Incorporating uncertainty into a supplier selection problem

Lei Li, Zelda B. Zabinsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

97 Citations (Scopus)


Supplier selection is an important strategic supply chain design decision. Incorporating uncertainty of demand and supplier capacity into the optimization model results in a robust selection of suppliers. A two-stage stochastic programming (SP) model and a chance-constrained programming (CCP) model are developed to determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. Both models include several objectives and strive to balance a small number of suppliers with the risk of not being able to meet demand. The SP model is scenario-based and uses penalty coefficients whereas the CCP model assumes a probability distribution and constrains the probability of not meeting demand. Both formulations improve on a deterministic mixed integer linear program and give the decision maker a more complete picture of tradeoffs between cost, system reliability and other factors. We present Pareto-optimal solutions for a sample problem to demonstrate the benefits of the SP and CCP models. In order to describe the tradeoffs between costs and risks in an analytical form, we use multi-parametric programming techniques to more completely analyze the alternative Pareto-optimal supplier selection solutions in the CCP model. This analysis gives insights into the robustness of the solutions with respect to number of suppliers, costs and probability of not meeting demand.

Original languageEnglish
Pages (from-to)344-356
Number of pages13
JournalInternational Journal of Production Economics
Issue number2
Publication statusPublished - Dec 2011
Externally publishedYes


  • Chance-constraint programming
  • Multi-parametric programming
  • Plan for uncertainty
  • Robust supplier selection
  • Stochastic programming
  • Tradeoffs between risk and cost


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