Demand 278>supply 260 Warehouse Factories Amarillo Teaneck Chicago Sioux Falls 250 420 380 280 Sunnyvale 45 1,280 990 1,440 1,520 Dublin 120 1,550 1,420 1,660 1,730 Bangkok 95 M M M M A 18 90 78 55 55
Demand 278>supply 260 Amarillo Teaneck Chicago Sioux Falls Warehouse Factories Sunnyvale Dublin Bangkok 250 420 380 280 1,280 990 1,440 1,520 1,550 1,420 1,660 1,730 45 120 95 90 78 55 55 A 18 M M M M
Generalizations of the Transportation Example 6.1 Variables x11 x12x13 x14 x21 X22 x23 x24 x31x32 x33 x34 x41 x42 x43 x44 Oper ator Value Values 0 00 45 42 78 0 0 48 0 47 0 0 0 8 10 Objective 155142 1E+01E+01E+0 Coeff 250 420380280 1280 990 1440 1520 00 16601730 1E+06 Min 1.8E+07 66 6 st LHS RHS Constraint 1 45 45 Constraint 2 1 1 1 1 = 120 120 Constraint 3 11 1 1 = 95 95 Constraint 4 18 18 Constraint 5 1 1 1 1 90 90 Constraint 6 1 1 1 1 = 78 78 Constraint 7 55 55 Constraint 8 1 1 1 1 = 55 55
Generalizations of the Transportation Example 6.1 Variables x11 x12 x13 x14 x21 x22 x23 x24 x31 x32 x33 x34 x41 x42 x43 x44 Oper ator Value Values 0 0 0 45 42 78 0 0 48 0 47 0 0 0 8 10 Objective Coeff 250 420 380 280 1280 990 1440 1520 155 0 142 0 1660 1730 1E+0 6 1E+0 6 1E+0 6 1E+06 Min 1.8E+07 st LHS RHS Constraint 1 1 1 1 1 = 45 45 Constraint 2 1 1 1 1 = 120 120 Constraint 3 1 1 1 1 = 95 95 Constraint 4 1 1 1 1 = 18 18 Constraint 5 1 1 1 1 = 90 90 Constraint 6 1 1 1 1 = 78 78 Constraint 7 1 1 1 1 = 55 55 Constraint 8 1 1 1 1 = 55 55
Treatment for LP Unbalanced transportation problem can be formulated as LP by inequality (demand or supply )constraints. When the demand exceeds the anticipated,use equality supply constraint(first three)to make sure of complete shipment;and use less than or equal demand constraint
Treatment for LP • Unbalanced transportation problem can be formulated as LP by inequality (demand or supply )constraints. • When the demand exceeds the anticipated, use equality supply constraint (first three) to make sure of complete shipment; and use less than or equal demand constraint