Duality and existence of optimal policies in generalized joint replenishment

Daniel Adelman*, Diego Klabjan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We establish a duality theory for a broad class of deterministic inventory control problems on continuous spaces that includes the classical joint replenishment problem and inventory routing. Using this theory, we establish the existence of an optimal policy, which has been an open question. We show how a primal-dual pair of infinite dimensional linear programs encode both cyclic and noncyclic schedules, and provide various results regarding cyclic schedules, including an example showing that they need not be optimal.

Original languageEnglish (US)
Pages (from-to)28-50
Number of pages23
JournalMathematics of Operations Research
Issue number1
StatePublished - Feb 2005


  • Cyclic schedule
  • Deterministic inventory theory
  • Existence of optimal policies
  • Infinite linear programming duality
  • Semi-Markov decision process

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research


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