{"id":15,"date":"2023-11-03T21:05:07","date_gmt":"2023-11-03T21:05:07","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=15"},"modified":"2023-11-10T12:26:52","modified_gmt":"2023-11-10T12:26:52","slug":"chapter-1-fig-1-01","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-1-fig-1-01\/","title":{"rendered":"Chapter 1 (Fig. 1.01) &#8211; Mathematical formulation of the transportation model and the corresponding GAMS code"},"content":{"rendered":"\n<pre class=\"wp-block-preformatted\">$Title Chapter 1 (Fig. 1.1)\r\n$Title Mathematical formulation of the transportation model and the corresponding GAMS code\r\n\r\n$onText\r\n\r\nIf using this code, please cite:\r\n\r\n---------------------------------------------------------------------------------\r\nEmrouznejad, A., P. Petridis, and V. Charles (2023). Data Envelopment Analysis\r\nwith GAMS: A Handbook on Productivity Analysis, and Performance Measurement,\r\nSpringer, ISBN: 978-3-031-30700-3.\r\n---------------------------------------------------------------------------------\r\n\r\nWebsite: https:\/\/dataenvelopment.com\/GAMS\/\r\n\r\n$offText\r\n\r\nSets i Plants \/Plant1*Plant3\/\r\n     j Markets \/Market1*Market4\/;\r\nParameter S(i) Supply of plant i\r\n\/\r\nPlant1 150\r\nPlant2 100\r\nPlant3 250\/;\r\n\r\nParameter D(j) Demand of market j\r\n\/\r\nMarket1 100\r\nMarket2 100\r\nMarket3 200\r\nMarket4 100\/;\r\n\r\nTable c(i,j) unit transportation cost\r\n        Market1 Market2 Market3 Market4\r\nPlant1   0.54    0.32     0.1    0.29\r\nPlant2   0.3     0.78     0.76   0.27\r\nPlant3   0.44    0.19     0.61   0.97;\r\n\r\n\r\nVariables\r\nTC Total cost\r\n\r\nNonnegative variables\r\nx(i,j) quantity transported from plant i to market j\r\n\r\nEquations\r\nTotalCost objective function\r\nSupply(i) supply constraint\r\nDemand(j) demand constraint;\r\n\r\nTotalCost.. TC=E=SUM(i,SUM(j,c(i,j)*x(i,j)));\r\n\r\nSupply(i).. SUM(j,x(i,j))=L=S(i);\r\nDemand(j).. SUM(i,x(i,j))=G=D(j);\r\n\r\nModel Transportation_example \/All\/\r\nSolve Transportation_example min TC using LP\r\nDisplay TC.l, x.l, x.m;<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>$Title Chapter 1 (Fig. 1.1) $Title Mathematical formulation of the transportation model and the corresponding GAMS code $onText If using this code, please cite: &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212; Emrouznejad, A., P. Petridis, and V. Charles (2023). Data Envelopment Analysis with GAMS: A Handbook on Productivity Analysis, and Performance Measurement, Springer, ISBN: 978-3-031-30700-3. &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212; Website: https:\/\/dataenvelopment.com\/GAMS\/ $offText Sets i [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/15"}],"collection":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/comments?post=15"}],"version-history":[{"count":6,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/15\/revisions"}],"predecessor-version":[{"id":78,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/15\/revisions\/78"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=15"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=15"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=15"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}