Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms
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 t...
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| Veröffentlicht in: | Operations research 2013-07, Vol.61 (4), p.1014-1029 |
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| container_title | Operations research |
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| creator | Buchbinder, Niv Kimbrel, Tracy Levi, Retsef Makarychev, Konstantin Sviridenko, Maxim |
| description | 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. |
| doi_str_mv | 10.1287/opre.2013.1188 |
| format | Article |
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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.</description><identifier>ISSN: 0030-364X</identifier><identifier>EISSN: 1526-5463</identifier><identifier>DOI: 10.1287/opre.2013.1188</identifier><identifier>CODEN: OPREAI</identifier><language>eng</language><publisher>Linthicum: INFORMS</publisher><subject>Algorithms ; Analysis ; Approximation ; competitive analysis ; Cost efficiency ; Deadlines ; Demand ; Inventory control ; joint replenishment problem ; Linear programming ; Logistics ; Make to order ; Mathematical problems ; METHODS ; online algorithm ; Operations research ; Optimization algorithms ; primal dual ; Production planning ; Simulations ; Studies ; Variable costs</subject><ispartof>Operations research, 2013-07, Vol.61 (4), p.1014-1029</ispartof><rights>2013 INFORMS</rights><rights>COPYRIGHT 2013 Institute for Operations Research and the Management Sciences</rights><rights>Copyright Institute for Operations Research and the Management Sciences Jul/Aug 2013</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c425t-7180ba3b43915b78eca36293853aa2b53c4acf5befe9ab18adc5a275257a88b93</citedby><cites>FETCH-LOGICAL-c425t-7180ba3b43915b78eca36293853aa2b53c4acf5befe9ab18adc5a275257a88b93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/23481811$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://pubsonline.informs.org/doi/full/10.1287/opre.2013.1188$$EHTML$$P50$$Ginforms$$H</linktohtml><link.rule.ids>314,776,780,799,3679,27901,27902,57992,58225,62589</link.rule.ids></links><search><creatorcontrib>Buchbinder, Niv</creatorcontrib><creatorcontrib>Kimbrel, Tracy</creatorcontrib><creatorcontrib>Levi, Retsef</creatorcontrib><creatorcontrib>Makarychev, Konstantin</creatorcontrib><creatorcontrib>Sviridenko, Maxim</creatorcontrib><title>Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms</title><title>Operations research</title><description>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.</description><subject>Algorithms</subject><subject>Analysis</subject><subject>Approximation</subject><subject>competitive analysis</subject><subject>Cost efficiency</subject><subject>Deadlines</subject><subject>Demand</subject><subject>Inventory control</subject><subject>joint replenishment problem</subject><subject>Linear programming</subject><subject>Logistics</subject><subject>Make to order</subject><subject>Mathematical problems</subject><subject>METHODS</subject><subject>online algorithm</subject><subject>Operations research</subject><subject>Optimization algorithms</subject><subject>primal dual</subject><subject>Production planning</subject><subject>Simulations</subject><subject>Studies</subject><subject>Variable costs</subject><issn>0030-364X</issn><issn>1526-5463</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>N95</sourceid><recordid>eNqFkU1r3DAQhkVpIduk194Chl6rrT5tubdl2zQpCVtCC70J2Tve1da2HI0cyL-vzYYmOfUyw_A-88G8hLznbMmFKT6FIcJSMC6XnBvziiy4FjnVKpevyYIxyajM1e8T8hbxwBgrda4X5HbTt76H7Mb9AZoC3cQtxOx78H3KbmFoofe472CqbsIW2s_Zj-g719Ivo2uzdegGSD75e8hW7S5En_YdnpE3jWsR3j3mU_Lr4uvP9SW93ny7Wq-uaa2ETrTghlVOVkqWXFeFgdrJXJTSaOmcqLSslasbXUEDpau4cdtaO1FooQtnTFXKU_LhOHeI4W4ETPYQxthPKy1XShacMW2eqJ1rwfq-CSm6uvNY25VUSnAllZioj8-oasTpJzgF9Lt9wp0bEV_iyyNex4AYobHD_Jb4YDmzsxl2NsPOZtjZjKnh_NhwwBTiP1pIZbjhfNLpUZ8PjB3-b95fPJ2UWg</recordid><startdate>20130701</startdate><enddate>20130701</enddate><creator>Buchbinder, Niv</creator><creator>Kimbrel, Tracy</creator><creator>Levi, Retsef</creator><creator>Makarychev, Konstantin</creator><creator>Sviridenko, Maxim</creator><general>INFORMS</general><general>Institute for Operations Research and the Management Sciences</general><scope>AAYXX</scope><scope>CITATION</scope><scope>N95</scope><scope>XI7</scope><scope>JQ2</scope><scope>K9.</scope></search><sort><creationdate>20130701</creationdate><title>Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms</title><author>Buchbinder, Niv ; Kimbrel, Tracy ; Levi, Retsef ; Makarychev, Konstantin ; Sviridenko, Maxim</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c425t-7180ba3b43915b78eca36293853aa2b53c4acf5befe9ab18adc5a275257a88b93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algorithms</topic><topic>Analysis</topic><topic>Approximation</topic><topic>competitive analysis</topic><topic>Cost efficiency</topic><topic>Deadlines</topic><topic>Demand</topic><topic>Inventory control</topic><topic>joint replenishment problem</topic><topic>Linear programming</topic><topic>Logistics</topic><topic>Make to order</topic><topic>Mathematical problems</topic><topic>METHODS</topic><topic>online algorithm</topic><topic>Operations research</topic><topic>Optimization algorithms</topic><topic>primal dual</topic><topic>Production planning</topic><topic>Simulations</topic><topic>Studies</topic><topic>Variable costs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Buchbinder, Niv</creatorcontrib><creatorcontrib>Kimbrel, Tracy</creatorcontrib><creatorcontrib>Levi, Retsef</creatorcontrib><creatorcontrib>Makarychev, Konstantin</creatorcontrib><creatorcontrib>Sviridenko, Maxim</creatorcontrib><collection>CrossRef</collection><collection>Gale Business: Insights</collection><collection>Business Insights: Essentials</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><jtitle>Operations research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Buchbinder, Niv</au><au>Kimbrel, Tracy</au><au>Levi, Retsef</au><au>Makarychev, Konstantin</au><au>Sviridenko, Maxim</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms</atitle><jtitle>Operations research</jtitle><date>2013-07-01</date><risdate>2013</risdate><volume>61</volume><issue>4</issue><spage>1014</spage><epage>1029</epage><pages>1014-1029</pages><issn>0030-364X</issn><eissn>1526-5463</eissn><coden>OPREAI</coden><abstract>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.</abstract><cop>Linthicum</cop><pub>INFORMS</pub><doi>10.1287/opre.2013.1188</doi><tpages>16</tpages></addata></record> |
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| subjects | Algorithms Analysis Approximation competitive analysis Cost efficiency Deadlines Demand Inventory control joint replenishment problem Linear programming Logistics Make to order Mathematical problems METHODS online algorithm Operations research Optimization algorithms primal dual Production planning Simulations Studies Variable costs |
| title | Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms |
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