Online make-to-order joint replenishment model: Primal-dual competitive algorithms

Niv Buchbinder, Tracy Kimbrel, Retsef Levi, Konstantin Makarychev, Maxim Sviridenko

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


In this paper, we study an online make-to-order variant of the classical joint replenishment problem (JRP) that has been studied extensively over the years and plays a fundamental role in broader planning issues, such as the management of supply chains. In contrast to the traditional approaches of the stochastic inventory theory, we study the problem using competitive analysis against a worst-case adversary. Our main result is a 3-competitive deterministic algorithm for the online version of the JRP. We also prove a lower bound of approximately 2.64 on the competitiveness of any deterministic online algorithm for the problem. Our algorithm is based on a novel primal-dual approach using a new linear programming relaxation of the offline JRP model. The primal-dual approach that we propose departs from previous primal-dual and online algorithms in rather significant ways. We believe that this approach can extend the range of problems to which online and primal-dual algorithms can be applied and analyzed.

Original languageEnglish
Pages (from-to)1014-1029
Number of pages16
JournalOperations Research
Issue number4
StatePublished - Jul 2013


FundersFunder number
Directorate for Engineering0846554
Engineering and Physical Sciences Research CouncilEP/J021814/1


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