Question

Problem 6-23 (Algorithmic) Find the shortest route from node 1 to node 7 in the network shown. If the constant is "1" it must be entered in the box. If your answer is zero enter "O". For negative values enter "minus" sign) 13 10 18 19 1 if the arc from node i to node j is on the shortest route otherwise 13 x1 In 3 X X32 + 19 X46 + 10x67 7x57 + Flow Out Flow In Node 1 1X14 1 x23 + Node 2 0 1X13 + 1 0 Node 3 X32 + -1x53 1 XX14 0 Node 4 -1X35 + 1 x52 + 0 Node 5 Node 6 1X67 0 -1 X X57 + -1X X67 Node 7 xij 2 0 for al and j Optimal Solution: VariableValue X12 X13 X14 X23 X25 X32 X35 X46 X52 x53 X57 X67 Shortest Route: 1-2-5-7 Length-

Answer 1

In the objective function, the coefficient for X32 will be 5 instead of 3

In the constraints, X14 will have a value of -1. You have entered this correctly. Most likely due to some space or otherwise it is showing error.

In node 7, you cannot have addition of two negative values and then equate them to a positive value. Thus the equation should be

(-1)X57 + (-1)X67 = -1

The formulation and the model is shown below with the answer on excel solver.

The optimal path is 1-2-5-7.

Thus in the answer, the following should have a value of 1

X12, X25, and X57

The rest of them will be 0

The length will be 1+5+7 = 13

|XV ,6 -SUMPRODUCT(B2:H&B13:H19) ミ 0 Total 13 18 13 19 10 10 7 Total out Floww 0 0 14 15 16 17 18 197 20 Total in 24 Sheet1 142 | Sheet 1 143 | Answer Report 5 Sheet1 148 | Sheet 1 144 Sheet 1 145 | Sheet1 146 … + 11596