studied. Consequently, the reported CPU times, method ranking, and value-of-information numbers remain valid for the model presented. We therefore do not plan to add a sensitivity table that artificially relaxes the single-binary restriction, as doing so would evaluate a non-equivalent problem. If the referee can suggest a concrete alternative ban-trigger logic that introduces extra binaries while preserving the induced-risk semantics, we would consider a targeted discussion, but under the current formulation no such table is required. revision: no
Circularity Check
No circularity: modeling assumptions and algorithmic motivation are presented as direct consequences of the chosen formulation, not reductions to self-citations or fitted inputs.
full rationale
The paper defines a two-stage stochastic MIP whose second-stage structure (one binary variable) is stated to follow from the modeling decision to encode export bans as triggered by projected shortages. This structure is then used to motivate the three alternating cut methods, with performance claims based on computational results on the oncology case study. No self-citation is invoked to justify the one-binary structure, no parameter is fitted to data and then relabeled as a prediction, and no uniqueness theorem or ansatz is smuggled in. The induced-risk relationship is explicitly an input modeling assumption rather than a derived result, making the derivation self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
Reference graph
Works this paper leans on
-
[1]
Pharma Manufacturing , year =
-
[2]
Manufacturing and Service Operations Management , pages =
Lu, Mengshi and Ran, Lun and Shen, Zuo-jun Max , doi =. Manufacturing and Service Operations Management , pages =
-
[3]
Computers and Industrial Engineering , keywords =
Li, Xueping and Zhang, Kaike , doi =. Computers and Industrial Engineering , keywords =
-
[4]
and Daskin, Mark S
Tucker, Emily L. and Daskin, Mark S. and Sweet, Burgunda V. and Hopp, Wallace J. , doi =. IISE Transactions , number =
-
[5]
Martha L. Effects of geopolitical strain on global pharmaceutical supply chain design and drug shortages , journal =. 2025 , issn =. doi:https://doi.org/10.1016/j.ejor.2025.05.002 , url =
-
[6]
Operations Management Research , pages =
Barbieri, Paolo and Boffelli, Albachiara and Elia, Stefano and Fratocchi, Luciano and Kalchschmidt, Matteo and Samson, Danny , doi =. Operations Management Research , pages =
-
[7]
Journal of Purchasing and Supply Management , number =
Hilletofth, Per and Eriksson, David and Tate, Wendy and Kinkel, Steffen , doi =. Journal of Purchasing and Supply Management , number =
-
[8]
International Journal Of Logistics: Research And Applications , number =
Mohiuddin, Muhammad and Rashid, Mamunur and Azad, Samim Al and Su, Zhan , doi =. International Journal Of Logistics: Research And Applications , number =
-
[9]
2021 , note =
ECLAC , pages =. 2021 , note =
2021
-
[10]
2020 , note =
WTO , pages =. 2020 , note =
2020
-
[11]
Casey, Christopher A and Cimino-Isaacs, Cathleen D , booktitle =
-
[12]
Rajan and Cunningham, Margaret H
Varadarajan, P. Rajan and Cunningham, Margaret H. , doi =. Journal of the Academy of Marketing Science , pages =
-
[13]
doi:10.1186/s40545-022-00439-7 , issn =
Journal of Pharmaceutical Policy and Practice , number =. doi:10.1186/s40545-022-00439-7 , issn =
-
[14]
and Iwamoto, Kotoji and Barr, Ronald D
Martei, Yehoda M. and Iwamoto, Kotoji and Barr, Ronald D. and Wiernkowski, John T. and Robertson, Jane , doi =. BMJ Global Health , number =
-
[15]
and Shapiro, Alexander and Homem-de-Mello, Tito , doi =
Kleywegt, Anton J. and Shapiro, Alexander and Homem-de-Mello, Tito , doi =. SIAM Journal on Optimization , number =
-
[16]
and Nemhauser, George and Shapiro, Alexander , doi =
Verweij, Bram and Ahmed, Shabbir and Kleywegt, Anton J. and Nemhauser, George and Shapiro, Alexander , doi =. Computational Optimization and Applications , number =
-
[17]
A stochastic programming approach for supply chain network design under uncertainty , journal =. 2005 , issn =. doi:https://doi.org/10.1016/j.ejor.2004.01.046 , url =
-
[18]
Opsearch , number =
Chatzoglou, Prodromos and Chatzoudes, Dimitrios and Petrakopoulou, Zografia and Polychrou, Elena , doi =. Opsearch , number =
-
[19]
Kochan, Cigdem Gonul and Nowicki, David R. , doi =. International Journal of Physical Distribution and Logistics Management , number =
-
[20]
Transportation Research Part E: Logistics and Transportation Review , number =
Suryawanshi, Pravin and Dutta, Pankaj , doi =. Transportation Research Part E: Logistics and Transportation Review , number =
-
[21]
Building Resilience into the Nation's Medical Product Supply Chains , doi =
-
[22]
and Wheeler, Shamus and Mitchell, John E
Nguyen, Huy and Sharkey, Thomas C. and Wheeler, Shamus and Mitchell, John E. and Wallace, Willam A. , doi =. Omega , pages =
-
[23]
Journal of Operations Management , pages =
Ambulkar, Saurabh and Blackhurst, Jennifer and Grawe, Scott , doi =. Journal of Operations Management , pages =
-
[24]
International Business Review , number =
McIvor, Ronan and Bals, Lydia , doi =. International Business Review , number =
-
[25]
International Journal of Production Research , number =
Namdar, Jafar and Li, Xueping and Sawhney, Rupy and Pradhan, Ninad , doi =. International Journal of Production Research , number =
-
[26]
Transportation Research Part E: Logistics and Transportation Review , number =
Ghavamifar, Ali and Makui, Ahmad and Taleizadeh, Ata Allah , doi =. Transportation Research Part E: Logistics and Transportation Review , number =
-
[27]
European Journal of Operational Research , number =
Govindan, Kannan and Fattahi, Mohammad and Keyvanshokooh, Esmaeil , doi =. European Journal of Operational Research , number =
-
[28]
International Journal of Production Economics , pages =
Aldrighetti, Riccardo and Battini, Daria and Ivanov, Dmitry and Zennaro, Ilenia , doi =. International Journal of Production Economics , pages =
-
[29]
Journal of Industrial Engineering International , pages =
Singh, Chandra Shekhar and Soni, Gunjan and Badhotiya, Gaurav Kumar , doi =. Journal of Industrial Engineering International , pages =
-
[30]
and Juan, Angel A
Tordecilla, Rafael D. and Juan, Angel A. and Montoya-Torres, Jairo R. and Quintero-Araujo, Carlos L. and Panadero, Javier , doi =. Simulation Modelling Practice and Theory , number =
-
[31]
Transport Reviews , number =
Maharjan, Rajali and Kato, Hironori , doi =. Transport Reviews , number =
-
[32]
Snyder, Z¨ umb¨ ul Atan, Peng Peng, Ying Rong, Amanda J
Snyder, Lawrence V. and Atan, Z. IIE Transactions , number =. doi:10.1080/0740817X.2015.1067735 , issn =
-
[33]
and Turnquist, Mark A
Rawls, Carmen G. and Turnquist, Mark A. , doi =. Transportation Research Part B: Methodological , number =
-
[34]
and Machan, Jason T
Alevizakos, Michail and Detsis, Marios and Grigoras, Christos A. and Machan, Jason T. and Mylonakis, Eleftherios , doi =. Drugs , number =
-
[35]
2018 , publisher=
Managing Trust in Strategic Alliances , author=. 2018 , publisher=
2018
-
[36]
Uncertain Supply Chain Management , pages =
Singh, Harjit and Garg, R K and Sachdeva, Anish , doi =. Uncertain Supply Chain Management , pages =
-
[37]
AKCE International Journal of Graphs and Combinatorics , number =
Ouazine, Kahina and Slimani, Hachem and Tari, Abdelkamel , doi =. AKCE International Journal of Graphs and Combinatorics , number =
-
[38]
Journal of Operations Management , pages =
Jahre, Marianne and Kembro, Joakim and Rezvanian, Tina and Ergun, Ozlem and H. Journal of Operations Management , pages =. doi:10.1016/j.jom.2016.05.009 , issn =
-
[39]
Complexity , pages =
Franco, Carlos and Alfonso-Lizarazo, Edgar , doi =. Complexity , pages =
-
[40]
and Koberstein, Achim , booktitle =
Blossey, Gregor and Hahn, Gerd J. and Koberstein, Achim , booktitle =. doi:10.24251/hicss.2021.173 , isbn =
-
[41]
International Transactions in Operational Research , pages =
Li, Jinfeng and Liu, Yankui and Yang, Guoqing , doi =. International Transactions in Operational Research , pages =. 2023 , url =
2023
-
[42]
Pharmaceutical supply chain reliability and effects on drug shortages , journal =. 2022 , issn =. doi:https://doi.org/10.1016/j.cie.2022.108258 , author =
-
[43]
Transportation Research Part E: Logistics and Transportation Review , pages =
Akbarpour, Mina and. Transportation Research Part E: Logistics and Transportation Review , pages =. doi:10.1016/j.tre.2020.101867 , isbn =
-
[44]
Iacocca, Kathleen and Mahar, Stephen and. Omega , pages =. doi:10.1016/j.omega.2021.102589 , issn =
-
[45]
Annals of Operations Research , number =
Zandkarimkhani, Shiva and Mina, Hassan and Biuki, Mehdi and Govindan, Kannan , doi =. Annals of Operations Research , number =
-
[46]
and Koberstein, Achim , doi =
Blossey, Gregor and Hahn, Gerd J. and Koberstein, Achim , doi =. International Journal of Production Economics , number =
-
[47]
and Liu, Songsong and Papageorgiou, Lazaros G
Sousa, Rui T. and Liu, Songsong and Papageorgiou, Lazaros G. and Shah, Nilay , doi =. Chemical Engineering Research and Design , number =
-
[48]
Susarla, Naresh and Karimi, I. A. , doi =. Computers and Chemical Engineering , pages =
-
[49]
Applied Soft Computing Journal , pages =
Goodarzian, Fariba and Hosseini-Nasab, Hasan and Mu. Applied Soft Computing Journal , pages =. doi:10.1016/j.asoc.2020.106331 , issn =
-
[50]
Journal of the Operational Research Society , volume =
Rafael Diaz and Sailesh Kolachana and Rodrigo Falcão Gomes , title =. Journal of the Operational Research Society , volume =. 2023 , publisher =. doi:10.1080/01605682.2022.2077661 , URL =
-
[51]
International Journal of Environmental Research and Public Health , number =
Li, Zhao and Xia, Tie and Shen, Wanzhi and Chen, Sheng , doi =. International Journal of Environmental Research and Public Health , number =
-
[52]
The mechanism of alliance promotes cooperation in the spatial multi-games , journal =. 2020 , issn =. doi:https://doi.org/10.1016/j.physleta.2020.126414 , url =
-
[53]
Transportation Research Part E: Logistics and Transportation Review , pages =
Hasani, Aliakbar and Khosrojerdi, Amirhossein , doi =. Transportation Research Part E: Logistics and Transportation Review , pages =
-
[54]
Computers and Industrial Engineering , pages =
Sabouhi, Fatemeh and Pishvaee, Mir Saman and Jabalameli, Mohammad Saeed , doi =. Computers and Industrial Engineering , pages =
-
[55]
and Keskinocak, Pinar , doi =
Duran, Serhan and Gutierrez, Marco A. and Keskinocak, Pinar , doi =. Interfaces , number =
-
[56]
doi:10.1080/24725854.2017.1408165 , issn =
IISE Transactions , number =. doi:10.1080/24725854.2017.1408165 , issn =
-
[57]
and Moniz, Samuel and de Sousa, Jorge Pinho and Barbosa-Povoa, Ana Paula and Reklaitis, Gintaras , doi =
Marques, Catarina M. and Moniz, Samuel and de Sousa, Jorge Pinho and Barbosa-Povoa, Ana Paula and Reklaitis, Gintaras , doi =. Computers and Chemical Engineering , pages =
-
[58]
Frontiers in Pharmacology , pages =
Bochenek, Tomasz and Abilova, Vafa and Alkan, Ali and. Frontiers in Pharmacology , pages =. doi:10.3389/fphar.2017.00942 , issn =
-
[59]
2021 , note =
Aguiar, Esco and Kasper, Ernest , booktitle =. 2021 , note =
2021
-
[60]
2019 , doi =
Dyer, Owen , title =. 2019 , doi =. https://www.bmj.com/content/367/bmj.l6086.full.pdf , journal =
2019
-
[61]
and Kim, Katherine Callaway and Hernandez, Inmaculada and Gellad, Walid F
Suda, Katie J. and Kim, Katherine Callaway and Hernandez, Inmaculada and Gellad, Walid F. and Rothenberger, Scott and Campbell, Allen and Malliart, Lisa and Tadrous, Mina , doi =. Journal of the American Pharmacists Association , number =
-
[62]
and Meng, Fanwen , doi =
Goh, Mark and Lim, Joseph Y.S. and Meng, Fanwen , doi =. European Journal of Operational Research , number =
-
[63]
, booktitle =
Simon, David W. , booktitle =
-
[64]
Kalish, Ira and Wolf, Michael , booktitle =
-
[65]
Journal of Global Health , pages =
Tatar, Moosa and Shoorekchali, Jalal Montazeri and Faraji, Mohammad Reza and Seyyedkolaee, Mohammad Abdi and Pag. Journal of Global Health , pages =. doi:10.7189/jogh.12.03072 , issn =
-
[66]
Planning operations before market launch for balancing time-to-market and risks in pharmaceutical supply chains , journal =. 2015 , issn =. doi:https://doi.org/10.1016/j.ijpe.2014.10.010 , url =
-
[67]
International Journal of Logistics Research and Applications , keywords =
Shekarian, Mansoor and. International Journal of Logistics Research and Applications , keywords =. doi:10.1080/13675567.2020.1763935 , issn =
-
[68]
Donilon, Tom and Kress, Catherine and Lee, Stephanie and Spivey, Jackson , institution =
-
[69]
doi:https://doi.org/10.17016/IFDP.2022.1222r1 , editor =
Caldara, Dario and Iacoviell, Matteo , booktitle =. doi:https://doi.org/10.17016/IFDP.2022.1222r1 , editor =
-
[70]
Kress, Catherine and Patchen, Carl and Ratcliffe, Ron and Nostrand, Eric Van and Yang, Kemin , institution =
-
[71]
Fell, James and Duver, Andrew , doi =
-
[72]
Frontiers in Pharmacology , keywords =
Shukar, Sundus and Zahoor, Fatima and Hayat, Khezar and Saeed, Amna and Gillani, Ali Hassan and Omer, Sumaira and Hu, Shuchen and Babar, Zaheer-Ud-Din and Fang, Yu and Yang, Caijun , doi =. Frontiers in Pharmacology , keywords =
-
[73]
World Economic Forum , pages =
-
[74]
Thomas, Katie and Kaplan, Sheila , booktitle =
-
[75]
Varas, Antonio and Varadarajan, Raj and Goodrich, Jimmy and Yinug, Falan , institution =
-
[76]
Pariazar, Mahmood and Root, Sarah and Sir, Mustafa Y. , doi =. Computers and Industrial Engineering , keywords =
-
[77]
and Harun, Sarah , doi =
Bhuiyan, Tanveer Hossain and Medal, Hugh R. and Harun, Sarah , doi =. European Journal of Operational Research , keywords =
-
[78]
IISE Transactions , keywords =
Li, Shanshan and He, Yong and Huang, Hongfu and Lin, Junyi and Ivanov, Dmitry , doi =. IISE Transactions , keywords =
-
[79]
, institution =
Margulies, Susan S. , institution =
-
[80]
Operations Research , keywords =
Cui, Tingting and Ouyang, Yanfeng and Shen, Zuo Jun Max , doi =. Operations Research , keywords =
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.