Use the solver in Excel to find the maximum flow from node S to node T in a directed network.
Formulate the problem
To formulate this maximum flow problem, answer the following three questions.
- What are the decisions to be made? For this problem, we need Excel to find the flow on each arc. For example, if the flow on SB is 2, cell D5 equals 2. (in yellow)
- What are the constraints on these decisions? The Net Flow (Flow Out – Flow In) of node A, B, C, D and E should be equal to 0. In other words, Flow Out = Flow In. Also, each arc has a fixed capacity. The flow on each arc should be less than this capacity. (in light blue)
- What is the overall measure of performance for these decisions? The overall measure of performance is the maximum flow, so the objective is to maximize this quantity. The maximum flow equals the Flow Out of node S. (in dark blue)
Name the following ranges:
And insert the following functions:
Solve the model
Enter the solver parameters:
The optimal solution: