{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:24:04Z","timestamp":1740108244320,"version":"3.37.3"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,7,26]],"date-time":"2016-07-26T00:00:00Z","timestamp":1469491200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71301110"],"award-info":[{"award-number":["71301110"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Humanities and Social Sciences Foundation of the Ministry of Education","award":["13XJC630015"],"award-info":[{"award-number":["13XJC630015"]}]},{"DOI":"10.13039\/501100013286","name":"Research Fund for the Doctoral Program of Higher Education of China","doi-asserted-by":"crossref","award":["20130181120059"],"award-info":[{"award-number":["20130181120059"]}],"id":[{"id":"10.13039\/501100013286","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Project of Education Department of Sichuan Province","award":["14ZB0173"],"award-info":[{"award-number":["14ZB0173"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s00186-016-0557-x","type":"journal-article","created":{"date-parts":[[2016,7,26]],"date-time":"2016-07-26T17:19:14Z","timestamp":1469553554000},"page":"567-595","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Network equilibrium of production, transportation and pricing for multi-product multi-market"],"prefix":"10.1007","volume":"84","author":[{"given":"Jiuping","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guomin","family":"Fang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zezhong","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,7,26]]},"reference":[{"key":"557_CR1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1111\/j.0013-0427.2005.00407.x","volume":"72","author":"T Aadachi","year":"2005","unstructured":"Aadachi T (2005) Third-degree price discrimination, consumption externalities and social welfare. Economica 72:171\u2013178","journal-title":"Economica"},{"issue":"6","key":"557_CR2","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1287\/opre.1070.0411","volume":"55","author":"H-S Ahn","year":"2007","unstructured":"Ahn H-S, Gumus M, Kaminsky P (2007) Pricing and manufacturing decisions when demand is a function of prices in multiple periods. Oper Res 55(6):1039\u20131057","journal-title":"Oper Res"},{"key":"557_CR3","volume-title":"Convex optimization","author":"S Boyd","year":"2009","unstructured":"Boyd S, Vandenberghe L (2009) Convex optimization. Cambridge University Press, New York"},{"key":"557_CR4","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0165-0114(94)90096-5","volume":"66","author":"GA Chalam","year":"1994","unstructured":"Chalam GA (1994) Fuzzy goal programming (FGP) approach to a stochastic transportation problem under budgetary constraint. Fuzzy Sets Syst 66:293\u2013299","journal-title":"Fuzzy Sets Syst"},{"key":"557_CR5","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/BF00940320","volume":"74","author":"GY Chen","year":"1992","unstructured":"Chen GY (1992) Existence of solutions for a vector variational inequality: an extension of Hartmann-Stampacchia theorem. J Optim Theory Appl 74:445\u2013456","journal-title":"J Optim Theory Appl"},{"key":"557_CR6","first-page":"239","volume":"49","author":"GY Chen","year":"1999","unstructured":"Chen GY, Goh CJ, Yang XQ (1999) Vector network equilibrium problems and nonlinear scalarization methods. Math Meth Oper Res 49:239\u2013253","journal-title":"Math Meth Oper Res"},{"issue":"3","key":"557_CR7","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1287\/opre.1060.0284","volume":"54","author":"TCE Cheng","year":"2006","unstructured":"Cheng TCE, Wu YN (2006) A multiproduct, multicriterion supply-demand network equilibrium model. Oper Res 54(3):544\u2013554","journal-title":"Oper Res"},{"key":"557_CR8","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/0022-247X(90)90270-P","volume":"153","author":"GY Chen","year":"1990","unstructured":"Chen GY, Yang XQ (1990) The vector complementarity problem and its equivalences with the weak minimal element in ordered Banach spaces. J Math Anal Appl 153:136\u2013158","journal-title":"J Math Anal Appl"},{"issue":"1","key":"557_CR9","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.ejor.2008.05.018","volume":"197","author":"AJ Dalal","year":"2009","unstructured":"Dalal AJ, Alghalith M (2009) Production decisions under joint price and production uncertainty. Eur J Oper Res 197(1):84\u201392","journal-title":"Eur J Oper Res"},{"key":"557_CR10","doi-asserted-by":"crossref","DOI":"10.1515\/9781400884179","volume-title":"Linear programming 2: theory and extensions","author":"GB Dantzig","year":"1963","unstructured":"Dantzig GB, Thapa MN (1963) Linear programming 2: theory and extensions. Princeton University Press, New Jersey"},{"key":"557_CR11","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1287\/mnsc.1050.0491","volume":"52","author":"SM Deng","year":"2006","unstructured":"Deng SM, Yano CA (2006) Joint production and pricing decisions with setup costs and capacity constraints. Manag Sci 52:741\u2013756","journal-title":"Manag Sci"},{"key":"557_CR12","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.asoc.2014.01.041","volume":"19","author":"A Ebrahimnejad","year":"2014","unstructured":"Ebrahimnejad A (2014) A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers. Appl Soft Comput 19:171\u2013176","journal-title":"Appl Soft Comput"},{"key":"557_CR13","doi-asserted-by":"crossref","first-page":"3231","DOI":"10.1016\/j.cor.2005.02.038","volume":"33","author":"SD Eksioglu","year":"2006","unstructured":"Eksioglu SD, Romeijn HE, Pardalos PM (2006) Cross-facility management of production and transportation planning problem. Comput Oper Res 33:3231\u20133251","journal-title":"Comput Oper Res"},{"key":"557_CR14","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/02331939208843795","volume":"24","author":"A Fischer","year":"1992","unstructured":"Fischer A (1992) A special Newton-type optimization method. Optimization 24:269\u2013284","journal-title":"Optimization"},{"doi-asserted-by":"crossref","unstructured":"Goh CJ, Yang XQ (2000) Scalarization methods for vector variational inequality. In: Giannessi F (ed) Vector variational inequalities and vector equilibria. Kluwer Academic Publishers, Dordrecht, pp 217\u2013232","key":"557_CR15","DOI":"10.1007\/978-1-4613-0299-5_12"},{"key":"557_CR16","doi-asserted-by":"crossref","first-page":"4248","DOI":"10.1016\/j.nonrwa.2010.05.011","volume":"11","author":"Y He","year":"2010","unstructured":"He Y, He J, Zhu DL, Zhou J (2010) Traffic network equilibrium with capacity constraints and generalized Wardrop equilibrium. Nonlinear Anal Real World Appl 11:4248\u20134253","journal-title":"Nonlinear Anal Real World Appl"},{"key":"557_CR17","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/j.ijpe.2012.09.010","volume":"141","author":"YJ He","year":"2013","unstructured":"He YJ (2013) Sequential price and quantity decisions under supply and demand risks. Int J Prod Econ 141:541\u2013551","journal-title":"Int J Prod Econ"},{"key":"557_CR18","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1002\/sapm1941201224","volume":"20","author":"FL Hitchcock","year":"1941","unstructured":"Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20:224\u2013230","journal-title":"J Math Phys"},{"issue":"1","key":"557_CR19","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1137\/0806014","volume":"6","author":"DS Hochbaum","year":"1996","unstructured":"Hochbaum DS, Hong SP (1996) On the complexity of the production-transportation problem. SIAM J Optim 6(1):250\u2013264","journal-title":"SIAM J Optim"},{"key":"557_CR20","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.cie.2011.08.017","volume":"62","author":"S Huang","year":"2012","unstructured":"Huang S, Yang C, Zhang X (2012) Pricing and production decisions in dual-channel supply chains with demand disruptions. Comput Ind Eng 62:70\u201383","journal-title":"Comput Ind Eng"},{"key":"557_CR21","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.econmod.2012.10.009","volume":"30","author":"S Huang","year":"2013","unstructured":"Huang S, Yang C, Liu H (2013) Pricing and production decisions in a dual-channel supply chain when production costs are disrupted. Econ Model 30:521\u2013538","journal-title":"Econ Model"},{"key":"557_CR22","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1002\/j.2325-8012.2008.tb00919.x","volume":"75","author":"V Kaftal","year":"2008","unstructured":"Kaftal V, Pal D (2008) Third degree price discrimination in linear-demand markets: effects on number of markets served and social welfare. South Econ J 75:558\u2013573","journal-title":"South Econ J"},{"key":"557_CR23","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1016\/j.asoc.2011.10.014","volume":"12","author":"A Kaur","year":"2012","unstructured":"Kaur A, Kumar A (2012) A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers. Appl Soft Comput 12:1201\u20131213","journal-title":"Appl Soft Comput"},{"key":"557_CR24","volume-title":"An introduction to variational inequalities and their application","author":"D Kinderlehrer","year":"1980","unstructured":"Kinderlehrer D, Stampacchia G (1980) An introduction to variational inequalities and their application. Academic Press, New York"},{"key":"557_CR25","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.orl.2012.11.002","volume":"41","author":"U Koc","year":"2013","unstructured":"Koc U, Toptal A, Sabuncuoglu I (2013) A class of joint production and transportation planning problems under different delivery policies. Oper Res Lett 41:54\u201360","journal-title":"Oper Res Lett"},{"key":"557_CR26","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/S0362-546X(97)00578-6","volume":"34","author":"GM Lee","year":"1998","unstructured":"Lee GM, Kim DS, Lee BS, Yen ND (1998) Vector variational inequality as a tool for studing vector optimization problems. Nonlinear Anal 34:745\u2013765","journal-title":"Nonlinear Anal"},{"key":"557_CR27","doi-asserted-by":"crossref","first-page":"2076","DOI":"10.1016\/j.na.2009.10.007","volume":"72","author":"Z Lin","year":"2010","unstructured":"Lin Z (2010) On existence of vector equilibrium flows with capacity constraints of arcs. Nonlinear Anal 72:2076\u20132079","journal-title":"Nonlinear Anal"},{"key":"557_CR28","doi-asserted-by":"crossref","first-page":"4208","DOI":"10.1016\/j.apm.2010.04.018","volume":"34","author":"B Liu","year":"2010","unstructured":"Liu B, Zhang R, Xiao MD (2010) Joint decision on production and pricing for online dual channel supply chain system. Appl Math Model 34:4208\u20134218","journal-title":"Appl Math Model"},{"key":"557_CR29","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/S0377-2217(02)00731-2","volume":"153","author":"SL Liu","year":"2004","unstructured":"Liu SL, Kao C (2004) Solving fuzzy transportation problems based on extension principle. Eur J Oper Res 153:661\u2013674","journal-title":"Eur J Oper Res"},{"key":"557_CR30","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.omega.2012.03.007","volume":"41","author":"SS Liu","year":"2013","unstructured":"Liu SS, Papageorgiou LG (2013) Multiobjective optimisation of production, distribution and capacity planning of global supply chains in the process industry. Omega 41:369\u2013382","journal-title":"Omega"},{"key":"557_CR31","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1016\/j.egypro.2012.01.222","volume":"16","author":"LY Li","year":"2012","unstructured":"Li LY, Zhang TZ (2012) Study on the multi-products dynamic pricing model under uncertain demands. Energy Proced 16:1401\u20131407","journal-title":"Energy Proced"},{"key":"557_CR32","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.tre.2013.10.003","volume":"60","author":"F Meisel","year":"2013","unstructured":"Meisel F, Kirschstein T, Bierwirth C (2013) Integrated production and intermodal transportation planning in large scale production\u2013distribution-networks. Transp Res Part E 60:62\u201378","journal-title":"Transp Res Part E"},{"key":"557_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3005-0","volume-title":"Network economics: a variational inequality approach, Revised 2nd edn","author":"A Nagurney","year":"1999","unstructured":"Nagurney A (1999) Network economics: a variational inequality approach, Revised 2nd edn. Kluwer Academic Publishers, Berlin"},{"key":"557_CR34","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/S0895-7177(00)00142-4","volume":"32","author":"A Nagurney","year":"2000","unstructured":"Nagurney A (2000) A multiclass, multicriteria traffic network equilibrium model. Math Comput Model 32:393\u2013411","journal-title":"Math Comput Model"},{"key":"557_CR35","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/S0191-2615(01)00013-3","volume":"36","author":"A Nagurney","year":"2002","unstructured":"Nagurney A, Dong J (2002) A multiclass, multicriteria traffic network equilibrium model with elastic demand. Transp Res Part B 36:445\u2013469","journal-title":"Transp Res Part B"},{"key":"557_CR36","doi-asserted-by":"crossref","first-page":"2256","DOI":"10.1016\/j.apm.2009.10.034","volume":"34","author":"A Ojha","year":"2010","unstructured":"Ojha A, Das B, Mondal SK, Maiti M (2010) A stochastic discounted multi-objective solid transportation problem for breakable items using analytical hierarchy process. Appl Math Model 34:2256\u20132271","journal-title":"Appl Math Model"},{"key":"557_CR37","doi-asserted-by":"crossref","first-page":"1464","DOI":"10.1016\/j.apm.2013.08.022","volume":"38","author":"A Ojha","year":"2014","unstructured":"Ojha A, Das B, Mondal SK, Maiti M (2014) A transportation problem with fuzzy-stochastic cost. Appl Math Model 38:1464\u20131481","journal-title":"Appl Math Model"},{"key":"557_CR38","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF01231552","volume":"2","author":"E Pennings","year":"2001","unstructured":"Pennings E (2001) Price or quantity setting under uncertain demand and capacity constraints: an Examination of the Profits. J Econ 2:157\u2013171","journal-title":"J Econ"},{"issue":"2","key":"557_CR39","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1287\/opre.47.2.183","volume":"47","author":"N Petruzzi","year":"1999","unstructured":"Petruzzi N, Dada M (1999) Pricing and the newsvendor problem: a review with extensions. Oper Res 47(2):183\u2013194","journal-title":"Oper Res"},{"issue":"4","key":"557_CR40","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1287\/trsc.30.4.291","volume":"30","author":"H Pirkul","year":"1996","unstructured":"Pirkul H, Jayaraman V (1996) Production, transportation, and distribution planning in a multi-commodity tri-echelon system. Transp Sci 30(4):291\u2013302","journal-title":"Transp Sci"},{"key":"557_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0377-2217(00)00104-1","volume":"131","author":"M Sakawa","year":"2001","unstructured":"Sakawa M, Nishizaki I, Uemura Y (2001) Fuzzy programming and profit and cost allocation for a production and transportation problm. Eur J Oper Res 131:1\u201315","journal-title":"Eur J Oper Res"},{"key":"557_CR42","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s11590-010-0191-0","volume":"5","author":"TC Sharkey","year":"2011","unstructured":"Sharkey TC (2011) Network flow problems with pricing decisions. Optim Lett 5:71\u201383","journal-title":"Optim Lett"},{"key":"557_CR43","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.ejor.2013.10.070","volume":"236","author":"S Sibdari","year":"2014","unstructured":"Sibdari S, Pyke DF (2014) Dynamic pricing with uncertain production cost: an alternating-move approach. Eur J Oper Res 236:218\u2013228","journal-title":"Eur J Oper Res"},{"key":"557_CR44","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF00940445","volume":"77","author":"PK Subramanian","year":"1993","unstructured":"Subramanian PK (1993) Gauss\u2013Newton methods for the complementarity problem. J Optim Theory Appl 77:467\u2013482","journal-title":"J Optim Theory Appl"},{"key":"557_CR45","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1287\/mnsc.16.11.747","volume":"16","author":"LJ Thomas","year":"1970","unstructured":"Thomas LJ (1970) Price-production decisions with deterministic demand. Manag Sci 16:747\u2013750","journal-title":"Manag Sci"},{"key":"557_CR46","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1287\/opre.22.3.513","volume":"22","author":"LJ Thomas","year":"1974","unstructured":"Thomas LJ (1974) Price and production decisions with stochastic demand. Oper Res 22:513\u2013518","journal-title":"Oper Res"},{"issue":"6","key":"557_CR47","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1287\/opre.1060.0326","volume":"54","author":"Y Wang","year":"2006","unstructured":"Wang Y (2006) Joint pricing-production decisions in supply chains of complementary products with uncertain demand. Oper Res 54(6):1110\u20131127","journal-title":"Oper Res"},{"key":"557_CR48","doi-asserted-by":"crossref","first-page":"11209","DOI":"10.1016\/j.eswa.2011.02.168","volume":"38","author":"J Wei","year":"2011","unstructured":"Wei J, Zhao J (2011) Pricing decisions with retail competition in a fuzzy closed-loop supply chain. Expert Syst Appl 38:11209\u201311216","journal-title":"Expert Syst Appl"},{"key":"557_CR49","volume-title":"Variational analysis and applications","author":"XQ Yang","year":"2005","unstructured":"Yang XQ, Yu H (2005) Vector variational inequalities and dynamic traffic equilibria. In: Giannessi F, Maugeri A (eds) Variational analysis and applications. Springer, New York"},{"key":"557_CR50","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1016\/j.omega.2006.04.003","volume":"36","author":"DQ Yao","year":"2008","unstructured":"Yao DQ, Yue XH, John L (2008) Vertical cost information sharing in a supply chain with value-adding retailers. Omega 36:838\u2013851","journal-title":"Omega"},{"key":"557_CR51","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/j.ejor.2011.07.026","volume":"216","author":"J Zhao","year":"2012","unstructured":"Zhao J, Tang WS, Zhao R, Wei J (2012) Pricing decisions for substitutable products with a common retailer in fuzzy environments. Eur J Oper Res 216:409\u2013419","journal-title":"Eur J Oper Res"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-016-0557-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00186-016-0557-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-016-0557-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-016-0557-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,3]],"date-time":"2022-07-03T21:20:22Z","timestamp":1656883222000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00186-016-0557-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,26]]},"references-count":51,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["557"],"URL":"https:\/\/doi.org\/10.1007\/s00186-016-0557-x","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"type":"print","value":"1432-2994"},{"type":"electronic","value":"1432-5217"}],"subject":[],"published":{"date-parts":[[2016,7,26]]}}}