matlab求解 产销平衡,求解运输价最优.doc

问题：产销平衡，求解运输价最优： 完成者： 产销平衡及单位运价表：产地销地1 2 3 4产量1232 2 2 110 8 5 47 6 6 8366销量 4 3 4 4解：设：从第i个产地运输到第j个产地的产品量为， 为第i个产地运输到第j个产地的产品的单位运价。s.t =1,2,3, 2,3，4, i=1,2,3 j=1,2,3，4解决次模型的lingo程序为：Model:sets: Warehouse /1.3/: a; Customer /1.4/: b; Routes( Warehouse, Customer) : c, x;endsetsdata: a = 3, 6, 6; b = 4, 3, 4, 4; c = 2, 2,2,1, 10,8,5,4, 7,6,6,8;enddataOBJ min = sum( Routes: c * x);for( Warehouse(i): SUP sum( Customer(j): x(i,j) = a(i);for( Customer(j): DEM sum( Warehouse(i): x(i,j) = b(j);End下面是此程序运行的结果： Global optimal solution found. Objective value: 69.00000 Total solver iterations: 2 Variable Value Reduced Cost A( 1) 3.000000 0.000000 A( 2) 6.000000 0.000000 A( 3) 6.000000 0.000000 B( 1) 4.000000 0.000000 B( 2) 3.000000 0.000000 B( 3) 4.000000 0.000000 B( 4) 4.000000 0.000000 C( 1, 1) 2.000000 0.000000 C( 1, 2) 2.000000 0.000000 C( 1, 3) 2.000000 0.000000 C( 1, 4) 1.000000 0.000000 C( 2, 1) 10.00000 0.000000 C( 2, 2) 8.000000 0.000000 C( 2, 3) 5.000000 0.000000 C( 2, 4) 4.000000 0.000000 C( 3, 1) 7.000000 0.000000 C( 3, 2) 6.000000 0.000000 C( 3, 3) 6.000000 0.000000 C( 3, 4) 8.000000 0.000000 X( 1, 1) 3.000000 0.000000 X( 1, 2) 0.000000 1.000000 X( 1, 3) 0.000000 1.000000 X( 1, 4) 0.000000 1.000000 X( 2, 1) 0.000000 4.000000 X( 2, 2) 0.000000 3.000000 X( 2, 3) 2.000000 0.000000 X( 2, 4) 4.000000 0.000000 X( 3, 1) 1.000000 0.000000 X( 3, 2) 3.000000 0.000000 X( 3, 3) 2.000000 0.000000 X( 3, 4) 0.000000 3.000000 Row Slack or Surplus Dual Price OBJ 69.00000 -1.000000 SUP( 1) 0.000000 0.000000 SUP( 2) 0.000000 -4.000000 SUP( 3) 0.000000 -5.000000 DEM( 1) 0.000000 -2.000000 DEM( 2) 0.000000 -1.000000 DEM( 3) 0.000000 -1.000000 DEM( 4) 0.000000 0.000000由lingo运行的结果可知：由1产地向1销地运送3个单位物品。由2产地向3销地运送2个单位物品。由2产地向4销地运送