{"type":"ScholarlyArticle","title":"Competitive Analysis for Multi-Commodity Ski-Rental Problem","authors":[{"name":"Binghan Wu","slug":"binghan-wu","given":"Binghan","family":"Wu","affiliation":"Faculty of Engineering , The University of Sydney"},{"name":"Wei Bao","slug":"wei-bao","given":"Wei","family":"Bao","affiliation":"Faculty of Engineering , The University of Sydney"},{"name":"Dong Yuan","slug":"dong-yuan","given":"Dong","family":"Yuan","affiliation":"Faculty of Engineering , The University of Sydney"},{"name":"Bing Zhou","slug":"bing-zhou","given":"Bing","family":"Zhou","affiliation":"Faculty of Engineering , The University of Sydney"}],"abstract":"We investigate an extended version of the classical ski-rental problem with multiple commodities. A customer uses a set of commodities altogether, and he/she needs to choose payment options to cover the usage of each commodity without the knowledge of the future. The payment options of each commodity include (1) renting: to pay for an on-demand usage and (2) buying: to pay for the lifetime usage. It is a novel extension of the classical ski-rental problem which deals with only one commodity. To address this problem, we propose a new online algorithm called the Multi-Object Break-Even (MOBE) algorithm and conduct competitive analysis. We show that the tight lower and upper bounds of MOBE algorithm's competitive ratio are e/e-1 and 2 respectively against adaptive adversary under arbitrary renting and buying prices. We further prove that MOBE algorithm is an optimal online algorithm if commodities have the same rent-to-buy ratio. Numerical results verify our theoretical conclusion and demonstrate the advantages of MOBE in a real-world scenario.","doi":"10.24963/ijcai.2022/648","url":"https://ijcai.org/proceedings/2022/648","pdf":"https://ijcai.org/proceedings/2022/0648.pdf","markdown":"https://ijcai.org/proceedings/2022/648.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/648","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Planning and Scheduling","track":"Main Track","number":648,"pages":{"first":4672,"last":4678},"keywords":["Planning and Scheduling: Planning under Uncertainty","Planning and Scheduling: Theoretical Foundations of Planning","Planning and Scheduling: Applications"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986627","length_sec":89,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984770","length_sec":339,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Ai et al., 2014] L. 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