Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms

• 成果类型: Article
• 署名作者: Buchbinder, Niv; Kimbrel, Tracy; Levi, Retsef; Makarychev, Konstantin; Sviridenko, Maxim
• 署名单位: Tel Aviv University; National Science Foundation (NSF); Massachusetts Institute of Technology (MIT); Microsoft; University of Warwick
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2013.1188
• 发表日期: 2013
• 页码: 1014-1029
• 关键词: packing; bounds

摘要

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.