Flow balancing with uncertain demand for automated package sorting centers

Luis J. Novoa*, Ahmad I. Jarrah, David P. Morton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Package carriers use sophisticated automated sorting facilities to efficiently process inbound packages and sort them to their down line destinations. During each of several daily processing windows, primary sorters perform high level sortation of the packages and direct them to one of several secondary sorters that are then used to segregate the packages by their outbound loading destinations. We examine the problem of assigning package destinations to the secondary sorters in a way that balances the workload in the facility, while incorporating the day-to-day fluctuation in package volumes and adhering to the outbound loading capacities of the various work centers in the facility. We present a general stochastic modeling framework using chance constraints to balance the flows, and robust constraints to model the capacity limits. We propose and evaluate the performance of three alternative mixed integer nonlinear formulations for the problem and determine which is most effective. Significant improvement in package flow balance and loading capacity robustness is shown for the test sorting facilities by comparing the solutions from the proposed new model to those obtained when ignoring, partially or completely, the stochasticity in the package volumes.

Original languageEnglish (US)
Pages (from-to)210-227
Number of pages18
JournalTransportation Science
Issue number1
StatePublished - Jan 1 2018


  • Automated sortation
  • Chance constraints
  • Cross-docking
  • Mixed integer nonlinear programming
  • Package carriers
  • Postal services
  • Robust optimization
  • Stochastic programming
  • Transshipment

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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