In this work, the problem of allocating a set of production lots to satisfy customer orders is considered. This research is of relevance to lot-to-order matching problems in semiconductor supply chain settings. We consider that lot-splitting is not allowed during the allocation process due to standard practices. Furthermore, lot-sizes are regarded as uncertain planning data when making the allocation decisions due to potential yield loss. In order to minimize the total penalties of demand un-fulfillment and over-fulfillment, a robust mixed-integer optimization approach is adopted to model is proposed the problem of allocating a set of work-in-process lots to customer orders, where lot-sizes are modeled using ellipsoidal uncertainty sets. To solve the optimization problem efficiently we apply the techniques of branch-and-price and Benders decomposition. The advantages of our model are that it can represent uncertainty in a straightforward manner with little distributional assumptions, and it can produce solutions that effectively hedge against the uncertainty in the lot-sizes using very reasonable amounts of computational effort.

Original languageEnglish (US)
Pages (from-to)557-570
Number of pages14
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - Sep 16 2010


  • Branch-and-price
  • Generalized Benders
  • Lot assignment
  • Robust optimization
  • Semiconductor supply chain
  • Uncertainty modeling

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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