{"title":"Online multiple one way non-preemptive time series search with interrelated prices","authors":"Jinghan Zhao, Yongxi Cheng, Jan Eube, Haodong Liu","doi":"10.1007/s10878-024-01247-2","DOIUrl":null,"url":null,"abstract":"<p>This paper studies the online multiple time series search problem with interrelated prices (MTSS-ip). This perspective narrows the distance between the problem and the reality of market prices with limited variation. In MTSS-ip, the products arrive periodically, and the decision maker has a limited storage size without knowing future prices. The prices of two adjacent periods are interrelated. This study proposes an online zero-inventory algorithm (ZIA) and proves an upper bound of <span>\\(K+1-\\frac{K}{\\theta _2}\\)</span> on the competitive ratio of ZIA. In addition, a lower bound on the competitive ratio of problem MTSS-ip for any deterministic online algorithm is established. For the case with a large storage size <i>K</i>, a lower bound of <span>\\(\\frac{K}{48\\log _{\\theta _2} K}\\)</span> on the competitive ratio for MTSS-ip is proved.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"27 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10878-024-01247-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies the online multiple time series search problem with interrelated prices (MTSS-ip). This perspective narrows the distance between the problem and the reality of market prices with limited variation. In MTSS-ip, the products arrive periodically, and the decision maker has a limited storage size without knowing future prices. The prices of two adjacent periods are interrelated. This study proposes an online zero-inventory algorithm (ZIA) and proves an upper bound of \(K+1-\frac{K}{\theta _2}\) on the competitive ratio of ZIA. In addition, a lower bound on the competitive ratio of problem MTSS-ip for any deterministic online algorithm is established. For the case with a large storage size K, a lower bound of \(\frac{K}{48\log _{\theta _2} K}\) on the competitive ratio for MTSS-ip is proved.
期刊介绍：
The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering.
The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.
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