EXAMPLE 3: TRANSPORTATION/ASSIGNMENT PROBLEM USING LINDO -------------------------------------------------------- LINDO MODEL: EQUAL SUPPLY AND DEMAND -------------------------------------------------------- MIN 15 A1 +18 A2 +19 A3 +13 A4 + 20 B1 +14 B2 +15 B3 +17 B4 + 25 C1 +12 C2 +17 C3 +22 C4 SUBJECT TO A1+A2+A3+A4=50 B1+B2+B3+B4=30 C1+C2+C3+C4=70 A1+B1+C1=30 A2+B2+C2=60 A3+B3+C3=20 A4+B4+C4=40 END -------------------------------------------------------- LINDO RESULTS -------------------------------------------------------- LP OPTIMUM FOUND AT STEP 0 OBJECTIVE FUNCTION VALUE 1) 2090.000 VARIABLE VALUE REDUCED COST A1 30.000000 0.000000 A2 0.000000 12.000000 A3 0.000000 8.000000 A4 20.000000 0.000000 B1 0.000000 1.000000 B2 0.000000 4.000000 B3 10.000000 0.000000 B4 20.000000 0.000000 C1 0.000000 4.000000 C2 60.000000 0.000000 C3 10.000000 0.000000 C4 0.000000 3.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 -15.000000 3) 0.000000 -19.000000 4) 0.000000 -21.000000 5) 0.000000 0.000000 6) 0.000000 9.000000 7) 0.000000 4.000000 8) 0.000000 2.000000 NO. ITERATIONS= 0 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE A1 15.000000 1.000000 INFINITY A2 18.000000 INFINITY 12.000000 A3 19.000000 INFINITY 8.000000 A4 13.000000 8.000000 1.000000 B1 20.000000 INFINITY 1.000000 B2 14.000000 INFINITY 4.000000 B3 15.000000 4.000000 3.000000 B4 17.000000 1.000000 8.000000 C1 25.000000 INFINITY 4.000000 C2 12.000000 4.000000 INFINITY C3 17.000000 3.000000 4.000000 C4 22.000000 INFINITY 3.000000 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 50.000000 0.000000 0.000000 3 30.000000 0.000000 0.000000 4 70.000000 0.000000 0.000000 5 30.000000 0.000000 0.000000 6 60.000000 0.000000 0.000000 7 20.000000 0.000000 0.000000 8 40.000000 0.000000 0.000000